Testing a spatially distributed tracer‐aided runoff model in a snow‐influenced catchment: Effects of multicriteria calibration on streamwater ages

Integrating stable isotope tracers into rainfall‐runoff models allows investigation of water partitioning and direct estimation of travel times and water ages. Tracer data have valuable information content that can be used to constrain models and, in integration with hydrometric observations, test the conceptualization of catchment processes in model structure and parameterization. There is great potential in using tracer‐aided modelling in snow‐influenced catchments to improve understanding of these catchments' dynamics and sensitivity to environmental change. We used the spatially distributed tracer‐aided rainfall‐runoff (STARR) model to simulate the interactions between water storage, flux, and isotope dynamics in a snow‐influenced, long‐term monitored catchment in Ontario, Canada. Multiple realizations of the model were achieved using a combination of single and multiple objectives as calibration targets. Although good simulations of hydrometric targets such as discharge and snow water equivalent could be achieved by local calibration alone, adequate capture of the stream isotope dynamics was predicated on the inclusion of isotope data in the calibration. Parameter sensitivity was highest, and most local, for single calibration targets. With multiple calibration targets, key sensitive parameters were still identifiable in snow and runoff generation routines. Water ages derived from flux tracking subroutines in the model indicated a catchment where runoff is dominated by younger waters, particularly during spring snowmelt. However, resulting water ages were most sensitive to the partitioning of runoff sources from soil and groundwater sources, which was most realistically achieved when isotopes were included in the calibration. Given the paucity of studies where hydrological models explicitly incorporate tracers in snow‐influenced regions, this study using STARR is an important contribution to satisfactorily simulating snowpack dynamics and runoff generation processes, while simultaneously capturing stable isotope variability in snow‐influenced catchments.     

APPLICATION OF UNIT HYDROGRAPH TECHNIQUES TO SOLUTE TRANSPORT IN CATCHMENTS

Current models of solute movement in catchments are based on rainfall–runoff models and are consequently biased towards processes which determine the magnitude and timing of water flux. It is shown here that the instantaneous unit hydrograph (IUH), or runoff response function, obtained from a hydrograph is fundamentally different from the residence time distribution which governs the response to solutes/tracers. Using hydrometric and tracer data obtained from a small (25 ha) catchment in the humid tropics a modification of the IUH technique is demonstrated which also allows approximate modelling of the tracer data. New features of the modified conceptual model are identified with known hillslope processes.     

Using high resolution tracer data to constrain water storage,flux and age estimates in a spatially distributed rainfall‐runoff model

Models simulating stream flow and conservative tracers can provide a representation of flow paths, storage distributions and mixing processes that is advantageous for many predictive purposes. Compared with models that only simulate stream flow, tracer data can be used to investigate the internal consistency of model behaviour and to gain insight into model performance. Here, we examine the strengths and weaknesses of a data‐driven, spatially distributed tracer‐aided rainfall‐runoff model. The model structure allowed us to assess the influence of landscape characteristics on the routing and mixing of water and tracers. The model was applied to a site in the Scottish Highlands with a unique tracer data set; ~4 years of daily isotope ratios in stream water and precipitation were available, as well as 2 years of weekly soil and ground water isotopes. The model structure was based on an empirically based, lumped tracer‐aided model previously developed for the catchment. The best model runs were selected from Monte Carlo simulations based on dual calibration criteria using objective functions for both stream isotopes and discharge at the outlet. Model performance for these criteria was reasonable (Nash–Sutcliffe efficiencies for discharge and isotope ratios were ~0.4–0.6). The model could generally reproduce the variable isotope signals in the soils of the steeper hill slopes where storage was low, and damped isotope responses in valley bottom cells with high storage. The model also allowed us to estimate the age distributions of internal stores, water fluxes and stream flow. Average stream water age was ~1.6 years, integrating older groundwater in the valley bottom and dynamic younger soil waters. By tracking water ages and simulating isotopes, the model captured the changes in connectivity driven by distributed storage dynamics. This has substantially improved the representation of spatio‐temporal process dynamics and gives a more robust framework for projecting environmental change impacts. Copyright © 2016 The Authors Hydrological Processes Published by John Wiley & Sons Ltd.     

Towards a simple dynamic process conceptualization in rainfall–runoff models using multi‐criteria calibration and tracers in temperate,upland catchments

Empirically based understanding of streamflow generation dynamics in a montane headwater catchment formed the basis for the development of simple, low‐parameterized, rainfall–runoff models. This study was based in the Girnock catchment in the Cairngorm Mountains of Scotland, where runoff generation is dominated by overland flow from peaty soils in valley bottom areas that are characterized by dynamic expansion and contraction of saturation zones. A stepwise procedure was used to select the level of model complexity that could be supported by field data. This facilitated the assessment of the way the dynamic process representation improved model performance. Model performance was evaluated using a multi‐criteria calibration procedure which applied a time series of hydrochemical tracers as an additional objective function. Flow simulations comparing a static against the dynamic saturation area model (SAM) substantially improved several evaluation criteria. Multi‐criteria evaluation using ensembles of performance measures provided a much more comprehensive assessment of the model performance than single efficiency statistics, which alone, could be misleading. Simulation of conservative source area tracers (Gran alkalinity) as part of the calibration procedure showed that a simple two‐storage model is the minimum complexity needed to capture the dominant processes governing catchment response. Additionally, calibration was improved by the integration of tracers into the flow model, which constrained model uncertainty and improved the hydrodynamics of simulations in a way that plausibly captured the contribution of different source areas to streamflow. This approach contributes to the quest for low‐parameter models that can achieve process‐based simulation of hydrological response. Copyright © 2009 John Wiley & Sons, Ltd.     

Linking tracers,water age and conceptual models to identify dominant runoff processes in a sparsely monitored humid tropical catchment

Assessing catchment runoff response remains a key research frontier because of limitations in current observational techniques to fully characterize water source areas and transit times in diverse geographical environments. Here, we report a study that combines empirical data with modelling to identify dominant runoff processes in a sparsely monitored humid tropical catchment. The analysis integrated isotope tracers into conceptual rainfall–runoff models of varying complexity (from 5 to 11 calibrated parameters) that are able to simulate discharge and tracer concentrations and track the evolving age of stream water exiting the catchment. The model structures can be seen as competing hypotheses of catchment functioning and were simultaneously calibrated against uncertain streamflow gaugings and a 2‐year daily isotope rainfall–runoff record. Comparison of the models was facilitated using global parameter sensitivity analysis and the resulting effect on calibration. We show that a variety of tested model structures reproduced water and tracer dynamics in stream, but the simpler models failed to adequately reproduce both. The resulting water age distributions of the tested models varied significantly with little similarity between the stream water age and stored water age distributions. The sensitivity analysis revealed that only some of the more complex models (from eight parameters) could be better constrained to infer more plausible water age distributions and catchment storage estimates. These models indicated that the age of water stored in the catchment is generally older compared with the age of water fluxes, with evapotranspiration age being younger compared with streamflow. However, the water age distributions followed a similar temporal behaviour dominated by climatic seasonality. Stream water ages increased during the dry season (greater than 1 year) and decreased with increased streamflow (a few weeks old) during the wet season. We further show that the ratios of the streamwater age to stored water age distribution and the water age distribution of actual evapotranspiration to the stored water age distribution from constrained models could potentially serve as useful hydrological indicators of catchment functioning. Copyright © 2016 John Wiley & Sons, Ltd.     

Using lumped conceptual rainfall-runoff models to simulate daily isotope variability with fractionation in a nested mesoscale catchment

This paper presents 19 months of stable isotope (δ²H and δ¹⁸O) data to enhance understanding of water and solute transport at two spatial scales (2.3 km² and 122 km²) in the agricultural Lunan catchment, Scotland. Daily precipitation and stream isotope data, weekly lake and spring isotope data and monthly groundwater isotope data revealed important insights into flow pathways and mixing of water at both scales. In particular, a deeper groundwater flow path significantly contributes to total streamflow (25-50%). Upstream lake isotope dynamics, susceptible to evaporative fractionation, also appeared to have an important influence on the downstream isotope composition. This unique tracer data set facilitated the conceptualization of a lumped catchment-scale flow-tracer model. The incorporation of hydrological, mixing and fractionation processes based on these data improved simulations of the stream δ²H isotope response at the catchment outlet from 0.37 to 0.56 for the Nash-Sutcliffe statistic. The stable isotope data successfully aided model conceptualization and calibration in the quest for a simple water and solute transport model with improved representation of process dynamics.     

Using high‐resolution isotope data and alternative calibration strategies for a tracer‐aided runoff model in a nested catchment

Testing hydrological models over different spatio‐temporal scales is important for both evaluating diagnostics and aiding process understanding. High‐frequency (6‐hr) stable isotope sampling of rainfall and runoff was undertaken during 3‐week periods in summer and winter within 12 months of daily sampling in a 3.2‐km² catchment in the Scottish Highlands. This was used to calibrate and test a tracer‐aided model to assess the (a) information content of high‐resolution data, (b) effect of different calibration strategies on simulations and inferred processes, and (c) model transferability to <1‐km² subcatchment. The 6‐hourly data were successfully incorporated without loss of model performance, improving the temporal resolution of the modelling, and making it more relevant to the time dynamics of the isotope and hydrometric response. However, this added little new information due to old‐water dominance and riparian mixing in this peatland catchment. Time variant results, from differential split sample testing, highlighted the importance of calibrating to a wide range of hydrological conditions. This also provided insights into the nonstationarity of catchment mixing processes, in relation to storage and water ages, which varied markedly depending on the calibration period. Application to the nested subcatchment produced equivalent parameterization and performance, highlighting similarity in dominant processes. The study highlighted the utility of high‐resolution data in combination with tracer‐aided models, applied at multiple spatial scales, as learning tools to enhance process understanding and evaluation of model behaviour across nonstationary conditions. This helps reveal more fully the catchment response in terms of the different mechanistic controls on both wave celerites and particle velocities.     

Experimental study and mathematical modelling of soluble chemical transfer from unsaturated/saturated soil to surface runoff

A one‐dimensional, two‐layer solute transport model is developed to simulate chemical transport process in an initially unsaturated soil with ponding water on the soil surface before surface runoff starts. The developed mathematical model is tested against a laboratory experiment. The infiltration and diffusion processes are mathematically lumped together and described by incomplete mixing parameters. Based on mass conservation and water balance equations, the model is developed to describe solute transport in a two‐zone layer, a ponding runoff zone and a soil mixing zone. The two‐zone layer is treated as one system to avoid describing the complicated chemical transport processes near the soil surface in the mixing zone. The proposed model was analytically solved, and the solutions agreed well with the experimental data. The developed experimental method and mathematical model were used to study the effect of the soil initial moisture saturation on chemical concentration in surface runoff. The study results indicated that, when the soil was initially saturated, chemical concentration in surface runoff was significantly (two orders of magnitude) higher than that with initially unsaturated soil, while the initial chemical concentrations at the two cases were of the same magnitude. The soil mixing depth for the initially unsaturated soil was much larger than that for the initially saturated soil, and the incomplete runoff mixing parameter was larger for the initially unsaturated soil. The higher the infiltration rate of the soil, the greater the infiltration‐related incomplete mixing parameter. According to the quantitative analysis, the soil mixing depth was found to be sensitive for both initially unsaturated and saturated soils, and the incomplete runoff mixing parameter was sensitive for initially saturated soil but not for the initially unsaturated soil; the incomplete infiltration mixing parameter behaved just the opposite. Some suggestions are made for reducing chemical loss from runoff. Copyright © 2010 John Wiley & Sons, Ltd.     

Conceptual modelling to assess the influence of hydro-climatic variability on runoff processes in data scarce semi-arid Andean catchments

Using hydro-meteorological time series of 50 years and in situ measurements, the dominant runoff processes in perennial Andean headwater catchments in Chile were determined using the hydrological model HBV light. First, cluster analysis was used to identify dry, wet and intermediate years. From these, sub-periods were identified with contrasting seasonal climatic influences on streamflow. By calibrating the model across different periods, impacts on model performance, parameter sensitivity and identifiability were investigated, providing insights into differences in hydrological processes. The modelling approach suggested that, independently of a dry or wet period of calibration, the streamflow response is mostly consistent with flux from groundwater storage, while only a small fraction comes from direct routing of snowmelt. The variation of model parameters, such as the groundwater rate coefficient, was found to be consistent with differing recharge in wet and dry years. The resulting snowmelt–groundwater model is a realistic hypothesis of the hydrological operation of such complex, data scarce and semi-arid Andean catchments. This model may also be a useful tool for predictions of seasonal water availability and a basis for further field studies.     

Multi-functional heat pulse probe measurements of coupled vadose zone flow and transport

Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (EC_bulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.     

Comparison of two rainfall–runoff models: effects of conceptualization on water budget components

Rainfall–runoff models with different conceptual structures for the hydrological processes can be calibrated to effectively reproduce the hydrographs of the total runoff, while resulting in water budget components that are essentially different. This finding poses an open question on the reliability of rainfall–runoff models in reproducing hydrological components other than those used for calibration. In an effort to address this question, we use data from the Glafkos catchment in western Greece to calibrate and compare the ENNS model, a research-oriented lumped model developed for the river Enns in Austria developed for the river Enns in Austria, with the operational MIKE SHE model. Model performance is assessed in the light of the conceptual/structural differences of the modelled hydrological processes, using indices calculated independently for each year, rather than for the whole calibration period, since the former are stricter. We show that even small differences in the representation of hydrological processes may impact considerably on the water budget components that are not measured (i.e. not used for model calibration). From all water budget components, direct runoff exhibits the highest sensitivity to structural differences and related model parameters.

EDITOR M.C. Acreman

ASSOCIATE EDITOR S. Huang     

Solute transport by surface runoff from low‐angle slopes: theory and application

The removal of chemicals in solution by overland flow from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface‐mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright © 2000 John Wiley & Sons, Ltd.     

Studying the effect of different approaches to estimating model parameters on the accuracy of river runoff simulation by SWAP model

Different approaches to estimating the parameters of SWAP physically based model, which describes heat and water transfer processes in the soil-vegetaion (snow) cover-atmosphere system are examined. In particular, two methods of a priori estimation of parameter values and two variants of their calibration are discussed. The parameter sets obtained by different methods were used to simulate the runoff from 12 experimental catchments in the eastern USA. The calculations were conducted for a 39-year period (1960–1998) with a 3-hour step. The results of calculations were compared with each other and with measured river runoff values in order to identify the parameter set that is optimal for runoff evaluation. A strategy is proposed for a priori parameter estimation in the case of basins where observational data are too poor to enable parameter calibration.     

Uncertainty and multiple objective calibration in regional water balance modelling: case study in 320 Austrian catchments

We examine the value of additional information in multiple objective calibration in terms of model performance and parameter uncertainty. We calibrate and validate a semi‐distributed conceptual catchment model for two 11‐year periods in 320 Austrian catchments and test three approaches of parameter calibration: (a) traditional single objective calibration (SINGLE) on daily runoff; (b) multiple objective calibration (MULTI) using daily runoff and snow cover data; (c) multiple objective calibration (APRIORI) that incorporates an a priori expert guess about the parameter distribution as additional information to runoff and snow cover data. Results indicate that the MULTI approach performs slightly poorer than the SINGLE approach in terms of runoff simulations, but significantly better in terms of snow cover simulations. The APRIORI approach is essentially as good as the SINGLE approach in terms of runoff simulations but is slightly poorer than the MULTI approach in terms of snow cover simulations. An analysis of the parameter uncertainty indicates that the MULTI approach significantly decreases the uncertainty of the model parameters related to snow processes but does not decrease the uncertainty of other model parameters as compared to the SINGLE case. The APRIORI approach tends to decrease the uncertainty of all model parameters as compared to the SINGLE case. Copyright © 2006 John Wiley & Sons, Ltd.     

Solute transport routing in a small stream

Abstract

The impact of pollution incidents on rivers and streams may be predicted using mathematical models of solute transport. Practical applications require an analytical or numerical solution to a governing solute mass balance equation together with appropriate values of relevant transport coefficients under the flow conditions of interest. This paper considers two such models, namely those proposed by Fischer and by Singh and Beck, and compares their performances using tracer data from a small stream in Edinburgh, UK. In calibrating the models, information on the magnitudes and the flow rate dependencies of the velocity and the dispersion coefficients was generated. The dispersion coefficient in the stream ranged between 0.1 and 0.9 m²/s for a flow rate range of 13–437 L/s. During calibration it was found that the Singh and Beck model fitted the tracer data a little better than the Fischer model in the majority of cases. In a validation exercise, however, both models gave similarly good predictions of solute transport at three different flow rates.     

Effect of channel size on solute residence time distributions in rivers

The effect of channel size on residence time distributions (RTDs) of solute in rivers is investigated in this paper using tracer test data and the variable residence time (VART) model. Specifically, the investigation focuses on the influence of shear dispersion and hyporheic exchange on the shape of solute RTD, and how these two transport processes prevail in larger and smaller streams, respectively, leading to distinct tails of RTD. Simulation results show that (1) RTDs are dispersion-dependent and thereby channel-size (scale) dependent. RTDs increasing longitudinal dispersion coefficient. Small streams with negligible dispersion coefficient may display various types of RTD from upward curving patterns to a straight line (power-law distributions) and further to downward curving lognormal distributions when plotted in log–log coordinates. Moderate-sized rivers are transitional in terms of RTDs and commonly exhibit lognormal and power-law RTDs; (2) the incorporation of water and solute losses/gains in the VART model can improve simulation results and make parameter values more reasonable; (3) the ratio of time to peak concentration to the minimum mean residence time is equal to the recovery ratio of tracer. The relation provides a simple method for determining the minimum mean residence time; and (4) the VART model is able to reproduce various RTDs observed in rivers with 3–4 fitting parameters while no user-specified RTD functions are needed.     

Concentration–discharge relationships reflect chemostatic characteristics of US catchments

Concentration–discharge relationships have been widely used as clues to the hydrochemical processes that control runoff chemistry. Here we examine concentration–discharge relationships for solutes produced primarily by mineral weathering in 59 geochemically diverse US catchments. We show that these catchments exhibit nearly chemostatic behaviour; their stream concentrations of weathering products such as Ca, Mg, Na, and Si typically vary by factors of only 3 to 20 while discharge varies by several orders of magnitude. Similar patterns are observed at the inter‐annual time scale. This behaviour implies that solute concentrations in stream water are not determined by simple dilution of a fixed solute flux by a variable flux of water, and that rates of solute production and/or mobilization must be nearly proportional to water fluxes, both on storm and inter‐annual timescales. We compared these catchments' concentration–discharge relationships to the predictions of several simple hydrological and geochemical models. Most of these models can be forced to approximately fit the observed concentration–discharge relationships, but often only by assuming unrealistic or internally inconsistent parameter values. We propose a new model that also fits the data and may be more robust. We suggest possible tests of the new model for future studies. The relative stability of concentration under widely varying discharge may help make aquatic environments habitable. It also implies that fluxes of weathering solutes in streams, and thus fluxes of alkalinity to the oceans, are determined primarily by water fluxes. Thus, hydrology may be a major driver of the ocean‐alkalinity feedback regulating climate change. Copyright © 2009 John Wiley & Sons, Ltd.     

Impact of model simplifications on soil erosion predictions: application of the GLUE methodology to a distributed event‐based model at the hillslope scale

In this paper, we analyse how the performance and calibration of a distributed event‐based soil erosion model at the hillslope scale is affected by different simplifications on the parameterizations used to compute the production of suspended sediment by rainfall and runoff. Six modelling scenarios of different complexity are used to evaluate the temporal variability of the sedimentograph at the outlet of a 60 m long cultivated hillslope. The six scenarios are calibrated within the generalized likelihood uncertainty estimation framework in order to account for parameter uncertainty, and their performance is evaluated against experimental data registered during five storm events. The Nash–Sutcliffe efficiency, percent bias and coverage performance ratios show that the sedimentary response of the hillslope in terms of mass flux of eroded soil can be efficiently captured by a model structure including only two soil erodibility parameters, which control the rainfall and runoff production of suspended sediment. Increasing the number of parameters makes the calibration process more complex without increasing in a noticeable manner the predictive capability of the model. Copyright © 2015 John Wiley & Sons, Ltd.     

Ecohydrological modelling with EcH2O‐iso to quantify forest and grassland effects on water partitioning and flux ages

We used the new process‐based, tracer‐aided ecohydrological model EcH₂O‐iso to assess the effects of vegetation cover on water balance partitioning and associated flux ages under temperate deciduous beech forest (F) and grassland (G) at an intensively monitored site in Northern Germany. Unique, multicriteria calibration, based on measured components of energy balance, hydrological function and biomass accumulation, resulted in good simulations reproducing measured soil surface temperatures, soil water content, transpiration, and biomass production. Model results showed the forest “used” more water than the grassland; of 620 mm average annual precipitation, losses were higher through interception (29% under F, 16% for G) and combined soil evaporation and transpiration (59% F, 47% G). Consequently, groundwater (GW) recharge was enhanced under grassland at 37% (~225 mm) of precipitation compared with 12% (~73 mm) for forest. The model tracked the ages of water in different storage compartments and associated fluxes. In shallow soil horizons, the average ages of soil water fluxes and evaporation were similar in both plots (~1.5 months), though transpiration and GW recharge were older under forest (~6 months compared with ~3 months for transpiration, and ~12 months compared with ~10 months for GW). Flux tracking using measured chloride data as a conservative tracer provided independent support for the modelling results, though highlighted effects of uncertainties in forest partitioning of evaporation and transpiration. By tracking storage—flux—age interactions under different land covers, EcH₂O‐iso could quantify the effects of vegetation on water partitioning and age distributions. Given the likelihood of drier, warmer summers, such models can help assess the implications of land use for water resource availability to inform debates over building landscape resilience to climate change. Better conceptualization of soil water mixing processes and improved calibration data on leaf area index and root distribution appear obvious respective modelling and data needs for improved simulations.