Spatial aggregation of time‐variant stream water ages in urbanizing catchments

We calibrated an integrated flow–tracer model to simulate spatially distributed isotope time series in stream water in a 7.9‐km² catchment with an urban area of 13%. The model used flux tracking to estimate the time‐varying age of stream water at the outlet and both urbanized (1.7 km²) and non‐urban (4.5 km²) sub‐catchments over a 2.5‐year period. This included extended wet and dry spells where precipitation equated to >10‐year return periods. Modelling indicated that stream water draining the most urbanized tributary was youngest with a mean transit time (MTT) of 171 days compared with 456 days in the non‐urban tributary. For the larger catchment, the MTT was 280 days. Here, the response of urban contributing areas dominated smaller and more moderate runoff events, but rural contributions dominated during the wettest periods, giving a bi‐modal distribution of water ages. Whilst the approach needs refining for sub‐daily time steps, it provides a basis for projecting the effects of urbanization on stream water transit times and their spatial aggregation. This offers a novel approach for understanding the cumulative impacts of urbanization on stream water quantity and quality, which can contribute to more sustainable management. Copyright © 2015 John Wiley & Sons, Ltd.     

The composite method: an improved method for stream‐water solute load estimation

The composite method is an alternative method for estimating stream‐water solute loads, combining aspects of two commonly used methods: the regression‐model method (which is used by the composite method to predict variations in concentrations between collected samples) and a period‐weighted approach (which is used by the composite method to apply the residual concentrations from the regression model over time). The extensive dataset collected at the outlet of the Panola Mountain Research Watershed (PMRW) near Atlanta, Georgia, USA, was used in data analyses for illustrative purposes. A bootstrap (subsampling) experiment (using the composite method and the PMRW dataset along with various fixed‐interval and large storm sampling schemes) obtained load estimates for the 8‐year study period with a magnitude of the bias of less than 1%, even for estimates that included the fewest number of samples. Precisions were always <2% on a study period and annual basis, and <2% precisions were obtained for quarterly and monthly time intervals for estimates that had better sampling. The bias and precision of composite‐method load estimates varies depending on the variability in the regression‐model residuals, how residuals systematically deviated from the regression model over time, sampling design, and the time interval of the load estimate. The regression‐model method did not estimate loads precisely during shorter time intervals, from annually to monthly, because the model could not explain short‐term patterns in the observed concentrations. Load estimates using the period‐weighted approach typically are biased as a result of sampling distribution and are accurate only with extensive sampling. The formulation of the composite method facilitates exploration of patterns (trends) contained in the unmodelled portion of the load. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating minimum streamflow from measurements at ungauged sites in regions with streamflow‐gauging networks

Estimation of low flows in rivers continues to be a vexing problem despite advances in statistical and process‐based hydrological models. We develop a method to estimate minimum streamflow at seasonal to annual timescales from measured streamflow based on regional similarity in the deviations of daily streamflow from minimum streamflow for a period of interest. The method is applied to 1,019 gauged sites in the Western United States for June to December 2015. The gauges were clustered into six regions with distinct timing and magnitude of low flows. A gamma distribution was fit each day to the deviations in specific discharge (daily streamflow divided by drainage area) from minimum specific discharge for gauges in each region. The Kolmogorov–Smirnov test identified days when the gamma distribution was adequate to represent the distribution of deviations in a region. The performance of the gamma distribution was evaluated at gauges by comparing daily estimates of minimum streamflow with estimates from area‐based regression relations for minimum streamflow. Each region had at least 8 days during the period when streamflow measurements would provide better estimates than the regional regression equation, but the number of such days varied by region depending on aridity and homogeneity of streamflow within the region. Synoptic streamflow measurements at ungauged sites have value for estimating minimum streamflow and improving the spatial resolution of hydrological model in regions with streamflow‐gauging networks.     

Using stable isotopes to estimate travel times in a data‐sparse Arctic catchment: Challenges and possible solutions

Use of isotopes to quantify the temporal dynamics of the transformation of precipitation into run‐off has revealed fundamental new insights into catchment flow paths and mixing processes that influence biogeochemical transport. However, catchments underlain by permafrost have received little attention in isotope‐based studies, despite their global importance in terms of rapid environmental change. These high‐latitude regions offer limited access for data collection during critical periods (e.g., early phases of snowmelt). Additionally, spatio‐temporal variable freeze–thaw cycles, together with the development of an active layer, have a time variant influence on catchment hydrology. All of these characteristics make the application of traditional transit time estimation approaches challenging. We describe an isotope‐based study undertaken to provide a preliminary assessment of travel times at Siksik Creek in the western Canadian Arctic. We adopted a model–data fusion approach to estimate the volumes and isotopic characteristics of snowpack and meltwater. Using samples collected in the spring/summer, we characterize the isotopic composition of summer rainfall, melt from snow, soil water, and stream water. In addition, soil moisture dynamics and the temporal evolution of the active layer profile were monitored. First approximations of transit times were estimated for soil and streamwater compositions using lumped convolution integral models and temporally variable inputs including snowmelt, ice thaw, and summer rainfall. Comparing transit time estimates using a variety of inputs revealed that transit time was best estimated using all available inflows (i.e., snowmelt, soil ice thaw, and rainfall). Early spring transit times were short, dominated by snowmelt and soil ice thaw and limited catchment storage when soils are predominantly frozen. However, significant and increasing mixing with water in the active layer during the summer resulted in more damped steam water variation and longer mean travel times (~1.5 years). The study has also highlighted key data needs to better constrain travel time estimates in permafrost catchments.     

Hydrological transit times in nested urban and agricultural watersheds in the Greater Toronto Area,Canada

Watershed mean transit times (MTTs) are used to characterize the hydrology of watersheds. Watershed MTTs could have important implications for water quality, as relatively long MTTs imply lengthier water retention, thereby allowing more time for pollutant transformation and more moderate release of pollutants into streams. Although estimates of MTTs are common for undisturbed watersheds, only a few studies to date have applied MTT models to urbanized watersheds. In the present study, we use δ¹⁸O to compare estimates of MTTs for paired suburban‐industrial and agricultural watersheds in Toronto, Canada. Although differences in precipitation δ¹⁸O between the two watersheds were negligible, there were significant differences in stream δ¹⁸O, suggesting differences in water transport pathways. Less damping between input precipitation δ¹⁸O and output stream δ¹⁸O in the suburban‐industrial watershed indicated a larger streamflow contribution from quick‐flow transport pathways. We applied three transit time models to quantify MTTs. Considering overall model fit, root mean square error, and uncertainty in model parameters, the exponential model performed the best of the three models. Optimized MTTs using this distribution across the suburban‐industrial subwatersheds ranged from 2.1 to 2.9 months, whereas those in the agricultural subwatersheds ranged from 2.7 to 7.5 months. The relatively small difference between urban and agricultural MTTs coincides with observations elsewhere. Model efficiencies could potentially be improved, and MTTs estimated more reliably, with a higher sampling frequency that captures a greater volume of overall discharge. Overall, this work provides a distinct first glimpse into the separation of MTTs between paired watersheds with such a large contrast in their land use.     

Catchment transit times and landscape controls—does scale matter?

Mean transit times (MTTs) can give useful insights into the internal processes of hydrological systems. However, our understanding of how they vary and scale remains unclear. We used MTT estimates obtained from δ¹⁸O data from 20, mostly nested, contrasting catchments in North East Scotland, ranging from 1 to 1700 km². The estimated MTTs ranged between 270 and 1170 days and were used to test a previously developed multiple linear regression (MLR) model for MTT prediction based on metrics of soil cover, landscape organization and climate. We show that the controls on MTT identified by the MLR model hold with the independent data from these 20 sites and that the MLR can be used to predict MTT in ungauged montane catchments. The dominant controls also remain unchanged over four orders of magnitude of catchment size, suggesting no major change of dominant flow paths and mixing processes at larger scales. This is consistent with the fact that only the variance of MTT, rather than MTT, showed a scaling relationship. MTTs appeared to converge with increasing catchment scale, apparently due to the integration of heterogeneous headwater responses in larger downstream catchments. Copyright © 2009 John Wiley & Sons, Ltd.     

Wetlands and low-gradient topography are associated with longer hydrologic transit times in Precambrian Shield headwater catchments

The estimation of hydrologic transit times in a catchment provides insights into the integrated effects of water storage, mixing dynamics, and runoff generation processes. There has been limited effort to estimate transit times in southern boreal Precambrian Shield landscapes, which are characteristically heterogeneous with surface cover including till, thin soils, bedrock outcrops, and depressional wetland features that play contrasting hydrologic roles. This study presents approximately 3.5 years of precipitation and streamflow water isotope data and estimates mean transit times (MTTs) and the young water fraction (p_y) across six small catchments in the Muskoka-Haliburton region of south-central Ontario. The main objectives were to define a typical range of MTTs for headwater catchments in this region and to identify landscape variables that best explain differences in MTTs/p_y using airborne light detection and ranging and digital terrain analysis. Of the transit time distributions, the two parallel linear reservoir and gamma distributions best describe the hydrology of these catchments, particularly because of their ability to capture more extreme changes related to events such as snowmelt. The estimated MTTs, regardless of the modelling approach or distribution used, are positively associated with the percent wetland area and negatively with mean slope in the catchments. In this landscape, low-gradient features such as wetlands increase catchment scale water storage when antecedent conditions are dryer and decrease transit times when there is a moisture surplus, which plausibly explains the increases in MTTs and mean annual runoff from catchments with significant coverage of these landscape features.     

Predicting acid neutralizing capacity from landscape classification: application to Galloway,south‐west Scotland

Regional estimates of acid neutralizing capacity (ANC) in stream waters are found using a regression model. The model has landscape classifications based on catchment characteristics as its main independent variables. It also includes continuously varying covariates. Landscape classifications and covariates are selected from a priori scientific understanding of acidification processes. Parameter estimates for the model are found using measurements of ANC in 50 streams in Galloway, south‐west Scotland with a history of acidification. The parameterized model is then used to provide ANC simulations for streams throughout a subregion, assuming conservative mixing of ANC through the flow network. The stream water sampling survey is designed to reduce the variance of parameter estimates. A variance model is suggested for the concentrations, and this is used to simulate the variance of ANC concentrations throughout the subregion. Monte Carlo simulation is used to estimate the distribution of the length of river reach with ANC less than zero. © Crown Copyright 2004. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.     

Influence of lowland aquifers and anthropogenic impacts on the isotope hydrology of contrasting mesoscale catchments

We examined the isotope hydrology of eight, contrasting mesoscale (104–488 km²) catchments characterized by a systematic change in the relative importance of upland and lowland areas that reflects the relative distribution of metamorphic and sedimentary rocks. Precipitation and stream water were monitored over a 12‐month period, and stable isotopes were used to examine spatial variations in the hydrometric and tracer dynamics of the catchments. Isotopic tracers were used to examine the temporal dynamics of different runoff sources, and geochemical tracers (alkalinity) were used to identify the geographic sources of runoff. Input–output relationships of isotopic tracers were explored using a gamma function to fit a transit time distribution, which was used to test the hypothesis that the length of mean transit times increased systematically with the cover of sandstone aquifers in the catchments. However, in three catchments, the increased influence of anthropogenic factors, notably reservoir storage, urban runoff and agricultural abstraction for irrigation, prevented reliable transit time estimation. For sites where tentative mean transit time estimates were possible, these varied from around 1.6 years in upland catchments dominated by metamorphic rocks (>75%) and responsive soils to around 4 years in catchments with 34% sandstone cover and freely draining soils. These preliminary results were consistent with inferences of geochemical tracers on the increased role of sedimentary aquifers as runoff sources in lowland areas, but observation from a larger number of sites is needed to confirm this. Copyright © 2012 John Wiley & Sons, Ltd.     

Dense 3D residual moveout analysis as a tool for HTI parameter estimation

Three‐dimensional residual moveout analysis is the basic step in velocity model refinement. The analysis is generally carried out using horizontal and/or vertical semblances defined on a sparse set of in‐lines or cross‐lines with densely sampled source–receiver offsets. An alternative approach, which we call dense residual moveout analysis (DRMA), is to use all the bins of a three‐dimensional survey but sparsely sampled offsets. The proposed technique is very fast and provides unbiased and statistically efficient estimates of the residual moveout. Indeed, for the sparsest possible offset distribution, when only near‐ and far‐angle stacks are used, the variance of the residual moveout estimate is only 1.4 times larger than the variance of the least‐squares estimate obtained using all offsets. The high performance of DRMA makes it a useful tool for many applications, of which azimuthal velocity analysis is considered here. For a horizontal transverse isotropy (HTI) model, a deterministic procedure is proposed to define, at every point of residual moveout estimation, the azimuthal angle of the HTI axis of symmetry, the Thomsen anisotropy coefficients, and the interval (or root‐mean‐square) velocities in both the HTI isotropy and symmetry planes. The procedure is not restricted by DRMA assumptions; for example, it is also applicable to semblance‐based residual moveout estimates. The high resolution of the technique is illustrated by azimuthal velocity analysis over an oilfield in West Siberia.     

Catchment water storage variation with elevation

One of the most important functions of catchments is the storage of water. Catchment storage buffers meteorological extremes and interannual streamflow variability, controls the partitioning between evaporation and runoff, and influences transit times of water. Hydrogeological data to estimate storage are usually scarce and seldom available for a larger set of catchments. This study focused on storage in prealpine and alpine catchments, using a set of 21 Swiss catchments comprising different elevation ranges. Catchment storage comparisons depend on storage definitions. This study defines different types of storage including definitions of dynamic and mobile catchment storage. We then estimated dynamic storage using four methods, water balance analysis, streamflow recession analysis, calibration of a bucket‐type hydrological model Hydrologiska Byråns Vattenbalansavdelning model (HBV), and calibration of a transfer function hydrograph separation model using stable isotope observations. The HBV model allowed quantifying the contributions of snow, soil and groundwater storages compared to the dynamic catchment storage. With the transfer function hydrograph separation model both dynamic and mobile storage was estimated. Dynamic storage of one catchment estimated by the four methods differed up to one order of magnitude. Nevertheless, the storage estimates ranked similarly among the 21 catchments. The largest dynamic and mobile storage estimates were found in high‐elevation catchments. Besides snow, groundwater contributed considerably to this larger storage. Generally, we found that with increasing elevation the relative contribution to the dynamic catchment storage increased for snow, decreased for soil, but remained similar for groundwater storage.     

The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution

The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.     

Correcting Transit Time Distributions in Coarse MODFLOW‐MODPATH Models

In low to medium resolution MODFLOW models, the area occupied by sink cells often far exceeds the surface area of the streams they represent. As a result, MODPATH will calculate inaccurate particle traces and transit times. A frequency distribution of transit times for a watershed will also be in error. Such a distribution is used to assess the long‐term impact of nonpoint source pollution on surface waters and wells. Although the inaccuracies for individual particles can only be avoided by increased model grid resolution or other advanced modeling techniques, the frequency distribution can be improved by scaling the particle transit times by an adjustment factor during post‐processing.     

Linking metrics of hydrological function and transit times to landscape controls in a heterogeneous mesoscale catchment

Long‐term river flow data and one year of isotopic tracer data in a nested 749 km² catchment were analysed conjunctively to evaluate the relationships between hydrometric statistics, transit times, and catchment characteristics. The catchment comprised two distinct geomorphic provinces; upland headwaters draining glaciated landscapes underlain by crystalline geology and lowland headwaters draining a major regional sandstone aquifer. In the uplands, flow regimes were ‘flashy’ with high runoff coefficients for storm hydrographs, steep recession curves and strong nonlinearity in event responses. In the lowlands, runoff coefficients were low, recessions less steep, and event responses more linear. Flow data from the catchment outfall showing damping of these extremes, but was most strongly influenced by the upland headwaters where precipitation was highest. The damping of variability in stable water isotopes between precipitation inputs and streamflow outputs reflected this; with upland tributaries least damped and lowland tributaries most damped. Attempts to quantify the mean transit times of the sampling points met with mixed success; partly reflecting the short run (1 year) of data, but mainly as a result of the marked damping in lowland sites. As a consequence, MTT estimates can only be said to be in the order of a few years in upland sites, but are probably decadal or greater in lowland tributaries. Again, the catchment outfall averages these extremes, but is more similar to the upland headwaters. Despite the difficulties in quantifying MTTs, it is clear that they, like the hydrological response, primarily reflect the dominant control of catchment soil cover, which in turn is determined by geology and glacial history. Copyright © 2011 John Wiley & Sons, Ltd.     

Transit time evaluation using a chloride concentration input step shift after forest cutting in a Japanese headwater catchment

Mean transit times were estimated for a small headwater catchment in Japan (the Fukuroyamasawa Experimental Watershed) using the step shift in input chloride (Cl^?) concentrations that occurred immediately after an episode of forest clear‐cutting. Measured Cl^? concentrations in stream water began to decrease immediately after clear‐cutting, and this trend continued for 6 years. Before clear‐cutting, the input Cl^? concentrations were controlled by wet and dry deposition processes, and most of the dry Cl^? deposition was collected by the forest canopy and reached the ground as throughfall and stemflow. After clear‐cutting, dry deposition was no longer collected by the canopy in this way, thus causing a sharp decrease in input Cl^? concentrations. By comparing measured Cl^? concentrations in stream water with estimates based on the input and evaporative Cl^? concentrations, it was shown that the decrease in stream water Cl^? concentrations was caused mainly by this step shift in the Cl^? input. It was proposed that the change in Cl^? concentrations after forest cutting could be used to represent the replacement of ‘old’ water that existed before cutting by ‘new’ water that was supplied after cutting. The breakthrough curve for the new water fraction gave an approximately exponential distribution of transit times in flow‐corrected time. The mean flow‐corrected transit time was estimated as 1068 days (runoff: 3497 mm). It was therefore concluded that the step change in input Cl^? concentrations immediately following forest clear‐cutting could be successfully used to estimate transit times for the entire catchment. Copyright © 2009 John Wiley & Sons, Ltd.     

Soil production and hillslope transport in mid‐latitudes during the last glacial–interglacial cycle: a combined data and modelling approach in northern Ardennes

The relative efficiency of various hillslope processes through Quaternary glacial–interglacial cycles in the mid‐latitudes is not yet well constrained. Based on a unique set of topographic and soil thickness data in the Ardennes (Belgium), we combine the new CLICHE model of climate‐dependent hillslope evolution with an inversion algorithm in order to get deeper insight into the ways and timing of hillslope dynamics under one such climatic cycle. We simulate the evolution of a synthetic hill reproducing the slope, curvature, and contributing area distributions of the hillslopes of a ~ 2500 km² real area under a simple two‐stage 120‐kyr‐long climatic scenario with linear transitions between cold and warm stages. The inversion method samples a misfit function in the model parameter space, based on estimates of the fit of topographic derivative distributions in classes of soil thickness and of the relative frequencies of the predicted soil thickness classes. Though the inversion results show remarkable convergence patterns for most parameters, no unique solution emerges. We obtain five clusters of good fits, whose centroids are taken as acceptable model solutions. Based on the predicted time series of average denudation rate and soil thickness, plus snapshots of the soil distribution at characteristic times, we discuss these solutions and, comparing them with independent data not involved in the misfit function, we identify the most realistic scenario. Beyond providing first‐order estimates of several parameters that compare well with published data, our results show that denudation rates increase dramatically for a short time at both warm–cold and cold–warm transitions, when the mean annual temperature passes through the [0, ?5 °C] range. We also point to the overwhelming importance of solifluction in shaping hillslopes and transporting soil, and the role of depth‐dependent creep (including frost creep) throughout the climatic cycle, whereas the contributions of simple creep and overland flow are minor. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic shear distribution among interconnected cantilever walls of different lengths

Mid‐rise to high‐rise buildings in seismic areas are often braced by slender reinforced concrete (RC) walls, which are interconnected by RC floor diaphragms. In design, it is typically assumed that the lateral forces are distributed in proportion to the wall's elastic stiffness. Pushover analyses of systems comprising walls of different lengths have, however, shown that large compatibility forces can develop between them, which should be considered in design, but the analyses have also shown that the magnitude of the computed forces is very sensitive to the modelling assumptions. Using the results of a complex shell element model as benchmark, different simple hand‐calculation methods and inelastic beam element models are assessed and improved to yield reliable estimates of the base shear distribution among the individual walls comprising the interconnected wall system. Copyright © 2014 John Wiley & Sons, Ltd.     

Spatial discretization of large watersheds and its influence on the estimation of hillslope sediment yield

The combined use of water erosion models and geographic information systems has facilitated soil loss estimation at the watershed scale. Tools such as the Geo‐spatial interface for the Water Erosion Prediction Project (GeoWEPP) model provide a convenient spatially distributed soil loss estimate but require discretization to identify hillslopes and channels. In GeoWEPP, the TOpographic PArameteriZation (TOPAZ) model is used as an automated procedure to extract a watershed boundary, hillslopes and channels from a digital elevation model (DEM). Previous studies in small watersheds have shown that the size of the hillslopes and the channel distribution affect the model estimates, but in large watersheds, the effects on the soil loss estimates have yet to be tested. Therefore, the objective of this study was to evaluate the effect of discretization on the hillslope sediment yield estimates using GeoWEPP in two large watersheds (>10 km²). The watersheds were selected and discretized varying the TOPAZ parameters [critical source area (CSA) and minimum source channel length (MSCL)] in a 30‐m resolution digital elevation model. The drainage networks built with TOPAZ were compared with each other using the drainage density index. The results showed that the discretization affected hillslope sediment yield estimates and their spatial distribution more than the total runoff. The drainage density index and the hillslope sediment yield were proportional but inversely related; thus, soil loss estimates were highly affected by the spatial discretization. As a result of this analysis, a method to choose the CSA and MSCL values that generates the greatest fraction of hillslopes having profile lengths less than 200 m was developed. This slope length condition is particularly crucial when using the WEPP and GeoWEPP models, in order for them to produce realistic estimates of sheet and rill erosion. Finally, and as a result of this analysis, a more reliable method was developed for selecting the TOPAZ channel network parameters (CSA and MSCL). Copyright © 2015 John Wiley & Sons, Ltd.