Timing the time of concentration: shedding light on a paradox

From the origins of hydrology, the time of concentration, t_c, has conventionally been tackled as a constant quantity. However, theoretical proof and empirical evidence imply that t_c exhibits significant variability against rainfall, making its definition and estimation a hydrological paradox. Adopting the assumptions of the Rational method and the kinematic approach, an effective procedure in a GIS environment for estimating the travel time across a catchment’s longest flow path is provided. By application in 30 Mediterranean basins, it is illustrated that t_c is a negative power function of excess rainfall intensity. Regional formulas are established to infer its multiplier (unit time of concentration) and exponent from abstract geomorphological information, which are validated against observed data and theoretical literature outcomes. Besides offering a fast and easy solution to the paradox, we highlight the necessity of implementing the varying t_c concept within hydrological modelling, signalling a major shift from current engineering practices.     

Improving streamflow estimation in ungauged basins using a multi-modelling approach

ABSTRACT

In this study, a multi-modelling approach is proposed for improved continuous daily streamflow estimation in ungauged basins using regionalization—the process of transferring hydrological data from gauged to ungauged watersheds. Four regionalization models, two data-driven and two hydrological, were used for continuous daily streamflow estimation. Comparison of the individual models reveals that each of the four models performed well on a limited number of ungauged basins while none of them performed well for the entire 90 selected watersheds. The results obtained from the four models are evaluated and reported in a deterministic way by a model combination approach along with its uncertainty range consisting of 16 ensemble members. It is shown that a combined model of the four individual models performed well on all 90 watersheds and the ensemble range can account for the uncertainty of models. The combined model was more efficient and appeared more robust compared to the individual models. Furthermore, continuous ranked probability scores (CRPS) calculated for the ensemble model outputs indicate better performance compared to individual models and competitive with the combined model.

EDITOR A. Castellarin ASSOCIATE EDITOR G. Di Baldassarre     

Observed hydrographs: on their ability to infer a time‐invariant hydrological transfer function for flow prediction in ungauged basins

Streamflow measurements provide information about the flow generation characteristics of land surfaces as well as the flow transferring nature of the channel network. In this study, such flow transferring properties of the channel network that were obtained from downstream flow observations were used for predicting flow in ungauged basins. A temporally averaged transfer function (ATF) of the channel segments of Kentucky River Basin (KRB) in Kentucky, USA, was extracted from observed hydrographs in a time‐invariant system as a function of drainage area. The ATF was regionalized through multiple regression analysis for 194 combinations of drainage areas that differ in topography, terrain, and geology. The application of ATF for flow prediction in ungauged basins was performed for Goose Creek, a subbasin of KRB by integrating ATF with the TOPMODEL. In addition, the ATF was shown to be capable of providing calibration and validation data for ungauged basins in a backward technique from a measured stream gauge downstream, with minimal data requirement of drainage area. The applicability of ATF was illustrated across a range of streamflow conditions from watersheds that varied greatly in their terrain and geology. Nash–Sutcliffe efficiency of the proposed method, as a function of drainage areas of the corresponding basins, to predict daily streamflow from ungauged basins ranged from 0.83 to 0.92. The results of the study concluded that the ATF obtained from measured streamflow thus proved to be a quick and simple tool for assessment of streamflow in both operational and modeling hydrology. Copyright © 2012 John Wiley & Sons, Ltd.     

Water and nutrient predictions in ungauged basins: set-up and evaluation of a model at the national scale

Abstract

A dynamic water quality model, HYPE, was applied to a large, data-sparse region to study whether reliable information on water quantity and water quality could be obtained for both gauged and ungauged waterbodies. The model (called S-HYPE) was set up for all of Sweden (～450 000 km²), divided into sub-basins with an average area of 28 km². Readily available national databases were used for physiographic data, emissions and agricultural practices, fixed values for representative years were used. Daily precipitation and temperature were used as the dynamic forcing of the model. Model evaluation was based on data from several hundred monitoring sites, of which approximately 90% had not been used in calibration on a daily scale. Results were evaluated using the Nash-Sutcliffe efficiency (NSE), correlation and relative errors: 92% of the spatial variation was explained for specific water discharge, and 88% and 59% for total nitrogen and total phosphorus concentrations, respectively. Day-to-day variations were modelled with satisfactory results for water discharge and the seasonal variation of nitrogen concentrations was also generally well captured. In 20 large, unregulated rivers the median NSE for water discharge was 0.84, and the corresponding number for 76 partly-regulated river basins was 0.52. In small basins, the NSE was typically above 0.6. These major achievements relative to previous similar experiments were ascribed to the step-wise calibration process using representative gauged basins and the use of a modelling concept, whereby coefficients are linked to physiographic variables rather than to specific sites.

Editor D. Koutsoyiannis

Citation Strömqvist, J., Arheimer, B., Dahné, J., Donnelly, C. and Lindström, G., 2012. Water and nutrient predictions in ungauged basins: set-up and evaluation of a model at the national scale. Hydrological Sciences Journal, 57 (2), 229–247.     

Stochastic models in hydrology

A stochastic approach to the analysis of hydrologic processes is defined along with a discussion of causes of tendency, periodicity and stochasticity in hydrologic series. Sources of temporal non-stationarity are described along with objectives and methods of analysis of processes and, in general, of information extraction from data. Transferred information as measured by correlation coefficients is compared with the transferable information as measured by entropy coefficients. Various multivariate approaches to hydrologic stochastic modeling are classified in light of complexities of spatial/temporal hydrologic processes. Alternatives of time series structural decomposition and modeling are compared. A special approach to modeling of space properties further contributes to approximate simulations of spatial/temporal processes over large areas. Several aspects of stochastic models in hydrology are concisely reviewed.     

Use of a parsimonious rainfall–run‐off model for predicting hydrological response in ungauged basins

A new parameter parsimonious rainfall–run‐off model, the Distance Distribution Dynamics (DDD) model, is used to simulate hydrological time series at ungauged sites in the Lygne basin in Norway. The model parameters were estimated as functions of catchment characteristics determined by geographical information system. The multiple regression equations relating catchment characteristics and model parameters were trained from 84 calibrated catchments located all over Norway, and all model parameters showed significant correlations with catchment characteristics. The significant correlation coefficients (with p‐value < 0.05) ranged from 0.22 to 0.55. The suitability of DDD for predictions in ungauged basins was tested for 17 catchments not used to estimate the multiple regression equations. For ten of the 17 catchments, deviations in Nash–Sutcliffe efficiency (NSE) criteria between the calibrated and regionalised model were less than 0.1, and for two calibrated catchments within the Lygne basin, the deviations were less than 0.08. The median NSE for the regionalized DDD for the 17 catchments for two time series was 0.66 and 0.72. Deviations in NSE between calibrated and regionalised models are well explained by the deviations between calibrated and regressed parameters describing spatial snow distribution and snowmelt respectively. The quality of the simulated run‐off series for the ungauged sites in the Lygne basin was assessed by comparing flow indices describing high, medium and low flow estimated from observed run‐off at the 17 catchments and for the simulated run‐off series. The indices estimated for the simulated series were generally well within the ranges defined by the 17 observed series. Copyright © 2014 John Wiley & Sons, Ltd.     

Diurnal variations in discharge and suspended sediment concentration,including runoff‐delaying characteristics,of the Gangotri Glacier in the Garhwal Himalayas

Diurnal variations in discharge and suspended sediment concentration (SSC), including runoff delaying characteristics, have been studied for the Gangotri Glacier, the largest glacier in the Garhwal Himalayas (glacierized area 286 km²; drainage area 556 km²). Hourly discharge and SSC data were collected near the snout of the glacier (∼4000 m) at an interval of about 15 days for an entire ablation period (May–October 2001). Diurnal variability in SSC was found to be much higher than the discharge. Hysteresis trends between discharge and SSC were established. Results indicate that, for the study glacier, clockwise hysteresis dominated for the entire melt season, indicating that most of the time the SSC led the discharge. During the peak melt period, anticlockwise hysteresis was also observed for a few hours. Assessment of runoff‐delaying characteristics was made by estimating the time lag between the occurrence of melting and its appearance as runoff along with estimation of time to peak. A comparison of runoff‐delaying parameters with discharge ratio clearly indicated that changes in time lag and time to peak are inversely correlated with variations in discharge. Attempts have also been made to establish the relationship between discharge and SSC using short‐interval data. Copyright © 2004 John Wiley & Sons, Ltd.     

Predicting dry‐season flows with a monthly rainfall–runoff model: Performance for gauged and ungauged catchments

Hydrologic models are useful to understand the effects of climate and land‐use changes on dry‐season flows. In practice, there is often a trade‐off between simplicity and accuracy, especially when resources for catchment management are scarce. Here, we evaluated the performance of a monthly rainfall–runoff model (dynamic water balance model, DWBM) for dry‐season flow prediction under climate and land‐use change. Using different methods with decreasing amounts of catchment information to set the four model parameters, we predicted dry‐season flow for 89 Australian catchments and verified model performance with an independent dataset of 641 catchments in the United States. For the Australian catchments, model performance without catchment information (other than climate forcing) was fair; it increased significantly as the information to infer the four model parameters increased. Regressions to infer model parameters from catchment characteristics did not hold for catchments in the United States, meaning that a new calibration effort was needed to increase model performance there. Recognizing the interest in relative change for practical applications, we also examined how DWBM could be used to simulate a change in dry‐season flow following land‐use change. We compared results with and without calibration data and showed that predictions of changes in dry‐season flow were robust with respect to uncertainty in model parameters. Our analyses confirm that climate is a strong driver of dry‐season flow and that parsimonious models such as DWBM have useful management applications: predicting seasonal flow under various climate forcings when calibration data are available and providing estimates of the relative effect of land use on seasonal flow for ungauged catchments.     

流域蒸散耗水率对气候和下垫面变异响应关系的稳定性研究

气候条件的变异和流域下垫面特征的改变是影响流域蒸散耗水的重要因素。本文聚焦于1900 2008年间全球83个典型流域数据,基于Budyko水热耦合平衡方程,探究100多年间不同条件下流域蒸散耗水率（AET/P）对气候和下垫面特征变异响应关系的稳定性。结果表明：(1)从长时间尺度看,大部分流域蒸散耗水率与气候干燥指数（PET/P）和流域特征参数（n值）变异的响应关系呈现较强的时间稳定性。从短时间尺度而言,半湿润流域内蒸散耗水率对干燥指数的响应系数?（AET/P）/?（PET/P）在20世纪内持续降低。不同气候条件下蒸散耗水率对流域特征参数的响应系数?（AET/P）/?（n）的变化差异显著。分不同下垫面特征来看,低n值（n<2）流域内AET/P对n值的变化更为敏感;(2)气候条件（PET/P）是大多数湿润区内蒸散耗水率的主导因素,在干旱与半干旱流域内,下垫面特征参数（n值）对AET/P贡献最大。在湿润区内,PET/P对AET/P的贡献程度随时间小幅提升;半湿润区内PET/P对AET/P的贡献度呈下降趋势。在低n值（n<2;流域持水能力较弱）流域内,n值对AET/P的贡献更多。在...     

Inter‐catchment comparison to assess the influence of topography and soils on catchment transit times in a geomorphic province; the Cairngorm mountains,Scotland

A quantitative, process relevant analysis of ten mesoscale (ca 10–90 km²) catchments in the Cairngorm mountains, Scotland was carried out using 10‐m digital terrain models (DTMs). This analysis produced a range of topographic indices that described differences in the landscape organisation of the catchments in a way that helped explain contrasts in their hydrology. Mean transit time (MTT)—derived from isotopic tracer data—was used as a metric that characterised differences in the hydrological function of the ten catchments. Some topographic indices exhibited significant correlations with MTT. Most notably, the ratio of the median flow path length to the median flow path gradient was negatively correlated with MTT, whilst the median upslope area was positively correlated. However, the relationships exhibited significant scatter which precluded their use as a predictive tool that could be applied to ungauged basins in this region. In contrast, maps of soil hydrological properties could be used to differentiate hydrologically responsive soils (which are dominated by overland flow and shallow sub‐surface storm flow) from free draining soils (that facilitate deeper sub‐surface flows). MTT was negatively correlated with the coverage of responsive soils in catchments. This relationship provided a much better basis for predicting MTT in ungauged catchments in this geomorphic province. In the Cairngorms, the extensive cover of various glacial drift deposits appears to be a first order control on soil distributions and strongly influences the porosity and permeability of the sub‐surface. These catchment characteristics result in soil cover being a much more discerning indicator of hydrological function than topography alone. The study highlights the potential of quantitative landscape analysis in catchment comparison and the need for caution in extrapolating relationships between landscape controls and metrics of hydrological function beyond specific geomorphic provinces. Copyright © 2009 John Wiley & Sons, Ltd.     

Identification of factors influencing hydrologic model performance using a top-down approach in a large number of U.S. catchments

Investigating the performance that can be achieved with different hydrological models across catchments with varying characteristics is a requirement for identifying an adequate model for any catchment, gauged or ungauged, just based on information about its climate and catchment properties. As parameter uncertainty increases with the number of model parameters, it is important not only to identify a model achieving good results but also to aim at the simplest model still able to provide acceptable results. The main objective of this study is to identify the climate and catchment properties determining the minimal required complexity of a hydrological model. As previous studies indicate that the required model complexity varies with the temporal scale, the study considers the performance at the daily, monthly, and annual timescales. In agreement with previous studies, the results show that catchments located in arid areas tend to be more difficult to model. They therefore require more complex models for achieving an acceptable performance. For determining which other factors influence model performance, an analysis was carried out for four catchment groups (snowy, arid, and eastern and western catchments). The results show that the baseflow and aridity indices are the most consistent predictors of model performance across catchment groups and timescales. Both properties are negatively correlated with model performance. Other relevant predictors are the fraction of snow in the annual precipitation (negative correlation with model performance), soil depth (negative correlation with model performance), and some other soil properties. It was observed that the sign of the correlation between the catchment characteristics and model performance varies between clusters in some cases, stressing the difficulties encountered in large sample analyses. Regarding the impact of the timescale, the study confirmed previous results indicating that more complex models are needed for shorter timescales.     

Robustness of flood-model calibration using single and multiple events

ABSTRACT

Lack of discharge data for model calibration is challenging for flood prediction in ungauged basins. Since establishment and maintenance of a permanent discharge station is resource demanding, a possible remedy could be to measure discharge only for a few events. We tested the hypothesis that a few flood-event hydrographs in a tropical basin would be sufficient to calibrate a bucket-type rainfall–runoff model, namely the HBV model, and proposed a new event-based calibration method to adequately predict floods. Parameter sets were chosen based on calibration of different scenarios of data availability, and their ability to predict floods was assessed. Compared to not having any discharge data, flood predictions improved already when one event was used for calibration. The results further suggest that two to four events for calibration may considerably improve flood predictions with regard to accuracy and uncertainty reduction, whereas adding more events beyond this resulted in small performance gains.     

Multi‐site evaluation of hydrology component of SWAT in the coastal plain of southwest Georgia

Simulation of watershed scale hydrologic and water quality processes is important for watershed assessments. Proper characterization of the accuracy of these simulations, particularly in cases with limited observed data, is critical. The Soil & Water Assessment Tool (SWAT) is frequently used for watershed scale simulation. The accuracy of the model was assessed by extrapolating calibration results from a well studied Coastal Plain watershed in Southwest Georgia, USA, to watersheds within the same geographic region without further calibration. SWAT was calibrated and validated on a 16.7‐km² subwatershed within the Little River Experimental Watershed by varying six model parameters. The optimized parameter set was then applied to a watershed of similar land use and soils, a smaller watershed with different land use and soils and three larger watersheds within the same drainage system without further calibration. Simulation results with percent bias (PB) ±15% ≤ PB < ±25% and Nash–Sutcliffe efficiency (NSE) 0.50 < NSE ≤ 0.65 were considered to be satisfactory, whereas those with PB < ±10% and 0.75 < NSE ≤ 1.00 were considered very good. With these criteria, simulation results for the five non‐calibration watersheds were satisfactory to very good. Differences across watersheds were attributed to differences in soils, land use, and surficial aquifer characteristics. These results indicate that SWAT can be a useful tool for predicting streamflow for ungauged watersheds with similar physical characteristics to the calibration watershed studied here and provide an indication of the accuracy of hydrologic simulations for ungauged watersheds. Copyright © 2012 John Wiley & Sons, Ltd.     

Agricultural land use and hydrology affect variability of shallow groundwater nitrate concentration in South Florida

South Florida's Miami‐Dade agricultural area is located between two protected natural areas, the Biscayne and Everglades National Parks, subject to the costliest environmental restoration project in history. Agriculture, an important economic activity in the region, competes for land and water resources with the restoration efforts and Miami's urban sprawl. The objective of this study, understanding water quality interactions between agricultural land use and the shallow regional aquifer, is critical to the reduction of agriculture's potentially negative impacts. A study was conducted in a 4‐ha square field containing 0·9 ha of corn surrounded by fallow land. The crop rows were oriented NW–SE along the dominant groundwater flow in the area. A network of 18 monitoring wells was distributed across the field. Shallow groundwater nitrate–nitrogen concentration [N‐NO₃^?] was analyzed on samples collected from the wells biweekly for 3 years. Detailed hydrological (water table elevation [WTE] at each well, groundwater flow direction [GwFD], rainfall) and crop (irrigation, fertilization, calendar) data were also recorded in situ. Flow direction is locally affected by seasonal regional drainage through canal management exercised by the local water authority. The data set was analyzed by dynamic factor analysis (DFA), a specialized time series statistical technique only recently applied in hydrology. In a first step, the observed nitrate variation was successfully described by five common trends representing the unexplained variability. By including the measured hydrological series as explanatory variables the trends were reduced to only three. The analysis yields a quantification of the effects of hydrological factors over local groundwater nitrate concentration. Furthermore, a spatial structure across the field, matching land use, was found in the five remaining common trends whereby the groundwater [N‐NO₃^?] in wells within the corn rows could be generally separated from those in fallow land NW and SE of the crop strip. Fertilization, masked by soil/water/plant‐delayed processes, had no discernible effect on groundwater nitrate levels. Copyright © 2006 John Wiley & Sons, Ltd.     

Spatial prediction on river networks: comparison of top‐kriging with regional regression

Top‐kriging is a method for estimating stream flow‐related variables on a river network. Top‐kriging treats these variables as emerging from a two‐dimensional spatially continuous process in the landscape. The top‐kriging weights are estimated by regularising the point variogram over the catchment area (kriging support), which accounts for the nested nature of the catchments. We test the top‐kriging method for a comprehensive Austrian data set of low stream flows. We compare it with the regional regression approach where linear regression models between low stream flow and catchment characteristics are fitted independently for sub‐regions of the study area that are deemed to be homogeneous in terms of flow processes. Leave‐one‐out cross‐validation results indicate that top‐kriging outperforms the regional regression on average over the entire study domain. The coefficients of determination (cross‐validation) of specific low stream flows are 0.75 and 0.68 for the top‐kriging and regional regression methods, respectively. For locations without upstream data points, the performances of the two methods are similar. For locations with upstream data points, top‐kriging performs much better than regional regression as it exploits the low flow information of the neighbouring locations. Copyright © 2012 John Wiley & Sons, Ltd.     

Regionalization of constraints on expected watershed response behavior for improved predictions in ungauged basins

Approaches to modeling the continuous hydrologic response of ungauged basins use observable physical characteristics of watersheds to either directly infer values for the parameters of hydrologic models, or to establish regression relationships between watershed structure and model parameters. Both these approaches still have widely discussed limitations, including impacts of model structural uncertainty. In this paper we introduce an alternative, model independent, approach to streamflow prediction in ungauged basins based on empirical evidence of relationships between watershed structure, climate and watershed response behavior. Instead of directly estimating values for model parameters, different hydrologic response behaviors of the watershed, quantified through model independent streamflow indices, are estimated and subsequently regionalized in an uncertainty framework. This results in expected ranges of streamflow indices in ungauged watersheds. A pilot study using 30 UK watersheds shows how this regionalized information can be used to constrain ensemble predictions of any model at ungauged sites. Dominant controlling characteristics were found to be climate (wetness index), watershed topography (slope), and hydrogeology. Main streamflow indices were high pulse count, runoff ratio, and the slope of the flow duration curve. This new approach provided sharp and reliable predictions of continuous streamflow at the ungauged sites tested.     

Review of methods used to estimate catchment response time for the purpose of peak discharge estimation

Abstract

Large errors in peak discharge estimates at catchment scales can be ascribed to errors in the estimation of catchment response time. The time parameters most frequently used to express catchment response time are the time of concentration (T_C), lag time (T_L) and time to peak (T_P). This paper presents a review of the time parameter estimation methods used internationally, with selected comparisons in medium and large catchments in the C5 secondary drainage region in South Africa. The comparison of different time parameter estimation methods with recommended methods used in South Africa confirmed that the application of empirical methods, with no local correction factors, beyond their original developmental regions, must be avoided. The T_C is recognized as the most frequently used time parameter, followed by T_L. In acknowledging this, as well as the basic assumptions of the approximations T_L = 0.6T_C and T_C ≈ T_P, along with the similarity between the definitions of the T_P and the conceptual T_C, it was evident that the latter two time parameters should be further investigated to develop an alternative approach to estimate representative response times that result in improved estimates of peak discharge at these catchment scales.

Editor Z.W. Kundzewicz; Associate editor Qiang Zhang