Estimating time parameters of overland flow on impervious surfaces by the particle tracking method

Abstract

Travel time and time of concentration T_c are important time parameters in hydrological designs. Although T_c is the time for the runoff to travel to the outlet from the most remote part of the catchment, most researchers have used an indirect method such as hydrograph analysis to estimate T_c. A quasi two-dimensional diffusion wave model with particle tracking for overland flow was developed to determine the travel time, and validated for runoff discharges, velocities, and depths. Travel times for 85%, 95% and 100% of particles arrival at the outlet of impervious surfaces (i.e. T_t85, T_t95, and T_t100) were determined for 530 model runs. The correlations between these travel times and T_c estimated from hydrograph analysis showed a significant agreement between T_c and T_t85. All the travel times showed nonlinear relationships with the input variables (plot length, slope, roughness coefficient, and effective rainfall intensity) but showed linear relationships with each other.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Book Review

Abstract

The instantaneous unit hydrograph (IUH) of a watershed is the result of one instantaneous unit of rainfall excess distributed uniformly over the watershed. Although the geomorphological characteristics of the basin remain relatively constant, the variable characteristics of storms cause variations in the shape of the resulting hydrographs. It is, therefore, inadequate to use one typical IUH to represent the hydrological response generated from any specific storm. In this study, a variable IUH was derived that directly reflects the time-varying rainfall intensity during storms. The rainfall intensity used to generate the variable IUH at time t is the mean rainfall intensity occurring from the time t—T _c to t in which T _c is the watershed time of concentration. Hydrological records from three watersheds in Taiwan were used to demonstrate the applicability of the proposed model. The results show that better simulations can be obtained by using the proposed model than by using the conventional unit hydrograph method, especially for concentrated rainstorm cases.     

Reliability assessment of water structures subject to data scarcity using the SCS-CN model

ABSTRACT

When discharge measurements are not available, design of water structures relies on using frequency analysis of rainfall data and applying a rainfall–runoff model to estimate a hydrograph. The Soil Conservation Service (SCS) method estimates the design hydrograph first through a rainfall–runoff transformation and next by propagating runoff to the basin outlet via the SCS unit hydrograph (UH) method. The method uses two parameters, the Curve Number (CN) and the time of concentration (T_c). However, in data-scarce areas, the calibration of CN and T_c from nearby gauged watersheds is limited and subject to high uncertainties. Therefore, the inherent uncertainty/variability of the SCS parameters may have considerable ramifications on the safety of design. In this research, a reliability approach is used to evaluate the impact of incorporating the uncertainty of CN and T_c in flood design. The sensitivity of the probabilistic outcome against the uncertainty of input parameters is calculated using the First Order Reliability Method (FORM). The results of FORM are compared with the conventional SCS results, taking solely the uncertainty of the rainfall event. The relative importance of the uncertainty of the SCS parameters is also estimated. It is found that the conventional approach, used by many practitioners, might grossly underestimate the risk of failure of water structures, due to neglecting the probabilistic nature of the SCS parameters and especially the Curve Number. The most predominant factors against which the SCS-CN method is highly uncertain are when the average rainfall value is low (less than 20 mm) or its coefficient of variation is not significant (less than 0.5), i.e. when the resulting rainfall at the design return period is low. A case study is presented for Egypt using rainfall data and CN values driven from satellite information, to determine the regions of acceptance of the SCS-CN method.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Efstratiadis     

Time of concentration: a paradox in modern hydrology

Abstract

The time of concentration is a primary parameter for a variety of modern hydrological models adopted in professional and scientific communities. Nevertheless, a universally accepted working definition of this parameter is currently lacking and several definitions can be found in the technical literature along with related estimation procedures. This study brings to light the inherent variability of these definitions through the empirical analysis of four small basins. These case studies demonstrate that available approaches for the estimation of the time of concentration may yield numerical predictions that differ from each other by up to 500%.

Editor D. Koutsoyiannis

Citation Grimaldi, S., Petroselli, A., Tauro, F. and Porfiri, M., 2012. Time of concentration: a paradox in modern hydrology. Hydrological Sciences Journal, 57 (2), 217–228.     

Effectiveness of introducing crop coefficient and leaf area index to enhance evapotranspiration simulations in hydrologic models

Evapotranspiration (ET) is an essential component of the hydrological cycle and plays a critical role in water resource management. However, ET is often overlooked in order to transform rainfall to runoff for better streamflow simulation. Hydrological models are commonly used to estimate areal actual evapotranspiration (AET) after calibration against observed discharge. However, classical approaches are often inadequate to appropriately simulate other hydrologic components. Hence, it is important to introduce natural heterogeneity to enhance hydrological processes and reduce water balance errors. In this study, the effectiveness of introducing a constant crop coefficient (K_c), flux tower‐based K_c, and leaf area index (LAI) to three hydrological models (Three‐Parametric Hydrologic Model [TPHM], Génie Rural à 4 paramètres Journalier [GR4J], and Catchment hydrologic cycle Assessment Tool [CAT]) is assessed for the simulation of daily streamflow and AET in a mountainous mixed forest watershed (8.54 km²) in South Korea. The results show that the streamflow simulations after introduction of K_c and LAI to the original models are quite similar. However, the effectiveness of the AET estimation was significantly enhanced after introduction of the flux tower‐based K_c and LAI. The information criterion computed to compare the models reveals that the flux tower‐based K_c‐simulated AET demonstrated better agreement with the observed AET. The Pearson's correlation coefficients (R²) of the TPHM (8%), GR4J (55%), and CAT (55%) models also showed improvements that were greater than the constant based K_c simulation. Similarly, the limitations of the three models with respect to capturing seasonal variation as well as high and low flows were enhanced after the introduction of the flux tower‐based K_c, which adequately reproduced hydrological processes with minimum water balance errors and bias. A regression analysis revealed the potential of estimating K_c as a linear function of LAI (R² = 0.84). The results of this study indicate that introduction of K_c and LAI to the conceptual rainfall–runoff models can be considered an effective approach to reduce water balance errors and uncertainties in hydrological models and improve the reliability of climate change studies and water resource management.     

Performance of methods for estimating the time of concentration in a watershed of a tropical region

The time of concentration (T_c) is a fundamental parameter in the design of hydrological projects for watersheds. In this study a graphical methodology is described for estimating T_c in a watershed, and this is applied to 17 rainfall–runoff events from a rural watershed located near the capital city of Mato Grosso do Sul State, in the Brazilian Cerrado. The T_c values obtained through the graphical method were compared to T_c values estimated using 20 equations from various references. The equations were selected by considering those that were not developed using data for urban watersheds, and the results of the graphical method were compared to those derived by applying the equations to sub-basin data. The graphical method was reliable in determining T_c, and Ventura’s equation was found to present the best performance for a rural watershed in a tropical climate region.     

Analytical solutions to runoff on hillslopes with curvature: numerical and laboratory verification

Predicting the behavior of overland flow with analytical solutions to the kinematic wave equation is appealing due to its relative ease of implementation. Such simple solutions, however, have largely been constrained to applications on simple planar hillslopes. This study presents analytical solutions to the kinematic wave equation for hillslopes with modest topographic curvature that causes divergence or convergence of runoff flowpaths. The solution averages flow depths along changing hillslope contours whose lengths vary according hillslope width function, and results in a one-dimensional approximation to the two-dimensional flow field. The solutions are tested against both two-dimensional numerical solutions to the kinematic wave equation (in ParFlow) and against experiments that use rainfall simulation on machined hillslopes with defined curvature properties. Excellent agreement between numerical, experimental and analytical solutions is found for hillslopes with mild to moderate curvature. The solutions show that curvature drives large changes in maximum flow rate q_peak and time of concentration t_c , predictions frequently used in engineering hydrologic design and analysis.     

The timing of runoff response in design flood analysis

This study presents an investigation of the time to peak of unit response functions for design flood studies. It is based on an empirical analysis of observed rainfall–runoff data for 49 basins in the UK and explores the relationship between unit response time to peak (t_p) and flood peak magnitude (Q_p). The results show that t_p varies significantly between events but suggest a systematic relationship between t_p and Q_p. The relationships which have been developed suggest that t_p decreases with flood magnitude and approaches to an asymptotic value for very large values of Q_p. These findings confirm numerous physical and field investigations and also support the reduction in response time for probable maximum flood (PMF) recommended in the Soil Conservation Services method, the Flood Studies Report method and the Flood Estimation Handbook. The findings also suggest that t_p should be modified in unit hydrograph methods of design flood analysis for return periods that differ from those used in deriving unit hydrographs. A simple correction curve has been developed for adjusting t_p according to the design flood return period. Copyright © 2000 John Wiley & Sons, Ltd.     

Exploring the effect of different time resolutions to calculate the rainfall erosivity factor R in Calabria,southern Italy

The rainfall erosivity factor R of the Universal Soil Loss Equation is a good indicator of the potential of a storm to erode soil, as it quantifies the raindrop impact effect on the soil based on storm intensity. The R‐factor is defined as the average annual value of rainfall erosion index, EI, calculated by cumulating the EI values obtained for individual storms for at least 22 years. By definition, calculation of EI is based on rainfall measurements at short time intervals over which the intensity is essentially constant, i.e. using so‐called breakpoint data. Because of the scarcity of breakpoint rainfall data, many authors have used different time resolutions (Δt = 5, 10, 15, 30, and 60 min) to deduce EI in different areas of the world. This procedure affects the real value of EI because it is strongly dependent on Δt. In this contribution, after a general overview of similar studies carried out in different countries, the relationship between EI and Δt is explored in Calabria, southern Italy. The use of 17 139 storm events collected from 65 rainfall stations allowed the calculation of EI for different time intervals ranging from 5 to 60 min. The overall results confirm that calculation of EI is dependent on time resolution and a conversion factor able to provide its value for the required Δt is necessary. Based on these results, a parametric equation that gives EI as a function of Δt is proposed, and a regional map of the scale parameter a that represents the conversion factor for converting fixed‐interval values of (EI₃₀)_Δt to values of (EI₃₀)₁₅ is provided in order to calculate R anywhere in the region using rainfall data of 60 min. Copyright © 2015 John Wiley & Sons, Ltd.     

Real-time prediction of the peak suspended sediment concentration and sediment yield of the Lao-Nung River during storms

Based on rainfall erosion of soil and suspended sediment transport in storm events, a method is proposed to predict peak suspended sediment concentration and suspended sediment yield in watersheds based on rainfall characteristics prior to peak rainfall intensity. The rainfall characteristics factors that dominate peak suspended sediment concentration C_p are rainfall erosion factor R_ef, first peak rainfall intensity of area-average rainfall i_p1 and antecedent precipitation index I_ap; the rainfall characteristics factors that dominate suspended sediment yield Y_ss in storm events are total rainfall P, suspended sediment yield factor R_sf and antecedent precipitation index I_ap. This research focuses on watersheds in Liau-Kwei observation station along Lao-Nung River in southern Taiwan as the research object, and adopts the PSED-model to simulate the discharge hydrograph, suspended sediment concentration hydrograph and suspended sediment yield in 11 storm events for analysis. The analytical results show that there is a good correlation between the above-mentioned rainfall characteristics factors and C_p as well as Y_ss, thus enabling C_p and Y_ss to be predicted by using Expressions (13) and (14). These two expressions are utilized to predict C_p and Y_ss of Typhoon Morakot in 2009, and the results are compared with those from simulation by using the PSED-model. The result of comparison shows there is a good capability in predicting. For the watersheds where it is necessary to predict C_p and Y_ss of a storm event for the benefit of effective operation of water resource facilities, the aforesaid rainfall characteristics factors can be utilized to establish applicable models for prediction.     

Direct estimation of catchment response time parameters in medium to large catchments using observed streamflow data

In single‐event deterministic design flood estimation methods, estimates of the peak discharge are based on a single and representative catchment response time parameter. In small catchments, a simplified convolution process between a single‐observed hyetograph and hydrograph is generally used to estimate time parameters such as the time to peak (T_P), time of concentration (T_C), and lag time (T_L) to reflect the “observed” catchment response time. However, such simplification is neither practical nor applicable in medium to large heterogeneous catchments, where antecedent moisture from previous rainfall events and spatially non‐uniform rainfall hyetographs can result in multi‐peaked hydrographs. In addition, the paucity of rainfall data at sub‐daily timescales further limits the reliable estimation of catchment responses using observed hyetographs and hydrographs at these catchment scales. This paper presents the development of a new and consistent approach to estimate catchment response times, expressed as the time to peak (T_Px) obtained directly from observed streamflow data. The relationships between catchment response time parameters and conceptualised triangular‐shaped hydrograph approximations and linear catchment response functions are investigated in four climatologically regions of South Africa. Flood event characteristics using primary streamflow data from 74 flow‐gauging stations were extracted and analysed to derive unique relationships between peak discharge, baseflow, direct runoff, and catchment response time in terms of T_Px. The T_Px parameters are estimated from observed streamflow data using three different methods: (a) duration of total net rise of a multipeaked hydrograph, (b) triangular‐shaped direct runoff hydrograph approximations, and (c) linear catchment response functions. The results show that for design hydrology and for the derivation of empirical equations to estimate catchment response times in ungauged catchments, the catchment T_Px should be estimated from both the use of an average catchment T_Px value computed using either Methods (a) or (b) and a linear catchment response function as used in Method (c). The use of the different methods in combination is not only practical but is also objective and has consistent results.     

Transient Divergent Flow and Transport in an Infinite Anisotropic Porous Formation

When seeking to predict plume geometry resulting from fluid injection through partially penetrating wells, it is common to assume a steady-state spherically diverging flow field. In reality, the flow field is transient. The steady-flow assumption is likely to cause overestimation of injection plume radius since the accommodation of fluid by increases in porosity and fluid density is ignored. In this paper, a transient solution is developed, resulting in a nonlinear ordinary differential equation expressing plume radius as a function of time. It is shown that the problem can be fully described by one type curve. A critical time, t_c, is identified at which the percentage error of the steady-state flow solution compared to the fully dynamic problem is less than 1%. Only for large injection rates and low permeabilities, does t_c become greater than 1 h. Nevertheless, an improved approximate solution is obtained by a simple linearization procedure. The critical time, t_c for the new approximate solution is 0.3% of that required for the steady-state flow solution.     

Estimation of rainfall elasticity of streamflow in Australia

Abstract

Estimates of rainfall elasticity of streamflow in 219 catchments across Australia are presented. The rainfall elasticity of streamflow is defined here as the proportional change in mean annual streamflow divided by the proportional change in mean annual rainfall. The elasticity is therefore a simple estimate of the sensitivity of long-term streamflow to changes in long-term rainfall, and is particularly useful as an initial estimate of climate change impact in land and water resources projects. The rainfall elasticity of streamflow is estimated here using a hydrological modelling approach and a nonparametric estimator. The results indicate that the rainfall elasticity of streamflow (? _P ) in Australia is about 2.0–3.5 (observed in about 70% of the catchments), that is, a 1% change in mean annual rainfall results in a 2.0–3.5% change in mean annual streamflow. The rainfall elasticity of streamflow is strongly correlated to runoff coefficient and mean annual rainfall and streamflow, where streamflow is more sensitive to rainfall in drier catchments, and those with low runoff coefficients. There is a clear relation-ship between the ? _P values estimated using the hydrological modelling approach and those estimated using the nonparametric estimator for the 219 catchments, although the values estimated by the hydrological modelling approach are, on average, slightly higher. The modelling approach is useful where a detailed study is required and where there are sufficient data to reliably develop and calibrate a hydrological model. The nonparametric estimator is useful where consistent estimates of the sensitivity of long-term streamflow to climate are required, because it is simple to use and estimates the elasticity directly from the historical data. The nonparametric method, being model independent, can also be easily applied in comparative studies to data sets from many catchments across large regions.     

A shot noise model for the generation of soil moisture data

An attempt is made to estimate the expected contribution of rainfall to soil moisture during the irrigation season. Effective rainfall and evapotranspiration are the parameters considered in the water balance carried out in the root zone. Rainfall occurrence is simulated by a Poisson process whereas evapotranspiration is described by a simple deterministic function of potential evapotranspiration and soil moisture in the root zone. Using the theory of shot noise models a closed form solution is derived from the expected soil moisture in the root zone at the end of the time interval (0,t]. For illustration purposes the proposed model is applied to a series of data from Mikra meteorological station in Greece.List of symbols x change in water storage in the root zone during the time interval t - X infiltrated rainfall of thei th storm event - ET actual evapotranspiration during thej th day - Poisson rate - number of storm events in (0,t] - t _r duration of rainfall - t _b interarrival time - h _i rainfall depth of thei th storm event - i _m mean rainfall intensity - i(t) instantaneous rainfall intensity - x(0),x(t) available soil moisture in the root zone at time 0 andt, respectively - PET potential evapotranspiration rate - x _F available soil moisture in the root zone at field capacity - soil moisture depletion rate (=PET/x _F ) - w impulse shape of filtered Poisson processes - E[·] mean value - S _i time of thei th rainfall event - N(t) time of storm events in (0,t] - estimated standard deviation The following symbols were used in this paper     

Multifractal behaviour of long‐term karstic discharge fluctuations

Karstic watersheds are highly complex hydrogeological systems that are characterized by a multiscale behaviour corresponding to the different pathways of water in these systems. The main issue of karstic spring discharge fluctuations consists in the presence and the identification of characteristic time scales in the discharge time series. To identify and characterize these dynamics, we acquired, for many years at the outlet of two karstic watersheds in South of France, discharge data at 3‐mn, 30‐mn and daily sampling rate. These hydrological records constitute to our knowledge the longest uninterrupted discharge time series available at these sampling rates. The analysis of the hydrological records at different levels of detail leads to a natural scale analysis of these time series in a multifractal framework. From a universal class of multifractal models based on cascade multiplicative processes, the time series first highlights two cut‐off scales around 1 and 16 h that correspond to distinct responses of the aquifer drainage system. Then we provide estimates of the multifractal parameters α and C₁ and the moment of divergence q_D corresponding to the behaviour of karstic systems. These results constitute the first estimates of the multifractal characteristics of karstic spingflows based on 10 years of high‐resolution discharge time series and should lead to several improvements in rainfall‐karstic springflow simulation models. Copyright © 2012 John Wiley & Sons, Ltd.     

Uncertainty and sensitivity analysis of a travel-time distribution-based stream water electrical conductivity model

In this paper, we analyse the uncertainty and parameter sensitivity of a conceptual water quality model, based on a travel time distribution (TTD) approach, simulating electrical conductivity (EC) in the Duck River, Northwest Tasmania, Australia for a 2-year period. Dynamic TTDs of stream water were estimated using the StorAge Selection (SAS) approach, which was coupled with two alternate methods to model stream water EC: (1) a solute-balance approach and (2) a water age-based approach. Uncertainty analysis using the Differential Evaluation Adoptive Metropolis (DREAM) algorithm showed that: 1. parameter uncertainty was a small contribution to the overall uncertainty; 2. most uncertainty was related to input data uncertainty and model structure; 3. slightly lower total error was obtained in the water age-based model than the solute-balance model; 4. using time-variant SAS functions reduced the model uncertainty markedly, which likely reflects the effect of dynamic hydrological conditions over the year affecting the relative importance of different flow pathways over time. Model parameter sensitivity analysis using the Variogram Analysis of Response Surfaces (VARS-TOOL) framework found that parameters directly related to the EC concentration were most sensitive. In the solute-balance model, the rainfall concentration C_rain and in the age-based model, the parameter controlling the rate of change of EC with age (λ) were the most sensitive parameter. Model parameters controlling the age mixes of both evapotranspiration and streamflow water fluxes (i.e., the SAS function parameters) were influential for the solute-balance model. Little change in parameter sensitivity over time was found for the age-based concentration relationship; however, the parameter sensitivity was quite dynamic over time for the solute-balance approach. The overarching outcomes provide water quality modellers, engineers and managers greater insight into catchment functioning and its dependence on hydrological conditions.     

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     

Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments

Abstract

A novel approach is presented for combining spatial and temporal detail from newly available TRMM-based data sets to derive hourly rainfall intensities at 1-km spatial resolution for hydrological modelling applications. Time series of rainfall intensities derived from 3-hourly 0.25° TRMM 3B42 data are merged with a 1-km gridded rainfall climatology based on TRMM 2B31 data to account for the sub-grid spatial distribution of rainfall intensities within coarse-scale 0.25° grid cells. The method is implemented for two dryland catchments in Tunisia and Senegal, and validated against gauge data. The outcomes of the validation show that the spatially disaggregated and intensity corrected TRMM time series more closely approximate ground-based measurements than non-corrected data. The method introduced here enables the generation of rainfall intensity time series with realistic temporal and spatial detail for dynamic modelling of runoff and infiltration processes that are especially important to water resource management in arid regions.

Editor D. Koutsoyiannis

Citation Tarnavsky, E., Mulligan, M. and Husak, G., 2012. Spatial disaggregation and intensity correction of TRMM-based rainfall time series for hydrological applications in dryland catchments. Hydrological Sciences Journal, 57 (2), 248–264.     

Laboratory examination of linearity in rainfall–runoff relationships

ABSTRACT

Certain rainfall–runoff models, e.g. the unit hydrograph, assume linear relationships between the variables. These are proportionality of runoff discharges to (net) rainfall depth and linear summations of discharges resulting from (net) rainfalls during different time intervals or over different sectors of a watershed. This study examines the validity of these assumptions by use of an extensive two-dimensional laboratory experimentation. The results indicate that proportionality would be found under high rainfall intensity through a long duration. Spatial summations would more likely yield correct discharges in cases where rainfall duration is equal to, or is longer than, the time of concentration. Temporal summations may yield correct discharges when rainfall duration is longer than one half of the time of concentration. Here, the time of concentration is determined at the beginning of gradual approach of the discharge towards the equilibrium state.