Assessment of design rainfall uncertainty for hydrologic engineering applications in Hong Kong

Hydrologic engineering designs and analyses often require the specification of design storm which involves rainfall amount, duration and hyetograph. In practice, the determination of design rainfall in hydrologic engineering applications involves the frequency analysis of extreme rainfalls of different durations and the establishment of rainfall hyetograph for the design event under consideration. Sampling errors exist in the estimation of rainfall depth (or intensity) quantiles from frequency analysis, which will be transmitted in the process of determining the design rainfall hyetograph. This paper presents a practical methodological framework based on the bootstrap resampling scheme to assess the uncertainty features associated with the magnitude of estimated rainfall depth/intensity quantiles and the corresponding design hyetographs. The procedure is implemented to quantify uncertainty of design rainfall hyetograph following the Stormwater Drainage Manual of Hong Kong involving the use of rainfall intensity–duration–frequency (IDF) model. Of particular interesting is that the bootstrap resampling scheme implemented herein is modified to handle unequal record period of annual maximum rainfall data series of different durations and to account for their intrinsic correlations. According to the adopted rainfall IDF model, the design rainfall hyetograph is a function of the IDF model coefficients. Due to the correlation among rainfall quantiles of different durations, the IDF coefficients are found to be strongly related in a nonlinear fashion which should not be ignored in the establishment of the design hyetographs.     

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.     

Reliability analysis of hydraulic structures considering unit hydrograph uncertainty

Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.     

Reliability analysis of hydraulic structures considering unit hydrograph uncertainty

Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.     

Development of regional design hyetographs

A method is proposed to establish regional design hyetographs for facilitating the determination of design hyetographs at ungauged sites. The method is applied to the central area of Taiwan. First, the single‐station design hyetographs at all rain gauges are analysed using principal components analysis and cluster analysis. The principal components analysis shows that there are six dominant factors, and the cluster analysis indicates that the time to peak rainfall has the largest influence on the classification of hyetographs. It also shows that the single‐station hyetographs in the study area can be classified into three clusters. Finally, the homogeneous regions for these three clusters are delineated and the corresponding regional design hyetographs are proposed. Once the homogeneous regions and the regional hyetographs are available, the design hyetograph at the point of interest can be easily determined. The proposed method is expected to be useful for providing the design hyetographs at ungauged sites. Copyright © 2004 John Wiley & Sons, Ltd.     

Construction of design hyetographs for locations without observed data

A design hyetograph which represents the time distribution of design rainfall depth corresponding to a duration and a return period is essential in hydrologic design. However, for locations without observed data (ungauged sites), construction of design hyetographs is a difficult task because of the lack of data. Hence, an approach based on self‐organizing map (SOM) is proposed in this paper to construct design hyetographs at ungauged sites. SOM, which is a special kind of artificial neural networks (ANNs), is a powerful technique for extracting and visualizing salient features of data and for solving classification problems. The proposed approach is composed of three steps: classification, assignment and construction. First, the SOM‐based classification is performed to analyse gauged sites' design hyetographs. Second, based on the concept of indicator kriging, a method is developed to assign an ungauged site of interest to a certain cluster. Third, based on the spatial information, the clustering results, and the design hyetographs of gauged sites, the design hyetograph at the site of interest is constructed using the reciprocal‐distance‐squared method. An application is conducted to assess the advantages of the proposed approach over the conventional approaches. Moreover, cross‐validation tests are applied to evaluate the performance of the accuracy and the robustness of the proposed approach. The results confirm the improvement in performance by using the proposed approach instead of conventional approaches. The proposed approach is useful for constructing design hyetographs at ungauged sites. Copyright © 2009 John Wiley & Sons, Ltd.     

A steepness index unit volume flood hydrograph approach for sub‐daily flow disaggregation

The estimation of sub‐daily flows from daily flood flows is important for many hydrological and hydraulic applications. Flows during flood events often vary significantly within sub‐daily time‐scales, and failure to capture the sub‐daily flood characteristic can result in an underestimation of the instantaneous flood peaks, with possible risk of design failure. It is more common to find a longer record of daily flow series (observed or modelled using daily rainfall series) than sub‐daily flow data. This paper describes a novel approach, known as the steepness index unit volume flood hydrograph approach, for disaggregating daily flood flows into sub‐daily flows that takes advantage of the strong relationship between the standardized instantaneous flood peak and the standardized daily flood hydrograph rising‐limb steepness index. The strength of this relationship, which is considerably stronger than the relationship between the standardized flood peak and the event flood volume, is shown using data from six rivers flowing into the Gippsland Lakes in southeast Australia. The results indicate that the steepness index unit volume flood hydrograph approach can be used to disaggregate modelled daily flood flows satisfactorily, but its reliability is dependent on a model's ability to simulate the standardized daily flood hydrograph rising‐limb steepness index and the event flood volume. Copyright © 2007 John Wiley & Sons, Ltd.     

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     

ANALYSIS OF AN ISOLATED STORM EVENT HYDROGRAPH BY IDENTIFYING THE INFLOW SEQUENCE TO A NON-LINEAR CONCEPTUAL RESERVOIR

In an isolated storm event model relating gross rainfall to the flow hydrograph, the shape transformation component can be composed of a number of subsystems. It is assumed here that this component contains, along with other subsystems, a non-linear conceptual reservoir expressed in general terms. Given an isolated storm event, a procedure is described that directly identifies the particular inflow sequence that needs to be applied to this reservoir to reproduce the observed discharge hydrograph as outflow. This procedure makes use of information contained only in the observed hydrograph and does not rely on prior knowledge of the gross or net rainfall hyetographs. Nor is it necessary to identify in full the storage–outflow relation of the non-linear reservoir used. Future comparisons between the gross rainfall hyetograph and the identified inflow sequence should be facilitated by the procedure's ability to remove the long trailing recession belonging to the outflow.     

Nonlinear transformation of unit hydrograph

Unit hydrograph (UH) and its numerous derivatives have been popular for estimation of flood hydrographs. Two major assumptions still overshadow UH applications. One is the linearity and the other is time invariance. In theory, only peak discharge of an equilibrium hydrograph follows linear proportionality to excess rainfall intensity. In trying to relax the linearity constraint, this paper aims to propose a nonlinear way of transforming a given UH to other general hydrographs. The transformation or mapping technique relies on a simple rainfall ratio raised to a power less than unity. The case of nonlinear transformation is illustrated for a number of watershed geometries with either known kinematic wave analytic solutions or observed data. The nonlinear UH approach also relaxes the assumption of constant time base of the UH. The proposed nonlinear UH transformation may thus be viewed as a major step in closing the gap between physically based and traditional UH-based surface runoff simulation approaches.     

Monthly and annual effective infiltration coefficients in Dinaric karst: example of the Gradole karst spring catchment

Abstract

The method of “historic event” is used to generate synthetic hyetographs based on statistical analysis of precipitation data. A synthetic triangular model was developed based on rainfall data of Zioud watershed (central Tunisia) with a standard time step of one hour. A database of 2799 observed rainfall events was used to provide statistical parameters for a simple triangular-shaped hyetograph model. The developed model provides a synthetic hyetograph in dimensionless form for different storm durations (2, 3 and 4 hours). For a given season and location, the variation of the first dimensionless moment with duration was relatively small, with an average range of 13% for all the stations. The resulting dimensionless hyetographs were found to be nearly identical when they were non-dimensionalized using the rainfall depth and duration, showing some seasonal effect and insignificant effects of the rainfall duration. A good agreement between simulated and observed hyetographs was achieved based on not only visual impressions, but also statistical numerical and graphical tests.     

Flood simulation using the gauge‐adjusted radar rainfall and physics‐based distributed hydrologic model

This paper reports the results of an investigation into flood simulation by areal rainfall estimated from the combination of gauged and radar rainfalls and a rainfall–runoff model on the Anseong‐cheon basin in the southern part of Korea. The spatial and temporal characteristics and behaviour of rainfall are analysed using various approaches combining radar and rain gauges: (1) using kriging of the rain gauge alone; (2) using radar data alone; (3) using mean field bias (MFB) of both radar and rain gauges; and (4) using conditional merging technique (CM) of both radar and rain gauges. To evaluate these methods, statistics and hyetograph for rain gauges and radar rainfalls were compared using hourly radar rainfall data from the Imjin‐river, Gangwha, rainfall radar site, Korea. Then, in order to evaluate the performance of flood estimates using different rainfall estimation methods, rainfall–runoff simulation was conducted using the physics‐based distributed hydrologic model, Vflo^?. The flood runoff hydrograph was used to compare the calculated hydrographs with the observed one. Results show that the rainfall field estimated by CM methods improved flood estimates, because it optimally combines rainfall fields representing actual spatial and temporal characteristics of rainfall. Copyright © 2008 John Wiley & Sons, Ltd.     

Hydrograph characteristics of quick and slow runoffs of a watershed outlet,Taiwan

This study explores the hydrograph characteristics of quick and slow runoffs in watershed outlet hydrographs. The quick and slow runoffs were modelled using a conceptual model of three linear cascade reservoirs that have exponential decay response expressions. Mean rainfall for model inputs was estimated using the block Kriging method. The 107 storms during the 1966–2008 events were classified as large, medium and small events according to the observed streamflow. The optimal hydrograph parameters for 61 rainfall‐runoff events were calibrated using the shuffled complex evolution optimal algorithm. The efficacy of the model was verified using the seven averaged parameters of three types of 46 events and was compared with three evaluation criteria resulting from the Nash model. The 61 calibrations were used to analyse and compare the characteristics of quick and slow flows in early and later periods (1966–2002 and 2003–2008). Finally, the following five conclusions were obtained: (1) The base time of a slow runoff hydrograph is the same as that of a total runoff hydrograph. (2) A quick runoff with a long period occurs when soil antecedent moisture is low and with a short period under a high value. (3) The time to peak of hydrograph components is directly proportional to peak time of a hyetograph; the time to peak of quick and slow flows is about 0·97 and 1·12 times the peak time of a hyetograph, respectively. (4) The peak of hydrograph components is relative to a total runoff hydrograph; the percentages for quick runoff are approximately 71% and 13% for slow flow. Finally, (5) the volume of a quick runoff component is 49% of a total runoff volume and 37% for a slow runoff volume. Copyright © 2010 John Wiley & Sons, Ltd.     

Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Development of design flood hydrographs using probability density functions

Probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQ_P) and error of time to peak (ET_P) were computed. The best‐fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20‐, 50‐, 100‐ and 200‐year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20‐, 50‐, 100‐ and 200‐year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormal‐produced peak discharge was very close to the estimated design discharge in case of 20‐year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50‐, 100‐ and 200‐year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50‐, 100‐ and 200‐year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma. Copyright © 2009 John Wiley & Sons, Ltd.     

Effect of uncertainty in Digital Surface Models on the extent of inundated areas

The impact of uncertainty in ground elevation on the extent of areas that are inundated due to flooding is investigated. Land surface is represented through a Digital Surface Model (DSM). The effect of uncertainty in DSM is compared to that of the uncertainty due to rainfall. The Monte Carlo method is used to quantify the uncertainty. A typical photogrammetric procedure and conventional maps are used to obtain a reference DSM, later altered to provide DSMs of lower accuracy. Also, data from the Shuttle Radar Topography Mission are used. Floods are simulated in two stages. In the first stage, flood hydrographs for typical return periods are synthesized using generated storm hyetographs, the Soil Conservation Service–Curve Number method for effective rainfall, and the Soil Conservation Service synthetic unit hydrograph. In the second stage, hydrographs are routed via a one‐dimensional hydraulic model. Uncertainty in DSM is considered only in the second stage. Data from two real‐world basins in Greece are used. To characterize the inundated area, we employ the 90% quantile of the inundation extent and inundation topwidth for peak water level at specific river cross‐sections. For topwidths, apart from point estimates, also interval estimates are acquired using the bootstrap method. The effect of DSM uncertainty is compared to that for rainfall. Low uncertainty in DSM is found to widen the inundated area; whereas, the opposite occurred with high uncertainty. SRTM data proved unsuitable for our test basins and modelling context.     

Assessing sub-daily rainstorm variability and its effects on flood processes in the Yangtze River Delta region

ABSTRACT

Taking a representative catchment of the Yangtze River Delta region as the study area, this research evaluated sub-daily rainstorm variability and its potential effects on flood processes based on an integrated approach of the HEC-HMS model and design storm hyetographs. The results show that the intensities of rainfall on sub-daily scale are getting more extreme. The annual maximum 1-, 2- and 3-hour rainstorms followed significant upward trends with increases of 0.32, 0.43 and 0.44 mm per year, respectively, while the annual maximum 6-, 12- and 24-h events had non-significant rising trends. The detected significant trends in short-duration rainstorms were then used to redesign storm hyetographs to drive the HEC-HMS model, the results show that these changes in short-duration rainstorm characteristics would increase the flood peak discharge and flood volume. These findings indicate that regional flood control capabilities must be improved to manage the adverse impacts of rainfall variation under changing environments.     

Simple generalization approach for intensity–duration–frequency relationships

Rainfall intensity–duration–frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two‐parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well‐known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal–Wallis test statistic with respect to the parameters θ and η of the duration function. Because the approach proposed herein is based on lower‐order sample statistics, risks and uncertainties arising from sampling errors in higher‐order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two‐parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort. Copyright © 2012 John Wiley & Sons, Ltd.     

Curve‐Number/Green–Ampt mixed procedure for streamflow predictions in ungauged basins: Parameter sensitivity analysis

A procedure combining the Soil Conservation Service‐Curve Number (SCS‐CN) method and the Green–Ampt (GA) infiltration equation was recently developed to overcome some of the drawbacks of the classic SCS‐CN approach when estimating the volume of surface runoff at a sub‐daily time resolution. The rationale of this mixed procedure, named Curve Number for Green–Ampt (CN4GA), is to use the GA infiltration model to distribute the total volume of the net hyetograph (rainfall excess) provided by the SCS‐CN method over time. The initial abstraction and the total volume of rainfall given by the SCS‐CN method are used to identify the ponding time and to quantify the hydraulic conductivity parameter of the GA equation. In this paper, a sensitivity analysis of the mixed CN4GA parameters is presented with the aim to identify conditions where the mixed procedure can be effectively used within the Prediction in Ungauged Basin perspective. The effects exerted by changes in selected input parameters on the outputs are evaluated using rectangular and triangular synthetic hyetographs as well as 100 maximum annual storms selected from synthetic rainfall time series. When applied to extreme precipitation events, which are characterized by predominant peaks of rainfall, the CN4GA appears to be rather insensitive to the input hydraulic parameters of the soil, which is an interesting feature of the CN4GA approach and makes it an ideal candidate for the rainfall excess estimation at sub‐daily temporal resolution at ungauged sites. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling impacts of agricultural practice on flood peaks in upland catchments: An application of the distributed TOPMODEL

Upland agricultural land management activities such as grazing, vegetation burning, and bare ground restoration impact hydrological elements of headwater catchments, many of which may be important for downstream flood peaks (e.g., overland flow and soil water storage). However, there is poor understanding of how these management practices affect river flow peaks during high magnitude rainfall events. Using the distributed TOPMODEL, spatial configurations of land management were modelled to predict flood response in an upland catchment, which contains different regions operating subsidized agricultural stewardship schemes. Heavy grazing leading to soil compaction and loss of vegetation cover in stewardship regions covering 79.8% of the catchment gave a 42‐min earlier flow peak, which was 82.2% higher (under a 1‐hr 15‐mm storm) than the current simulated hydrograph. Light grazing over the same regions of the catchment had much less influence on river flow peaks (18 min earlier and 32.9% increase). Rotational burning (covering 8.8% of the catchment), most of which is located in the headwater areas, increased the peak by 3.2% in the same rainfall event. Vegetation restoration with either Eriophorum or Sphagnum (higher density) in bare areas (5.8%) of the catchment provided a reduction of flood peak (3.9% and 5.2% in the 15‐mm storm event), whereas the same total area revegetated with Sphagnum in riparian regions delivered a much larger decrease (15.0%) in river flow peaks. We show that changes of vegetation cover in highly sensitive areas (e.g., near‐stream zones) generate large impacts on flood peaks. Thus, it is possible to design spatially distributed management systems for upland catchments, which reduce flood peaks while at the same time ensuring economic viability for upland farmers.