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     

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.     

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.     

Salinograph trends as indicators of the recession characteristics of stream components

Compared to hydrograph recession analysis, which is widely applied in engineering hydrology, the quantitative assessment of stream salinity with time (i.e. the salinograph) has received significantly less attention. In particular, while in many previous hydrological studies an inverse relationship between hydrograph and salinograph responses is apparent, the concept of salinity accession (the inversely related salinity counterpart to hydrograph recession) has not been introduced nor quantitatively evaluated in previous literature. In this study, we conduct a mathematical analysis of salinograph accession, and determine new quantitative relationships between salinity accession and hydrograph recession parameters. An equation is formulated that reproduces the general trend in salinity accession. A salinity accession parameter k_c is then introduced and is shown to be the ratio of direct runoff to total stream flow recession parameters: k_r/k. The groundwater recession parameter k_g was estimated using a simple and rapid method that uses both salinograph and hydrograph data. Salinity accession type‐curves illustrate that under certain conditions, the relative steepness of individual salinographs is dependent upon the ratio of groundwater salinity to direct runoff salinity: C_g/C_r. The salinity accession algorithms are applied to two contrasting field settings: Scott Creek, South Australia and Sandy Creek, northern Queensland, Australia. It was found that k_g > k during periods of obvious stream flow recession, for the events analysed. Salinograph accession behaviour was fairly similar for both sites, despite contrasting environments. Using assumed end‐member salinities for groundwater and direct runoff based upon field observations, the behaviour of k_c from the Scott Creek site was approximately reproduced by varying the initial groundwater to runoff flow ratio: Q_g0/Q_r0, within reasonable parameter ranges. The use of salinograph information when used in addition to standard hydrograph analyses provided useful information on recession characteristics of stream components. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

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.     

An investigation of lag times for rainfall–runoff–sediment yield events in small river basins / Une analyse des temps de réponse d'événements pluie–débit–transport solide au sein de petits bassins versants

Abstract

River basin lag time (LAG), defined as the elapsed time between the occurrence of the centroids of the effective rainfall intensity pattern and the storm runoff hydrograph, is an important factor in determining the time to peak and the peak value of the instantaneous unit hydrograph, IUH. In the procedure of predicting a sedimentgraph (suspended sediment load as a function of time), the equivalent parameter is the lag time for the sedimentgraph (LAG_s ), which is defined as the elapsed time between the occurrence of the centroids of sediment production during a storm event and the observed sedimentgraph at the gauging station. Results of analyses of rainfall, runoff and suspended sediment concentration event data collected from five small Carpathian basins in Poland and from a 2.31-ha agricultural basin, in central Illinois, USA have shown that LAG_s was, in the majority of cases, smaller than LAG, and that a significant linear relationship exists between LAG_s and LAG.     

Assessment of detachment and sediment transport capacity of runoff by field experiments on a silt loam soil

The detachment capacity (D_c) and transport capacity (T_c) of overland flow are important variables in the assessment of soil erosion. They determine respectively the lower and upper limit of sediment transport by runoff and therefore control detachment and deposition pro‐cesses. In this study, the detachment and transport capacity of runoff was investigated by rainfall simulations and overland flow experiments on small field plots. On the bare field plots, it was found that T_c was strongly related to total runoff discharge. This was also observed for the plots covered by maize residues, but T_c was less due to the lower runoff velocity. A simple regression equation was derived to estimate T_c for both bare and covered soil. Comparing our observations with T_c equations mentioned in the literature revealed that T_c equations based on laboratory experiments overestimated, on average, our measurements. Although T_c can be assessed more easily in laboratory experiments, the applicability of the results to field conditions remains questionable. Detachment by runoff was also related to total runoff discharge. The D_c values were, however, 4–50 times smaller than the T_c at corresponding high and low runoff discharge. This indicates that detachment by runoff constitutes only part of the transported sediment. Interrill erosion supplies an important additional amount of sediment. In this study, however, only sealed soils were considered. In the case of freshly tilled, loose soils, the D_c of runoff may be larger, resulting in a larger contribution to the total soil loss. Copyright © 2008 John Wiley & Sons, Ltd.     

FLOOD MODELLING WITH GIS-DERIVED DISTRIBUTED UNIT HYDROGRAPHS

The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time–area curve of a watershed by the S-curve method. The time–area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time–area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km² watershed, using 1 km × 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km × 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time–area curve. The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology.     

Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan

Abstract

This study investigates the characteristics of hydrograph components from a watershed in Taiwan. Hydrograph components were modelled by using a model of three serial reservoirs with one parallel reservoir. Mean rainfall was calculated by using the block kriging method. The model parameters for 38 events were calibrated by using the shuffled complex evolution optimization algorithm. The model verification was made using 18 events. Based on the study results, the following findings were obtained: (1) for single-peak events, times to peak of hydrograph components are an increasing power function of the peak time of rainfall; (2) peak discharges of hydrograph components are linearly proportional to that of total runoff, and the ratios of quick and slow runoff are approximately 83% and 17% of total runoff, respectively; and (3) the total volume of quick runoff component is 52% of total runoff and that of slow runoff is 27%.

Editor D. Koutsoyiannis

Citation Li, Y.-J., Cheng, S.-J. Pao, T.-L. and Bi, Y.-J., 2012. Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan. Hydrological Sciences Journal, 57 (5), 861–877.     

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     

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.     

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.     

Turbulent transport of magnetic fields. V. Distribution of magnetic energy in a simple α2-dynamo

Abstract

In this paper we analyse the stationary mean energy density tensor T_ij = B_iB_j for the x ²-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for T_ij is found analytically. Only T_rr , T _θθ and T _φφ are unequal to zero, and we present their dependence on the radial distance r.

The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈?u²?τ_c/3 and the vorticity coefficient γ ≈ ?|?×u|²?τ_c/3 where u(r, t) is the turbulent velocity and _c its correlation time. But the solution is independent of the dynamo coefficient α≈??u·?×u?τ_c/3 although α does occur in the equation for T_ij . This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which T_ij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos.     

Travel times for snowmelt-dominated headwater catchments: Influences of wetlands and forest harvesting,and linkages to stream water quality

The time it takes water to travel through a catchment, from when it enters as rain and snow to when it leaves as streamflow, may influence stream water quality and catchment sensitivity to environmental change. Most studies that estimate travel times do so for only a few, often rain-dominated, catchments in a region and use relatively short data records (<10 years). A better understanding of how catchment travel times vary across a landscape may help diagnose inter-catchment differences in water quality and response to environmental change. We used comprehensive and long-term observations from the Turkey Lakes Watershed Study in central Ontario to estimate water travel times for 12 snowmelt-dominated headwater catchments, three of which were impacted by forest harvesting. Chloride, a commonly used water tracer, was measured in streams, rain, snowfall and as dry atmospheric deposition over a 31 year period. These data were used with a lumped convolution integral approach to estimate mean water travel times. We explored relationships between travel times and catchment characteristics such as catchment area, slope angle, flowpath length, runoff ratio and wetland coverage, as well as the impact of harvesting. Travel time estimates were then used to compare differences in stream water quality between catchments. Our results show that mean travel times can be variable for small geographic areas and are related to catchment characteristics, in particular flowpath length and wetland cover. In addition, forest harvesting appeared to decrease mean travel times. Estimated mean travel times had complex relationships with water quality patterns. Results suggest that biogeochemical processes, particularly those present in wetlands, may have a greater influence on water quality than catchment travel times.     

Runoff modelling at two field slopes: use of in situ measurements of air permeability to characterize spatial variability of saturated hydraulic conductivity

The time required at a field site to obtain a few measurements of saturated hydraulic conductivity (K_s) will allow for many measurements of soil air permeability (k_a). This study investigates if k_a measured in situ (k_{a, in situ}) can be a substitute for measurement of K_s in relation to infiltration and surface runoff modelling. Measurements of k_{a, in situ} were carried out in two small agricultural catchments. A spatial correlation of the log‐transformed values existed having a range of approximately 100 m. A predictive relationship between K_s and k_a measured on 100‐cm³ soil samples in the laboratory was derived for one of the field slopes and showed good agreement with an earlier suggested predictive K_s–k_a relationship. In situ measurements of K_s and k_a suggested that the predictive relationships also could be used at larger scale. The K_s–k_a relationships together with the k_{a, in situ} data were applied in a distributed surface runoff (DSR) model, simulating a high‐intensity rainfall event. The DSR simulation results were highly dependent on whether the geometric average of k_{a, in situ} or kriged values of k_{a, in situ} was used as model input. When increasing the resolution of K_s in the DSR model, a limit of 30–40 m was found for both field slopes. Below this limit, the simulated runoff and hydrograph peaks were independent of resolution scale. If only a few randomly chosen values of K_s were used to represent the spatial variation within the field slope, very large deviations in repeated DSR simulation results were obtained, both with respect to peak height and hydrograph shape. In contrast, when using many predicted K_s values based on a K_s–k_a relationship and measured k_{a, in situ} data, the DSR model generally captured the correct hydrograph shape although simulations were sensitive to the chosen K_s–k_a relationship. As massive measurement efforts normally will be required to obtain a satisfactory representation of the spatial variability in K_s, the use of k_{a, in situ} to assess spatial variability in K_s appears a promising alternative. Copyright © 2004 John Wiley & Sons, Ltd.     

A spatially distributed Clark’s unit hydrograph based hybrid hydrologic model (Distributed-Clark)

ABSTRACT

A hybrid hydrologic model (Distributed-Clark), which is a lumped conceptual and distributed feature model, was developed based on the combined concept of Clark’s unit hydrograph and its spatial decomposition methods, incorporating refined spatially variable flow dynamics to implement hydrological simulation for spatially distributed rainfall–runoff flow. In Distributed-Clark, the Soil Conservation Service (SCS) curve number method is utilized to estimate spatially distributed runoff depth and a set of separated unit hydrographs is used for runoff routing to obtain a direct runoff flow hydrograph. Case studies (four watersheds in the central part of the USA) using spatially distributed (Thiessen polygon-based) rainfall data of storm events were used to evaluate the model performance. Results demonstrate relatively good fit to observed streamflow, with a Nash-Sutcliffe efficiency (E_NS) of 0.84 and coefficient of determination (R²) of 0.86, as well as a better fit in comparison with outputs of spatially averaged rainfall data simulations for two models including HEC-HMS.     

Rainfall–runoff,flood inundation and sensitivity analysis of the 2014 Pakistan flood in the Jhelum and Chenab river basin

ABSTRACT

The major flood of 2014 in the two eastern, transboundary rivers, the Jhelum and Chenab in Punjab, Pakistan, was simulated using the two-dimensional rainfall–runoff model. The simulated hydrograph showed good agreement with the observed discharge at the model outlet and intervening barrages, with a Nash-Sutcliffe efficiency of 0.86 at the basin outlet. Further, simulated flood inundation extent showed good agreement with the MODIS imagery with a fit (%) of 0.87. For some affected areas that experienced short-duration flooding, local housing damage data confirmed the simulated results. Besides the rainfall–runoff and flood inundation modelling, parameter sensitivity analysis was undertaken to identify the influence of various river and floodplain parameters. The analysis showed that the river channel geometric parameters and the roughness coefficients exerted the primary influence over flood extent and peak flow.     

Derivation and verification of empirical catchment response time equations for medium to large catchments in South Africa

Despite uncertainties and errors in measurement, observed peak discharges are the best estimate of the true peak discharge from a catchment. However, in ungauged catchments, the catchment response time is a fundamental input to all methods of estimating peak discharges; hence, errors in estimated catchment response time directly impact on estimated peak discharges. In South Africa, this is particularly the case in ungauged medium to large catchments where practitioners are limited to use empirical methods that were calibrated on small catchments not located in South Africa. The time to peak (T_P), time of concentration (T_C) and lag time (T_L) are internationally the most frequently used catchment response time parameters and are normally estimated using either hydraulic or empirical methods. Almost 95% of all the time parameter estimation methods developed internationally are empirically based. This paper presents the derivation and verification of empirical T_P equations in a pilot scale study using 74 catchments located in four climatologically different regions of South Africa, with catchment areas ranging from 20 km² to 35 000 km². The objective is to develop unique relationships between observed T_P values and key climatological and geomorphological catchment predictor variables in order to estimate catchment T_P values at ungauged catchments. The results show that the derived empirical T_P equation(s) meet the requirement of consistency and ease of application. Independent verification tests confirmed the consistency, while the statistically significant independent predictor variables included in the regressions provide a good estimation of catchment response times and are also easy to determine by practitioners when required for future applications in ungauged catchments. It is recommended that the methodology used in this study should be expanded to other catchments to enable the development of a regional approach to improve estimation of time parameters on a national‐scale. However, such a national‐scale application would not only increase the confidence in using the suggested methodology and equation(s) in South Africa, but also highlights that a similar approach could be adopted internationally. Copyright © 2016 John Wiley & Sons, Ltd.     

Estimate of influence of U-Th-K radiogenic heat on cooling process of granitic melt and its geological implications

The U-Th-~(40)K concentrations of granite are on 1―2 orders of magnitude greater than those of basal- tic-ultrabasic rocks. Radiogenic heat of a granitic melt has significant influence on the cool- ing-crystallization period of the melt. In this paper we derived a formula to calculate prolongation period (tA) of cooling-crystallization of a granitic melt caused by radiogenic heat. Calculation using this for- mula and radioactive element concentrations (U=5.31×10-6; Th=23.1×10-6; K=4.55%) for the biotite adamellite of the Jinjiling batholith shows that the tA of the adamellite is 1.4 times of the cooling period of the granitic melt without considering radiogenic heat from the initial temperature (Tm=960℃) to crystallization temperature (Tc=600℃) of the melt. It has been demonstrated that the radiogenic heat produced in a granitic melt is a key factor influencing the cooling-crystallization process of the granitic melt, and is likely one of the reasons for inconsistence between emplacement ages and crystallization ages of many Meso-Cenozoic granitoids.