T
480 504
600 624
Rainfall DP AS GW
Fig. 11.8 Analysis of contributions to total Stream discharge of different sources in the Haute Menthue catchment using a threecomponent endmember mixing analysis (after Iorgulescu et al., 2005, with kind permission of John Wiley & Sons). DP, direct precipitation; AS, soil waters; GW, groundwater.
Fig. 11.9 Changing contributions of different sources of stream discharge in the Haute Menthue catchment with changing catchment storage (after lorgulescu et al., 2005, with kind permission of John Wiley & Sons). DP, direct precipitation; AS, soil waters; GW, groundwater.
Fig. 11.9 Changing contributions of different sources of stream discharge in the Haute Menthue catchment with changing catchment storage (after lorgulescu et al., 2005, with kind permission of John Wiley & Sons). DP, direct precipitation; AS, soil waters; GW, groundwater.
concentrations measured for each source also show some variability. Such variability should be expected to result in some uncertainty in the calculated proportions for each component. A number of different methods are available for assessing such uncertainty (see e.g. Joerin et al., 2002).
In some catchments, concentrations may be available for many different chemical constituents in waters from different sources. One way of trying to distinguish end members in this case is to use principal components analysis to determine linear combinations of the different concentration observations that provide separation between the end members. Burns et al. (2001), for example, used the first two principal components in an analysis of seven different chemical characteristics to allow a threecomponent separation of runoff sources in the Panola catchment, Georgia (in this case, hillslope runoff water, riparian groundwater and runoff from a bare granite outcrop in the catchment, Fig. 11.10).
11.4 Flowduration curves
For many problems in water engineering, the hydrologist is asked for the frequency of occurrence of specific river flows or for the length of time for which particular river flows are expected to be exceeded. Thus frequency analysis forms one of the important skills required of a hydrologist. Estimates of the frequencies of floods of a particular magnitude are important in assessing flood risk. Estimates of the frequencies of low flows are important in assessing reservoir yields and the potential for low head hydropower schemes in rivers. In attempting to provide any answer to the questions of frequency, good reliable hydrological records are essential, and these must if possible extend beyond the expected life of the engineering scheme being considered.
From the basic assemblage of river flow data comprising the daily mean discharges and the instantaneous peaks, analysis of the daily mean flows will be considered first. Taking the n years of flow records from a river gauging station, there are 365n + leap year days of daily mean discharges. The frequencies of occurrence in selected discharge classes (groups) are compiled, starting with the highest values. The cumulative frequencies converted into percentages of the total number of days are then the basis for the flowduration curve, which gives the percentage of time during which any selected
I 70
I 70
110 90
110 90
b) Hillslope runoff 
~ Hillslope runoff Stream runoff rate  
T 
110 90 110 90 Fig. 11.10 Stream discharge and proportions provided from different runoff sources (hillslope runoff, runoff from a bare granite outcrop and riparian groundwater) in the Panola catchment, Georgia (after Burns etal., 2001, with kind permission of John Wiley & Sons). Fig. 11.10 Stream discharge and proportions provided from different runoff sources (hillslope runoff, runoff from a bare granite outcrop and riparian groundwater) in the Panola catchment, Georgia (after Burns etal., 2001, with kind permission of John Wiley & Sons). discharge may be equalled or exceeded. An example is demonstrated in Table 11.4, in which the daily mean discharges for 4 years for the River Thames at Teddington Weir are analysed. The flowduration curve plotted on natural scales is seen in Fig. 11.11a. The area under the curve is a measure of the total volume of water that has flowed past the gauging station in the total time considered. For the reliable assessment of water supply, the flowduration curves for the wettest and driest years of the record should be derived and plotted. The representation of the flowduration curve is improved by plotting the cumulative discharge frequencies on logprobability paper (Fig. 11.11b). (The abscissa scale is based on the normal probability distribution; if the logarithms of the daily mean discharges were normally distributed, they would plot as a straight line on the logprobability paper.) From the plot (Fig. 11.11b), it can be readily seen e.g. that for 2 per cent of the 4year period, flows exceeded 290 m3s1. At the other extreme, flows of less than 12 m3 s1 occurred for the same proportion of the time. Alternatively it can be stated that for 96 per cent of that 4year period, the flow in the River
Thames at Teddington is between 12 and 290 m3 s1. The 50 per cent time point provides the median value (45 m3 s1). The shape of the flowduration curve gives a good indication of a catchment's characteristic response to its average rainfall history. An initially steeply sloped curve results from a very variable discharge, usually from small catchments with little storage where the stream flow directly reflects the rainfall pattern. Flowduration curves that have a very flat slope indicate little variation in flow regime, the resultant of the damping effects of large storages. Groundwater storages are provided naturally by extensive chalk or limestone aquifers, and large surface lakes or reservoirs may act as runoff regulators either naturally or controlled by man. Examples of some different flowduration curves are given in Fig. 11.12. Hydrographs for these same sites can be seen in Fig. 11.1. The comparisons are simplified by plotting the logarithms of the daily mean discharges as percentages of the overall daily mean discharge. The Cumbria Eden drains the Eastern Lake district and northern Pennines, whereas the catchment of the Mimram, a tributary of the Lee is nearly all chalk. The comparison of flowduration curves from different catchments can also be used to extend knowledge of the flow characteristics of a drainage area that has a very limited short record. At least 1 or 2 years of records are required overlapping with those of a longterm wellestablished gauging station on a nearby river, whose flowduration curve for the whole length of its record may be taken to represent longterm flow conditions. For satisfactory results, the two catchments should be in the same hydrological region and should experience similar meteorological conditions. JanDec DecMar JunSep JanDec DecMar JunSep % of time flow exceeded Fig. 11.12 Seasonal flowduration curves for: (a) Eden at Sheepmount (076007); and (b) the Mimram at Panshanger Park (038003). (Reproduced from the National River Flow Archive, Centre for Ecology and Hydrology. Copyright NERC CEH.) % of time flow exceeded Fig. 11.12 Seasonal flowduration curves for: (a) Eden at Sheepmount (076007); and (b) the Mimram at Panshanger Park (038003). (Reproduced from the National River Flow Archive, Centre for Ecology and Hydrology. Copyright NERC CEH.) The method for supplementing the shortterm record is to construct its longterm flowduration curve by relating the overlapping shortperiod flowduration curves of both catchments, as shown in Fig. 11.13. The available data are plotted and flowduration curves (in full lines) are drawn in Fig. 11.13a and b. Sa and Sy are flowduration curves for the short overlapping records; La is the flowduration curve for the longterm neighbouring record. Selected percentage discharge values from the two shortperiod flowduration curves are plotted in Fig. 11.13c, and a straightline relationship drawn. Time percentage discharge values for La are converted to corresponding percentage values for Ly via the Sa and Sy relation. The derived longterm duration curve for the shortperiod station, Ly, is shown by a broken line in Fig. 11.13. By these means, the variation in the flow characteristics embodied in the longterm flowduration curve has been translated to the shortperiod station. Flowduration curves from monthly mean and annual mean discharges can also be derived, but their usefulness is much less than those constructed from daily mean (a) Longterm station (b) Shortperiod station 5 102040 50 60 80 90 95 % time (b) Shortperiod station \ Derived Lh 5 102040 50 60 80 90 95 % time (c) Correlation of Sa and Sh La5% \ Derived Lh 510 2040 50 60 80 90 95 % time (c) Correlation of Sa and Sh La5%

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