2.2.1 Statistical methods (Frequency Analysis)

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1 2.' LITERATURE SURVEY 2.1 General Flood is considered as unusually high stage of the river. It is perhaps better described as that stage at which the stream channel gets filled and above which it overflows its bank. An annual peakflow is known as the largest instantaneous flow in any given year. Flow adopted for the design purposes is defined as desiga flow. It may be a corresponding to some desired frequency of occurrence depending upon the standard of security that should be provided against failure of a structure. Several methods are currently available for the estimation of peakflow rate, but many of these have different kind of limitations in practice according to their nature. In Engineering, the most widely used method for estimating a peak flood of a certain probability is the rational formula.. But it is not clear whether She imit hydrograph or whether any variations of regional flood frequency occupies second place (Linsley, 1986). Other than those methods the Curve Number method is also common in practice. Statistical methods are applicable where there are long period of historical flows. Regional flood transposition is a method by which the estimation of peak floods and design floods can be made in ungauged watersheds by extrapolation. Peakflow of ungauged watersheds estimated different ways. When flow data of an adjacent basin, or of a similar basin or of the same region are available then such flow data can be used to estimate the peakflow. In the absence of flow data, mere are methods to use rainfall as an input to obtain flow records. This also could be done either statistically or using various types of rainfall - runoff modess. Textbooks and journals in the field of Hydrology carry a plenty of publications presenting different kind of methods for peakflow estimation. However literature indicating the applicability of such methods to Sri Lankaai conditions are scarce. 2.2 Methods of Peakflow Estimation Statistical methods (Frequency Analysis) This is a method'to predict the future probability of occurrences by using past records of events. If stream gauging records of sufficient length are available, an analysis of the historic flood frequency is a reliable tool for estimating likelihood of future floods. But in most cases however, records extend over short lengths of 2-1

2 time and contain relatively few events. The analysis with such data is not representative of long term behaviour. Studies by Central Water Commission, India show that 33 to 40 years of records is necessary to predict a 100 year flood and 80 to 90 years of records are needed to predict a 250 years flood (Sharma & Sharma, 1977). Various theoretical and empirical distributions have been proposed as beir.g generally applicable to the annual series. The more useful amongst those which have been proposed include the following. i. The two parameter Log-normal distribution ii. iii. The Gumbel or Extreme value type I distribution and Log-gumble or Extreme value Type n distribution The Log-pearson type HI distribution The first two distributions involve only two parameters, and special graph papers have been derived for them, so that any distribution of that type plots as a straight line on the graph paper for that distribution. The Gumbel distribution is a theoretical asymptotic distribution of extreme values in a given interval of a process with an exponential distribution. The loggumbel distribution was found to give the best fit to the relatively short stream flow data available. The log-pearson type m distribution has been recommended by the US Water Resources Council as the basic method for flood frequency analysis. This distribution has been found to provide a good fit for many annual flood series. The two-parameter log-normal distribution is a special case of the log-pearson type DI distribution (TEA, 1977) Regional Flood Frequency Analysis The regional flood frequency analysis is adopted for the catchments where streamflow data are not available or the length of records is too short. The regional flood frequency analysis makes use of the available data of streams in statistical homogeneous regions. In such a region, the point data analyses are averaged to represent the frequency characteristics of the entire region. In the Analysis, mean annual flood which corresponds to a recurrence interval of 2.33 years is used for developing basic dimensionless frequency curve. Also tile variation of mean flood, Q m with drainage area and variation Qr/Qm w&n recurrence interval T are plotted. The combination of mean annual flood with the 2-2

3 basic frequency curve which is in terms of the mean annual flood give a frequency for any section. When the regional flood frequency curves are employed for assessing flood of an ungauged catchment, a correlation is established graphically by plotting mean annual floods against respective catchment areas of all gauged stations in the area of logarithmic paper. This relation is then used to obtain the mean annual flood for ungauged catchment. The flood for ungauged catchment for a given frequency is determined by computing the corresponding flood ratio from the regional frequency curve for region and multiplying it by the mean annual flood of the ungauged catchment (Sharma and Sharma 1976, WMO1989) Envelop curves Envelop curves are based on the theory that ths maximum flood per hectare experienced in one basin is quite likely to be experienced in a nearby bask in the same region and possessing similar characteristics. In this method the available flood peak data from a large number of catchments which do not significantly differ from each other in terms of meteorological and topographical characteristics are collected. The data are then plotted on a log-log paper as flood peak Vs catchment area. This would result in a plot in which the data would be scattered. If an enveloping curve mat would encompasses all the plotted data is drawn, it can be used to obtain maximum peak discharges for any given area. These curves are useful in getting quick but rough estimations of peak values (Subramanya 1984). Sharma and Sharma (1976), cites two different kinds of envelope curves developed by (1) Justin, Creager and Hinds and (2) Bird and Mailluraith. Both relate the discharge fo the drainage area using exponents obtained empirically. The first one is derived for basins with comparable drainage characteristics, and the second one is called the worid enveloping flood Flood Transposition and other Empirical formulae In regions having same climatic and topographical characteristics, if the available flood data are meagre, the flood transposition can be used to generate a series of annual maximum peakflows using regional gauged catchment The advantage of using Flood Transposition equation is that the computation of design flows could be done by directly using flow records. In other methods rainfall and other parameters are used to estimate flow records. Also most rainfall - runoff models require time consuming field data collection. Most of the flood transposition formulae assume that the area is the key factor influencing the peakflows. Hence the relationship is of the type of Q = CA n. Where n is aa exponent. 2-3

4 There are vast numbers of formulae of this kind proposed for various parts of the world; Several types of empirical relationships have been established based on the catchment properties mainly the basin area but in some cases rainfall characteristics, basin characteristics and flood frequency. Since these formulae refer invariably to particular physical and climatic conditions these are safely applicable to the areas or regions where the same were developed. A summary of various empirical formulae in literature is as follows. The most widely used formulae in South India are the Ryve's formula and the Dicken's formula. i. Ryve's Formulae, Q = CA 273 and Dicken's formula, Q = CA 3/4, when Q is the maximum flood discharge in cumecs, A is the catchment area in km2 and C is a coefficient varying from place to place depending upon the rainfall pattern of the zones in which the catchment is situated (Murthi, 1977) ii. Inglis Formula (Murthi 1977) Q = 123A / (A ) 5, Q in cumecs and A in km 2 ii. Madras Formulae (Sharma and Sharma, 1976) Q = 2000A ( 8 9 (1/I5 > 108 A), Q in cumecs and A in km 2 v. Hydrabad Formulae (Murthi, 1977) Q = ca ( ( 1 / 1 4 ), o 8 A ', Q in cumecs and A in km 2 Value of C taken from 48 to 60. This formula has been developed mainly for catchments of Deccan River in India. vi. Farmings Formula (Murthi, 1977) Q = CA 3 / 6, Q in cumecs and C in km 2 Where value of C is taken as 2.54 There are some other formulae which are involving not only basin area but also the other basin characteristics. The Rational formula, discussed earlier, is one such formula dealing with intensity of rainfall, slope of the catchment and land use etc. Two other formulae found in literature involving some other catchment characteristics with drainage area are as follows, the first one is involved with the length of the catchment and the next is related to the altitude of the catchment and percentage area of the reservoirs. vi. Q = CA / L ( 2 / 3 ) (Sharma and Sharma, 1976) Where C: Constant, L: Average length of the area and A: Drainage area.vii. Q = ( h ) A / r 1 7 (Subramanya, 1984) Where h: median altitude of the basin in ft above the outlet, r: percentage of lake, pond and reservoir area 2-4

5 2.2/5 Unit Hydrograph Methods The unit hydrograph is a simple linear model, said to be first proposed by Sharmen in 1932, which can be used to derive the hydrograph resulting from any amount of excess rainfall. This is a hypothetical hydrograph of a basin due to a flood of unit surface runoff in a given time. Three types of different approaches for peakflow estimation using unit hydrograph principles are the Snyders unit hydrograph, SCS dimensionless hydrographs, and instantaneous hydrograph. Among the different key parameters used in hydrograph analysis the time of concentration is considered as the most important one. Time of Concentration is generally estimated by means of empirical formulae. One of the most common formulae often used in the world was derived by Kirpich based on data from rural agricultural drainage basins (Maidment, 1993). Ponrajah recommended the use of velocity estimates for determining the time of concentration for the Sri Lankan catchments (ID, 1984). In theory, the principle of the unit hydrograph is applicable to basin of any size. However, in practice, to meet the basic assumptions it is essential to use storms uniformly distributed over the basin and producing rainfall excess (direct runoff) at a uniform rate. Such storms rarely occur on large areas. The method is said to be less accurate for small areas below 25 square kilometres (Sharma and Sharma, 1976) Snyder's Synthetic Unit Hydrograph Synthetic Unit hydrograph is a hydrograph developed on the basis of estimation of coefficients expressing various physical features of a catchment. Synthetic unit hydrograph is developed based on known physical characteristics of the basin, where adequate rainfall data are lacking. Snyder in 1938 has found various relationships between catchment parameters to derive a standard hydrograph (Sharma and Sharma, 1976) SCS Dimensionless Hydrograph The dimensionless unit hydrograph used by soil conservation service (1972) was developed by Mackus (1957). It was derived from a large number of natural unit hydrographs from drainage basins varying widely in size and geographical locations. The shape of this dimensionless unit hydrograph predetermines the time distribution of the runoff; time expressed in units of time to peak, and runoff rates are expressed in units of peak runoff rate (Ritzema, 1994). 2-5

6 Instantaneous Unit Hydrograph The instantaneous unit hydrograph (IUH) is a runoff hydrograph of resulting from instantaneous application of rainfall excess' volume of 1 cm spread uniformly in the drainage area and is expressed u (0, t) or U (t). The merit of fuh over a unit hydrograph is that the former is independent of duration of rainfall excess, thereby resulting in elimination of one variable in the hydrograph analysis (Sharma and Sharma, 1976) * Curve Number Method (SCS Method) For a drainage basin where no runoff has been measured, the curve number method can be used to estimate the depth of direct runoff from the rainfall depth, given an index describing runoff response characteristics. Runoff (Q) computations are carried out by using SCS formulae and a curve number. Curve number depends on the antecedent wetness of the watershed, soil, land cover and the hydrologic conditions. The antecedent moisture condition refers to three classes of antecedent moisture conditions (AMC) namely dry, average, and wet Hydrologic conditions are related to whether vegetation is dense and in good condition, and also whether soil is rich in organic matter and has a well aggregated structure. The hydrologic condition identifies the watershed capacity to result in high infiltration and low runoff. The Curve Number method was originally developed by the Soil Conservation Service in 1964 for conditions prevailing in the United States. Since then it has been adopted to conditions in other parts of the world. Although some regional research centres have developed additional criteria, the basic concept is still widely used all over the world Rational Formula The relationship between rainfall and peak runoff has been represented by many empirical or semi-empirical formulae. The Rational formula is one such formula, which is considered as one of the most common hydrologic methods for computing peak discharge. Although this formula is based on a number of assumptions, which cannot be readily satisfied under actual circumstances, it is very popular because of its simplicity. Generally the formula can be written as Q = RCIA. The parameter relates the peak flow to the Rainfall Intensity, Return period, Runoff coefficient of the watershed and the watershed area (JEA, 1977). The coefficient of runoff has been related to the catchment slope and coefficient of runoff of Sri Lankan catchments are in Table 2.1 (Ponrajah, 1984). 2-6

7 Table 2.1: Catchment Slopes and Corresponding Runoff Coefficients Rational Method in Catchment Slope Runoff coefficient 0to to4 0.4 = >4 0.5 Time of concentration for small watersheds and irrigation works are given by Ponrajah (1984). In his work he has computed time of concentration as a factor of travel length, average velocity and inlet time. Table 2.2 shows some typical values (ID, 1984). Table 2.2: Average Gradient of Stream and Corresponding Average Velocity in Rational Method Average Gradient of Stream Average Velocity (ft/s) Otol 1.5 lto to to >6 5.0 Rational formula is said to be a convenient and a reliable ferula for small watersheds up to 1000 acres. Rational formula gives too high estimates of peak flow values for large watersheds (Batuwitage et al., 1985) Multiple Regression Methods Multiple regression methods are also used to estimate peakflow from ungauged watersheds. In this method the key factors influencing peakflows are combined to an equation to find the regression coefficients. If a lengthy data set of annual peak flows are available then the annual average peakflow or return period flow for specified return period is regressed to obtain an equation. Usually these are done for regions and the regression equations are of the following type; Q = c Xi a b C X 2 X 3. Q could be either the mean annul peak or a return period peak and Xi* etc are factors controlling the flood peak. All such formulae include basin area as a factor and most contain some index of rainfall intensity and frequency, in addition to differing measures of several morphometric characteristics. Chorley (1985) cited following examples for regression equations. Q * _ A 0.17 TT-0.55 T> 093 o a Aj T P S (Region: Allegheny-Cumberland Plateau)

8 qv^bv-'v 7 2? 4-2^ (Region: Appalachian Plateau) Q =da 0 ' 7 7 R 2 ' 9 2 D 0 ' 8 1 (Region: United Kingdom) Where Q 10 = peak discharge (cusec/acre) for a ten year recurrence interval Q2.33 = peak discharge (cusec) m the mean annual Hood Ai ~ basin area (acres) P = rainfall intensity factor T = topography factor S - rainfall frequency factor t - topography factor A = basin area S = main channel slope (ft/mile) R = mean annual daily maximum rainfall (in) D = drainage density (miles/ square mile) University College, Gaiway (1985) cited a case study done for 57 catchments and computed regressions for the region and also for urban watersheds. (Curare, 1985). Regression equations cited is Qmean - c A 0 ' 94 STEMFEQ 0 ' 28 SI Soil 121 R 103 LAKE" 0 '* 6 URBAN Where A = area in km 2 STKMFQ = stream frequency SI - overland slope Soil = index for Soil/ Geology R ='- average annual rainfall LAKE = i&dex for catchment storage if URBAN is omitted the coefficients vary insignificantly to 0.94, 0.27, 0.15, 1.23, 1.03 aid respectively. Since these multiple regressions are done usually for return period based floods or rnei». annual peak floods this method may sot be &at advantageous to transpose peak floods to obtain return period floods for design purposes. 2-8

9 2.3 Accuracy of Peakflow Estimation Using Different Methods When hydrologists are asked about the accuracy of their estimated flood peaks, the most frequent response is that they lie within 20%. However a few optimists will say that the accuracy is 10% and the pessimists may say 30%. Almost all responses indicate that such errors are "acceptable" (Linsley, 1986). A Study done to determine the applicability of flood estimation methods to Sri Lankan catchments by considering 16 catchments in Sri Lanka, the accuracy of those methods is concluded as follows (Batuwitage et al, 1986). i. The method chosen for the determination of the time of concentration is vital, and has considerable effects on the design flood. ii. Estimated design floods from Snyder's techniques tends to give higher values than those obtained by statistical methods. iii. US Soil Conservation Service method usually gives higher or the highest values for the design floods as the catchment area increases. Even for small catchments generally the estimated floods are considerably higher than the values obtain by statistical methods. This study provides the peak flow estimates from different methods for comparison. A hydrological study of the Colombo Harbour and its watersheds indicated that four of the models used for peak flow estimation show consistency in the case of small watersheds but estimates made using Snyder's Unit Hydrograph Method appear to deviate in case of larger watersheds. Snyder's method, Rational formula, HEC 1 flood model and SCS hydrograph method were the methods used for this study (Wijesekera, 2000). 2.4 Factors affecting Peakfbw The peak flow of a basin is affected by many factors. All these factors are mostly related to one another. There are difficulties in quantifying some of the factors such as vegetation and land use, while in many cases measurement of others such as infiltration rates, rain fall intensities are simply not available. Often only other materials that can be obtained, other than river flow records are those such as slopes, area etc that can be derived from maps. The factors affecting flood peaks can be grouped mainly in two categories as climatic factors and catchment characteristics.

10 2.4.1 Climatic Factors The main effect of climate on peak flow is in rainfall intensity and duration. Rainfall intensity has a direct bearing on runoff because when the infiltration capacity is exceeded all the excess rain flows to the surface watercourses. Since intensity represents rainfall over a particular time, it cannot be considered separately from duration Rainfall Intensity Rainfall intensity influences both the rate and the volume of runoff. An intense storm exceeds the infiltration capacity by a greater margin man a gentle rain, thus the total volume of runoff is greater for the intense storm than a gentle storm even though total precipitation for the two rains is the same. Rainfall intensity is one of the major considerations when calculating peak flow using rational formula and unit hydrograph method. Estimation of rainfall intensity is usually done using rainfall intensity-frequency-duration curves for specified recurrence interval and duration Duration of Rainfall Total runoff from a storm is clearly related to the duration for a given intensity. A storm of short duration may produce lower runoff, whereas a storm of the same intensity but of long duration will result in higher runoff. Uniform - intensity storm causes the hydrograph of stream rise. Such storms may be defined as covering the whole catchment area, over which the depth of rainfall is reasonably constant and delivered at a constant rate. After a certain time, Tc (time of concentration), the rate of runoff becomes constant. The runoff at this point is the peak flow and to obtain the peak for a particular basin the duration of rainfall should not be less than the time of concentration Distribution of Rainfall Rate and volume of runoff are influenced by the distribution of rainfall and its intensity over the watershed. Generally maximum rate and volume of runoff occurs when the entire watershed contributes. However, an intense storm on one portion of the catchment may result in greater runoff than a moderate storm over the entire watershed. Therefore the distribution of rainfall would also influence the peak flow from a watershed. 2-10

11 Direction of Storm Movement The prevailing winds and storm movement usually have a particular seasonal pattern. The direction in which the storm centre moves across a basin with respect to the direction of flow of the drainage system has pronounced effect on the peak flow and the period of surface runoff. A storm moving in the direction of a stream produces higer peaks in a shorter period than a storm moving upstream Catchment Characteristics It is appropriate to consider how various characteristics of the catchment affect the rate and quantity of discharge from it By 'catchment' is meant the whole of the land and water surfaces area contributing to the discharge at a particular stream or river cross section, from which it is clear that every point on a stream channel has a unique catchment of its own, the size of the catchment increasing as the control point moves down stream, reaching its maximum size when the control is at the sea cost. At this point the catchment is called as river basin. The hydrologic behaviour of a catchment depends on certain characteristics of the drainage area. The characteristics are generally related to the physical drainage basin or to the channel. The physical characteristics of a catchment are the drainage area, its shape, slope, drainage density, mean elevation and land use etc Basin Area Larger the size of the basin, the greater the amount of rain it intercepts and higher the peak discharge it results. This rather obvious conclusion has been the basis for a large number of flood formula in general form: Q = CA n Where Q = peak discharge; A = basin area, C = a constant that varies according to the land use or topography of the basin; n = a constant that has a range from 0.2 to 0.9, depending on climate to some extent (Chorley et al, 1969). It should be noted that the effects of other factors are considered insignificant in these types of equations. 2-11

12 Basin Shape The shape of the catchment influences the runoff pattern of the stream. Thus for a semicircular catchment, the hydrograph is high and narrow, and for a long narrow rectangular catchment it is broad and shallow. Long narrow watersheds are likely to have lower runoff rates than compact watersheds of the same size. Because the runoff from the former does not concentrate as quickly as it does from the compact areas and long watersheds are less likely to be covered uniformly by intense storm. This is a feature which is difficult to express numerically. How ever a number of shape indices are cited in literature. The best known being the form factor and compactness coefficient. The former is the ratio of average width to axial length of the basin, while the latter demonstrates the compactness of the basin. (a) Form Factor The form factor is an index expressing the relation of average width to the axial length of the basin, to measure shape characteristics. Axial length is the length from outlet to the remotest point in the basin and the average width is the average width obtained perpendicular to the axial length. (Sharma and Sharma, 1977) (b) Compactness coefficient Compactness coefficient is the ratio of perimeter of the catchment to the circumference of a circle whose area is equal to that of the catchment. This coefficient is independent of the size of the catchment and is dependent only on the shape (Sharma and Sharma, 1977) Basin Elevation The altitudinal extent of the basin above the gauging station exercise direct and indirect control over the magnitude of the flood peak. With the slope and several additional factors, it determines the proportion of runoff, and indirectly it influences a number of other important controls, such as precipitation, temperature, vegetation, and soil type. Though it is difficult to compute a single term which gives a meaningful measure of basin elevation, several studies have shown it has no significant relation to the size of the flood peak (Chorley et al, 1973) Drainage Density The several characteristics of the flood hydrograph hinge on the efficiency of the drainage system of a basin. A quick rise to a high peak is the mark of a well 2-12

13 developed net work of short steep streams. Conversely, a minimal response to intense rain usually reflects an incipient channel system. Linear aspects of the channel system are expressed in terms of stream order, bifurcation ratio and stream length, other than the longest length of the stream channel, none of these measures, by mem selves have been shown to exercise control over the flood peak. On the other hand their inclusion with other factors has reduced the error of estimate of peak flow, and this also applies to areal relationships and channel gradients (Chorley et al, 1973). According to the literature cited, for a study of England floods ninety-three slope factors were computed and main channel slope was found as the most significant variable, hi this study peak flow showed no relation to drainage density, once channel slope has been taken in to account. Drainage density is expressed as total length of all streams, perennial and intermittent, per unit area of the basin. It is an index of the areal channel development in the catchment (Sharma and Sharma; 1977) Stream Slope Slope is an obvious control of peak discharge, but again it is a factor which is difficult to interpret meaningfully. Generally it is taken as total fall between the points divided by the stream length. Watersheds having extensive fiat areas or depressed areas without surface outlets have lower runoff than areas with steep, well-defined drainage patterns. In short and steep slopes, discharge is usually rapid. Runoff from long slopes is generally slower but lasts longer after the rainfall ceases. The factor slope is used in different formula for peak flow estimation. In rational formula Irrigation Department guidelines recommended to select the coefficient 'C according to the catchment slope (ID, 1988). Slope is a factor determining time of concentration in Kirpich equation and Bransby William equation. There are five classes of slopes introduced to determine Curve Number in SCS method for peak flow estimation Vegetation and Land use Vegetation and forests increase the infiltration and storage capacities of the soils, they cause considerable retardant to overland flow. Thus the vegetal cover reduces the peak flow..this effect is usually very pronounced in small catchments of area less man 150km 2. Further, the effect of the vegetal cover is prominent in small storms (Chorely et al, 1969). 2-13

14 This is a factor for selecting the Curve Number in the SCS method of peak flow estimation. In some instances the land use cover is employed as a factor determining the coefficient of runoff in rational formula (IE A. 1977). 2-14