1. UNIT – III FLOODS Types of floods Following are the various types of floods: 1.Probable Maximum Flood (PMF):This is the flood resulting from the most sever combination of critical meteorological and hydrological conditions that rare reasonably possible in the region. The PMF is computed by using the Probable Maximum Storm (PMS) which is an estimate of the physical upper limit to storm rainfall over the catchment. This is obtained from the studies of all the storms that have occurred over the region and maximizing them for the most critical atmospheric conditions.

2. 2. Standard Project Flood (SPF): This is the flood resulting from the most sever combination of meteorological and hydrological conditions considered reasonably characteristic of the region. The SPF is computed from the Standard Project Storm (SPS) over the watershed considered and may be taken as the largest storm observed in the region of the watershed. It is not maximized for the most critical atmospheric conditions but it may be transposed from an adjacent region to the watershed under consideration. 3. Flood of a specific return period: This flood is estimated by frequency analysis of the annual flood values of adequate length. Sometimes when the flood data is inadequate, frequency analysis recorded storm data is made and the storm of a particular frequency applied to the unit hydrograph to derive the design flood. This flood usually has a return period greater than the storm.

3. Various methods of flood estimation 1.Rational method 2.Empirical method 3.Flood frequency studies 4.Unit hydrograph technique

4. 1.Rational method 1. Consider a rainfall of uniform intensity and very long duration occurring over the basin. The runoff rate gradually increase from zero to constant value. 2. The runoff increase as more and more flow from remote areas of the catchment reach the outlet. 3. The time taken for drop of water from the farthest point of catchment to reach the outlet known as time of concentration. The peak value of flood is given by, Q = C A i Where C = coefficient of runoff A= area of catchment i = intensity of rainfall

5. 2. Empirical method Some of the empirical formulae for estimating flood are given below, most of these are in the form: Q = CA n Where, Q= flood discharge A= catchment area C= flood coefficient n= flood index

6. Dicken’s formula Q=CA 3/4 Where, Q= flood discharge in cumecs A= catchment area of basin in sq.m C= flood coefficient constant C depends upon the catchment and may be obtained from table- RegionC Northern India11.4 Central India13.9- 19.5 Western India22.2 - 25

7. Ryve’s formula Q=CA 2/3 Where Q= flood discharge in cumec A= catchment area of basin in sq.m C= flood coefficient constant C depends upon the catchment and may be obtained from table- Location of catchmentC Area within 24 km from the coast 6.75 Area within 24 km to 161km from the coast 8.45 Limited area near hills10.1

8. Inglis formula It is applicable for catchment of former Bombay Presidency 123 A Q= √A+ 10.4 Fanning Formula For American catchments Q=CA 2/3 Where average value of C may be taken equal to 2.54

9. Flood Frequency Studies Hydrological processes such as floods are exceedingly complex natural events. They are resultants of a number of component parameters (e.g. floods depend upon the characteristics of the catchment, rainfall and antecedent conditions, each one of these factors in turn depend upon a host constituent parameters) are therefore very difficult to model analytically. An alternate approach to the prediction of flood flows (and other hydrologic processes) is the statistical method of frequency analysis. The values of the annual maximum flood from a given catchment area for large number of successive years constitute a hydrologic data series called the annual series. The data in the series are then arranged in descending order of magnitude and the probability P of each event being equaled to or exceeded (plotting position) is calculated by the plotting position formula Hydrological processes such as floods are exceedingly complex natural events. They are resultants of a number of component parameters (e.g. floods depend upon the characteristics of the catchment, rainfall and antecedent conditions, each one of these factors in turn depend upon a host constituent parameters) are therefore very difficult to model analytically. An alternate approach to the prediction of flood flows (and other hydrologic processes) is the statistical method of frequency analysis. The values of the annual maximum flood from a given catchment area for large number of successive years constitute a hydrologic data series called the annual series. The data in the series are then arranged in descending order of magnitude and the probability P of each event being equaled to or exceeded (plotting position) is calculated by the plotting position formula P = m (N +1) P = m (N +1) where m = order number of the event and N = total number of events in the data series. The recurrence interval or return period or frequency T is given by where m = order number of the event and N = total number of events in the data series. The recurrence interval or return period or frequency T is given by T = 1/ P T = 1/ P For small return periods or where limited extrapolation is required, a simple best fitting curve through plotted points can be used as the probability distribution. A logarithmic scale for T is often advantageous. However, when larger extrapolations of T are involved, theoretical probability distributions have to be used. The general equation of hydrologic frequency analysis For small return periods or where limited extrapolation is required, a simple best fitting curve through plotted points can be used as the probability distribution. A logarithmic scale for T is often advantageous. However, when larger extrapolations of T are involved, theoretical probability distributions have to be used. The general equation of hydrologic frequency analysis

10. Some of the commonly used frequency distribution functions for the prediction of extreme flood values are: (i) Gumbel’s extreme value distribution, (ii) log-Pearson type III distribution, and (iii) log normal distribution. In frequency analysis of floods, the usual problem is to predict extreme flood events. For this, specific frequency distribution functions are assumed and the required statistical parameters are calculated from the available data. Using these parameters, the flood magnitude for a specific return period is estimated. The results of the frequency analysis depend upon the length of data. The minimum number of years of record required to obtain satisfactory estimates depends upon the variability of data and hence on the physical and climatological characteristics of the basin. Generally a minimum of 30 years of data is considered as essential. Frequency analysis should not be adopted if the length of records is less than 10 years. Flood frequency studies are most reliable in climates that are uniform from year to year. In such cases a relatively short record gives a reliable picture of the frequency distribution.

14. Flood routing 1. Flood routing is the technique of determining the flood hydrograph at a section of a river by utilizing the data of flood flow at one or more upstream sections. 2. Flood routing is used in (i) flood forecasting (ii) flood protection (iii) reservoir design (iv) design of spillway and outlet structures. 3. Food routing types: (a)reservoir routing (b) channel routing.

15. 4. A variety of routing methods are available and they can be grouped into (1) hydrologic routing, and (2) hydraulic routing. 5.Hydrologic routing methods employ essentially the equation of continuity, on the other hand hydraulic methods use continuity equation along with the equation of motion of unsteady flow (St. Venant equations) hence better than hydrologic methods.

16. Basic Equation for hydrologic routing The passage of a flood hydrograph through a reservoir or a channel reach is a gradually varied unsteady flow. If we consider some hydrologic system with input I(t), output O(t), and storage S(t), then the equation of continuity in hydrologic routing methods is the following: I −O =ds/dt If the inflow hydrograph, I(t) is known, this equation cannot be solved directly to obtain the outflow hydrograph, O(t), because both O and S are unknown. A second relation, the storage function is needed to relate S, I, and Q. The particular form of the storage equation depends on the system; a reservoir or a river reach.

17. Level Pool Reservoir Routing The effect of reservoir storage is to redistribute the hydrograph by shifting the centroid of the inflow hydrograph to the position of that of the outflow hydrograph in time. When a reservoir has a horizontal water surface elevation, the storage function is a function of its water surface elevation or depth in the pool. The outflow is also a function of the water surface elevation, or head on the outlet works. By combining these two functions, S = f(O) we get a single valued storage function (for rivers it becomes a loop: not single valued). For such reservoirs, the peak outflow occurs when the outflow hydrograph intersects the inflow hydrograph. Because maximum storage occurs when I- O = ds/dt=0

18. As the horizontal water surface is assumed in the reservoir, the reservoir storage routing is known as Level Pool Routing. The outflow from a reservoir (over a spillway) is a function of the reservoir elevation only. The storage in the reservoir is also a function of the reservoir elevation. Further due to passage of the flood wave through the reservoir the water level in the reservoir changes with time h = h(t) and hence the storage and discharge change with time. It is required to find the variations of S, h, and O with time for given inflow with time. In a small time interval t the difference between the total inflow and outflow in a reach is equal to the change in storage (S) in that reach I t −O t = S

19. Channel Routing In very long channels the entire flood wave also travels a considerable distance resulting in a time redistribution and time of translation as well. Thus, in a river, the redistribution due to storage effects modifies the shape, while the translation changes its position in time. In the reservoir the storage was a unique function of the outflow discharge S = f(O). However in channel the storage is a function of both outflow and inflow discharges and hence a different routing method is needed. The water surface in a channel reach is not only parallel to the channel bottom but also varies with time. The total volume in storage for a channel reach having a flood wave can be considered as prism storage + wedge storage.

21. Prism storage is the volume that would exist if uniform flow occurred at the downstream depth i.e. the volume formed by an imaginary plane parallel to the channel bottom drawn at the outflow section water surface. Wedge storage is the wedge like volume formed between the actual water surface profile and the top surface of the prism storage. Assuming that the cross sectional area of the flood flow section is directly proportional to the discharge at the section, the volume of prism storage is equal to KO where K is a proportionality coefficient, and the volume of the wedge storage is equal to KX(I - O), where X is a weighing factor having the range 0 < X < 0.5. The total storage is therefore the sum of two components S = K(XI + (1− X )O