Contents preface (VII) introduction 1—37

Data and computations for flow-duration curve (Example 2.6)

Daily mean	Number of days the flow in the	Total of	Cumul-	Pp =
discharge	stream belonged to the class	cols. 2, 3,	ative		m	× 100
	(N + 1)
(m^3/s)	interval				4, and 5		total, m			(%)
	1995	1996	1997	1998
1	2	3	4	5	6		7			8
150-125	0	1	4	2	7		7			0.48
124.9-100	2	5	8	4	19		26			1.78
99.9-75	20	52	40	48	160		186			12.72
74.9-50	95	90	100	98	383	569			38.92
49.9-40	140	125	117	124	506	1075			73.53
39.9-30	71	75	65	50	261	1336			91.38
29.9-20	15	10	20	21	66	1402			95.90
19.9-10	15	8	10	18	51	1453			99.38
9.9-5	7	0	1	0	8	1461			99.93
Total	365	366	365	365	N = 1461

68 IRRIGATION AND WATER RESOURCES ENGINEERING
Solution: Column 6 of the Table shows the total number of days in a period of 4 years for which the discharge in that class (Col. 1) was flowing in the stream. Column 7 gives the cumulative total of the values of column 6. The probability of flow in the class interval being equalled or exceeded is obtained from Eq. (2.20) and tabulated in column 8. The smallest value of discharge in a class (Col. 1) is plotted against P_p (col. 8) as shown in Fig. 2.19. From this figure, one can obtain the desired value of 80% dependable flow as 37 m³/s.
2.7. HYDROGRAPHS
Consider a concentrated storm producing a short-duration and reasonably uniform rainfall of duration t_r over a watershed. Part of this rainfall is retained on the land surface as detention storage. Yet another part of the rainfall infiltrates into the soil. The remaining part of the rainfall is termed rainfall excess (or effective rainfall) that is neither retained on the land surface nor infiltrated into the soil. This effective rainfall reaches the watershed outlet after flowing over the watershed surface. The flow over the watershed surface builds up some storage both in the overland and channel flow phases. This storage gradually depletes when the rainfall has ceased. There is, thus, a time lag between the occurrence of rainfall over a watershed and the time when the rainfall excess reaches the gauging station at the watershed outlet in the form of direct runoff. The runoff measured at the gauging station would typically vary with time as shown by the curve AMCE in the graph (known as hydrograph) of Fig. 2.20. The hydrograph is, therefore, the response of a given catchment (or watershed) to a rainfall input and can be regarded as an integral expression of the physiographic and climatic characteristics of the region that decide the rainfall-runoff relationship. It comprises all three phases of runoff, viz., surface runoff, interflow and base flow. Therefore, two different storms over the same watershed would, invariably, produce hydrographs of different shapes (i.e., peak rate of discharge, time base etc.) Likewise, identical storms over different watersheds would also produce different hydrographs.

Peak	M	N days
		Crest segment
		Point of inflection
Rising limb		Recession limb
Discharge		T
		D
A		C	E
	^tPk
	B

Time in days

Fig. 2.20 Base flow separation

The inter-relationship among rainfall, watershed and climatic characteristics is, generally, very complex and so is the shape of the resulting hydrograph (having kinks, multiple peaks etc.) much different from the simple single-peaked hydrograph of Fig. 2.20.

HYDROLOGY

69

A single-peaked hydrograph, Fig. 2.20, consists of (i) a rising limb, (ii) the crest segment, and (iii) the recession or falling limb. The rising limb (or concentration curve) of a hydrograph represents continuous increase in discharge (or runoff) at the watershed outlet. During the initial periods of the storm, the increase in runoff is rather gradual as the falling precipitation has to meet the initial losses in the form of high infiltration, depression storage and gradual building up of storage in channels and over the watershed surface. As the storm continues, losses decrease with time and more and more rainfall excess from distant parts of the watershed reaches the watershed outlet. The runoff, then, increases rapidly with time. When the runoff from all parts of the watershed reaches the watershed outlet simultaneously, the runoff attains the peak (i.e., maximum) value. This peak flow is represented by the crest segment of the hydrograph. The recession limb of the hydrograph starts at the point of inflection (i.e., the end of the crest segment) and continues till the commencement of the natural ground water flow.

The recession limb represents the withdrawal of water from the storage (in the channels and over the watershed surface) that was built-up during the initial periods of the storm. The point of inflection i.e., the starting point of recession limb represents the condition of maximum storage in the channels and over the watershed surface. After the cession of the rainfall, this storage starts depleting. Therefore, the shape of the recession limb depends only on the watershed characteristics and is independent of the storm characteristics. The shape of the hydrograph is mainly influenced by the physiographic characteristics of the watershed (described briefly in the following paragraph) and the climatic characteristics of the region (dealt with in Art. 2.5).
Physiographic characteristics of a catchment basin influencing the runoff and, therefore, the shape of the hydrograph include area, shape, elevation, slope, and orientation of the basin besides the type of soil, land use, and drainage network. All other conditions remaining the same, a larger basin area results in smaller peak flow with a larger time base of the hydrograph (i.e., relation depicting variability of stream discharge with time in chronological order) and better sustainable minimum flow in the stream due to the possibility of delayed subsurface runoff and base flow.
Different shapes (elongated or broad) of a catchment basin can be represented by the form factor defined as the ratio of average width to the axial length of the basin. In an elongated basin (form factor < 1), the precipitation falling at the farthest upstream end of the basin will take longer time to reach the downstream outlet end of the basin. This would, therefore, result in larger time base of the hydrograph with lesser peak flow. Catchment basin with higher slope would, obviously, hasten rise in the stream levels and peaking of the stream flow. Orientation of basins with respect to the sun would decide the magnitude of evapotranspiration and, thus, influence the runoff. Temperature, precipitation and other climatic characteristics of a region are influenced also by the mean elevation which, therefore, affects the runoff indirectly.
Soil characteristics affect the infiltration capacity and, hence, the runoff. A soil with high porosity increases the infiltration and, therefore, reduces the peak flow in the stream. Similarly, a forest area has larger capacity to retain water in its densely vegetated surface and, hence, reduces the peak flow (i.e., flooding) in the stream.
Over a period of time a network of natural rivulets ( i.e., smaller stream channels) develop in a drainage basin. These channels act as tributaries to the main stream of the drainage basin. A well-developed network of these smaller channels (i.e., drains) collect the precipitation and transport it quickly to the outlet end of the basin without giving much opportunity to the

70 IRRIGATION AND WATER RESOURCES ENGINEERING
precipitation to infiltrate into the ground. Therefore, peak flows in the stream would be higher. Minimum flows, however, are likely to be lower due to lesser infiltration.