Contents preface (VII) introduction 1—37

2.3.7. Depth—Area—Duration (DAD) Analysis
Depth-area-duration (DAD) curves, Fig. 2.9, are plots of accumulated average precipitation versus area for different durations of a storm period. Depth—area—duration analysis of a storm is performed to estimate the maximum amounts of precipitation for different durations and over different areas. A storm of certain duration over a specified basin area seldom results in uniform rainfall depth over the entire specified area. The difference between the maximum
rainfall depth over an area P₀ and its average rainfall depth P for a given storm, i.e., P₀ – P increases with increase in the basin area and decreases with increase in the storm duration. The depth-area-duration curve is obtained as explained in the following example :

HYDROLOGY

(cm)	28
24
depth
	20
	average
16
Maximum
	8
		12
	4
	0
	10

53


12 hours

8 hours

2 hours
1 hour

₁₀² ₁₀³ 5 × 10 ³ Area (km²)

Fig. 2.9 DAD curves
Example 2.3 The rainfall data of 8 rain gauge stations located in and around the basin, shown in Fig. 2.10, are as given in the following table :
Cumulative rainfall in mm (Example 2.3)

Time in	Gauge a	Gauge b	Gauge c	Gauge d	Gauge e	Gauge f	Gauge g	Gauge h
hours
2	8	6	5	4	4	3	2	0
4	14	11	10	8	10	8	7	3
6	23	20	17	15	17	14	11	8
8	35	29	26	22	25	18	25	18
10	48	42	38	35	35	28	33	24

The basin has an area of 5850 km². Obtain the depth-area-duration curves for 2, 4, and 6-hour durations.
Solution : Based on the rain gauge data at the end of the storm, isohyets and Thiessen polygons are drawn on the basin map (Fig. 2.10) as explained in Art. 2.3.3 and in Example 2.1. The isohyets (for 25, 35 and 45 mm) divide the entire basin into three zones, say zone I, zone II, and zone III. The polygon of any rain gauge station may lie in different zones of the basin. Each zone, at any time, will have a representative value of cumulative rainfall which would depend upon the rainfall depths of the influencing rain gauge stations at the same time and the areas of the corresponding polygons falling partly or fully into the zone. The zone I is made of part of the polygon of the rain gauge station a while the zone II is made up of part polygons of rain gauge stations a, b, d, and g, and full polygons of the rain gauge stations c and e. Similarly, zone III is made up of part polygons (of the raingauge stations b, d and g) and full polygons (of the rain gauge stations f and h). These details are given in the following table :

54		IRRIGATION AND WATER RESOURCES ENGINEERING
	25	d (35)
		45
		f
	(28)	b (42)
		a (48)
		I
h	III	II

24. 
    ₍₃₃₎
    

35
g
45

25 c (38)

e (35)
Fig. 2.10 Isohyets and Theissen polygons for Example 2.3

Area of Theissen polygons of different gauges in different zones (km²) (Example 2.3)

Zone	Gauge a	Gauge b	Gauge c	Gauge d	Gauge e	Gauge f	Gauge g	Gauge h	Total
I	100	0	0	0	0	0	0	0	100
II	350	1000	1200	100	50	0	200	0	2900
III	0	20	0	80	0	1400	1100	250	2850

The average cumulative depth of rainfall in any zone at any given time (since the beginning of the storm) is computed as

	mi
	∑ (Aij )(Pi )
P =	i = 1	(2.11)
m
	j
		i
	∑ ^Aij

i = 1
where, P_j = average cumulative rainfall depth at a given time for zone j,
A_ij = Part (or full) area of polygons of rain gauge station i whose polygon is falling partly (or fully) in the zone j,
P_i = cumulative rainfall depth at the same time, and
m_i = number of rain gauge stations influencing the average cumulative rainfall depth in zone j.
The values of cumulative rainfall depths for all the zones and at different times are

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55

computed and tabulated as below :

Cumulative average rainfalls in different zones in mm (Example 2.3)

Time	Zone I	Zone II	Zone III
2	8	5.45	2.4
4	14	10.55	7.2
6	23	18.28	12.39
8	35	27.9	20.89
10	48	40.1	29.87

Thereafter, cumulative average rainfalls for the progressively accumulated areas are worked out taking into account appropriate weights in proportion to the areas of the zones. For example, the cumulative average rainfall at a given time over all the three zones would be

^PI+II+III ^=	^AI ^PI ^+ ^AII ^PII ^+ ^AIII ^PIII	(2.12)
^AI ^+ ^AII ^+ ^AIII

where, A_I, A_II, and A_III are the area of zones I, II, and III, respectively, and P_I, P_II, and P _III are the average cumulative depths of rainfall for zones I, II and III, respectively, and at the same
specified time. The computed values are shown in the following Table:
Cumulative average rainfalls for progressively accumulated areas in mm (Example 2.3)

Time	Zone I	Zone (I + II)	Zone (I + II + III)
	100 km^2	3000 km^2	5850 km^2
2	8	5.54		4.01
4	14	10.67		8.98
6	23	18.44	15.49
8	35	28.14	24.61
10	48	40.36	35.25

Now the maximum average depths of rainfall for the desired durations of 2 hrs, 4 hrs and 6 hrs can be worked out for three areas of 100 km², 3000 km² and 5850 km² and tabulated as below and plotted as shown in Fig. 2.11.