In India it is sometimes arranged that a telegram shall, in the low-water stage of the river, be sent from the upper station when a rise of 2 feet occurs in twenty-four hours or any less period, with a further telegram for any such subsequent rise. The telegram states the exact reading on the gauge and whether the water is rising steady or falling. This is given as indicating the procedure that may be followed where the telegraph has to be used, but when long and frequent telegrams are not desirable.

The advancing end of a flood wave may, while the wave is rising and being formed, travel rapidly, but when the wave has been formed it travels at the ordinary rate of flow of the risen stream. The advancing end of a trough may, while it is being formed, travel rapidly, but after formation it travels at the ordinary rate of the fallen stream (Hydraulics, Chap. IX., Arts. 3 and 4). Thus the rate at which a change in water-level travels down a stream depends at first on the amount of the rise or fall, but afterwards on the water-level of the risen or fallen stream.

By taking the above facts into consideration and noting the actual times obtained from the diagram, it will be possible to arrive at the probable time that will be taken by any change. It will also be possible to predict the height of the flood. If it is worth while, an empirical formula can be got out. If there are tributaries, each with a gauge, the matter will be more difficult. Probably the floods in the tributaries will arrive at different times, but even in such cases empirical formulæ have been arrived at, especially in France, and are mentioned in various volumes of the Proceedings of the Institution of Civil Engineers.

In all cases predictions are liable to be more or less upset if rain falls in the tract between the upper and lower gauges. In very dry weather the speed of a flood wave may be somewhat reduced, and the height to which it rises will almost certainly be reduced.

The full effect of a change will not be felt at the lower station unless the change at the upper station is maintained for a sufficiently long period. A short wave or trough flattens out. Thus in any empirical formula or system of prediction, the time over which the change extends at the upper gauge must be taken into account, or else there must be several upper gauges and the readings of all of them be taken into account.

In mountainous districts landslips sometimes occur and block the valley of a stream which then forms a lake. The water gradually rises and eventually flows over the dam and sweeps it away causing a flood, which is of great suddenness and height but decreases very quickly in height as it travels down the valley. In a case which occurred in the Himalayas in 1888 the inhabitants of the valleys, from the dam to the point where the river debouches from the hills, were compelled by Government to vacate all habitations below the probable level of the flood, and no loss of life occurred. Similar floods, but on a smaller scale, may be caused by the bursting of ordinary reservoir dams. In some continental rivers ice may obstruct the stream and cause floods.

5. Prevention of Floods.—The extended use of field drains has, in recent years, done much to increase the severity of floods in England and other countries. One method of mitigating or preventing floods is the construction of reservoirs for storing the water. Reservoirs locally known as “washes,” formed by setting back the embankments, exist on the Fen rivers. One wash, on the Nene, below Peterborough, is 12 miles long and half a mile wide and is filled, in floods, to a depth of 7 feet and holds 1 inch of rainfall over the river basin, and this is found to be sufficient. Reservoir construction is, however, in most cases, impracticable owing to the expense. To store the water which is given by 1 inch of rain in the basin of the Thames, a reservoir would be needed 50 feet deep and covering about 7 square miles. It might cost £7,000,000.

The afforestation or reforestation of river basins ([Chap. II., Art. 4]) is also occasionally undertaken, but is not generally practicable.[20]

The most practicable methods for preventing flooding are lowering the water-level of the stream and constructing embankments along it. These will be considered in the next two articles.

6. Lowering the Water-Level.—The water-level of a given length of stream can be lowered by lowering the bed, widening the channel or straightening the channel. The efficiency of these processes is in the order named. As stated in [Chap. I., Art. 4], the alteration to the channel must in any case be continued to some point downstream of the reach under consideration. Let the channel be supposed to be of “shallow” section with sloping sides. Let W be the mean width, D the depth, and S the slope. Let it be required to lower the water-level by an amount equal to D/5. This can be effected by lowering the bed by about 25 per cent. of D, or by increasing the width by about 50 per cent., or by increasing the slope by about 100 per cent. If the bed is lowered, V is not affected, and the mean width is reduced. Increase in W reduces D, and therefore reduces the hydraulic radius and the velocity. Hence the large amount of widening necessary. When S is increased the velocity, if R remains the same, is affected only as √S (Hydraulics, Chap. VI., Art. 2), but the depth of water is reduced and R therefore reduced. Dressing the sides of a channel, so as to make it smoother, produces the same effect as a slight widening.