records back to 1226 show numerous floods, generally occurring in the autumn.

From 1832 to 1890 there were 188 floods. Of these, 46 were great enough to cause gage heights of 13 to 16 feet or over at Mirabeau, 54 miles above the mouth of the stream and above which the Durance has a drainage area of 4150 square miles. Of the 46 floods, 7 reached 16.5-foot stages at Mirabeau. There were as many as 9 floods in a single year, as in 1848 and 1856; and there were only 9 years during the whole period which were exempt from floods reaching at least a 10-foot stage at Mirabeau.

The 7 exceptional floods (16.5-foot or higher gage records at Mirabeau) occurred in 1836, 1843, 1863, 1882, and 3 in 1886. The greatest flood was the last of the three in 1886, which occurred on November 10-11, causing a discharge at Mirabeau of about 237,000 second feet, or 57 second feet per square mile. This was practically equalled by the flood of 1843. Such floods cause approximately 20foot stages in the Durance at Mirabeau. The shifting character of the material in the stream bed prevents a closer comparison of different floods by means of gage heights. The flood of October 28, 1882, had a maximum discharge at Mirabeau of 203,000 second feet; the flood of October 26-27, 1886, a maximum of 176,700 second feet; and the flood of November 8, 1886, a maximum of 191,000 second feet. The Durance floods generally occur either in spring, from March 15th to June 15th, or in the fall, from September 15th to December 15th. Spring floods are rarely very high. Fall floods are often high and dangerous. Due to the distribution and form of the precipitation, winter and summer are almost totally free from floods. Floods of the Durance seldom coincide with those of the Rhone, owing to the very complex regimen of the latter as compared with that of the former. This paper, by the engineer in charge of the studies on the Durance at the time, outlines the results of the work done by order of the government to establish a basis for flood prevention measures. The government ordered this study made because of the great damage done by the three floods of 1886.

Floods in the Tiber River*

The drainage area of the Tiber is 6455 square miles. The mean annual rainfall over the basin is 34.8 inches, and there is no appreciable snow fall.

* From the Proceedings of the Institution of Civil Engineers.

The Works on the Tiber, by M. Ronna. Bulletin de la Société d'Encouragement pour l'Industrie Nationale. November, 1898.

Deutsche Bauzeitung, 1893, p. 99.

Ueber die Tiberregulierung, Wochenschrift des Oesterreichischen Ingenieure und Architekten Verein. 1877, p. 114.

The first flood recorded at Rome was in 413 B. C. The greatest flood ever recorded was that of 1598, A. D., when the maximum discharge was 106,000 second feet, or 16.4 second feet per square mile. The second greatest flood was the disastrous flood of 1870, when the maximum stage was 8 feet lower than in 1598. However, the actual discharge during this flood was but little less than that of the flood of 1598, the great difference in stage being due to obstructions and encroachments in the channel. The stage in 1598 was 64.2 feet, in 1870 it was 56.5 feet. The 1870 flood was 12 feet deep in the streets along the quays, and covered about one half the inhabited area of the city. The water surface slope was 2.89 feet per mile in the 6-mile course through the city. In the upper part it was only 0.8 foot per mile, but in the lower part it was 5.81 feet per mile. The obstruction at one of the bridges caused a difference in level of 22 inches.

CHAPTER XII.-APPLICATION TO MIAMI

VALLEY OF STUDY OF GREAT
STORMS

In preparing plans for flood prevention in the Miami Valley one of the first problems requiring definite decision was the size of the maximum flood against which protection should be provided. The engineer at once recognizes that the size of the maximum possible flood cannot be determined directly from the size of the maximum possible rainstorm, vital as this may be, since the greatest rainstorms do not necessarily cause the greatest floods. Moreover, the flood prevention works of the Miami Valley on occasion will submerge large areas of valuable agricultural land. As the frequency and depth of this flooding will have a marked effect on the value of these lands, the design of the works was materially affected by the desire to secure flood protection with a minimum damage to the land above the dams. The ability to make accurate estimates of the frequency of floods of any given magnitude therefore is of great value.

In determining the size of the greatest flood within the bounds of probability, which may occur over a given area, there are three primary conditions to be considered. They are:

(1) Topographic conditions affecting the rate of runoff, such as: size, shape, and slope of drainage area; slope and condition of channel of main stream and tributaries; number and position of tributaries; and surface cover of watershed.

(2) Geographic location of the drainage area with regard to direction and path of storm movement, sources of moisture, distance from ocean bodies, and location of mountain ranges.

(3) Past records of great storms and corresponding stream stages, so far as they may throw light on the maximum storm which may occur in the future. The time-area-depth relations, season of occurrence, frequency, and geographic location are the principal features of former storms to be examined in determining their bearing on any flood problem. The study of former storms should not be confined to those which have occurred over the given drainage basin, especially if the past record is for comparatively few years, since greater storms may have chanced to occur over other areas which are comparable in nearly every respect. This raises the difficult question as to just. what other areas are comparable in the matter of the greatest storms to which they are subject.

SIZE OF FLOOD SELECTED AS BASIS OF DESIGN

In working out the plans for protecting the Miami Valley against floods, all three of the factors just mentioned were thoroughly investigated. The second and third factors, geographic location, and past records of storms, are the subjects treated in this volume. After mature consideration of all of these factors the Official Plan for flood protection was designed to provide against a hypothetical storm which would cause a maximum flood runoff almost 40 per cent in excess of that of the storm of March 23-27, 1913, the latter having caused the greatest rate of runoff during the 100 years of record for the Miami River. The reasons for adopting this basis will now be discussed in considerable detail.

GEOGRAPHIC LOCATION OF MIAMI VALLEY IN ITS RELATION TO STORMS

As has been previously stated, the general direction of storm movement in the United States is from west to east. The low barometric centers which accompany storms generally originate in the northwest, west, and southwest. Their most frequented tracks converge and focus in eastern Texas, Oklahoma, and Arkansas, and then either extend up the Mississippi and Ohio Valleys or pass off the south Atlantic coast in Georgia or South Carolina. Occasionally a storm travels northwest across the gulf, then changes its direction to north or northeast through Texas, Oklahoma, Missouri, Illinois, Indiana, and Ohio. This is the characteristic path of West Indian hurricanes. The location of the 160 largest storms which occurred in the eastern part of the United States during the 25-year period 1892-1916 can be clearly seen by referring to figures 50 to 57.

Heavy, long-continued rains in the United States obtain their supply of water largely from the Gulf of Mexico and the Atlantic Ocean. A large part of the rain of the Miami Valley doubtless comes from the ocean and gulf, and on account of the long distance of land travel, and the higher latitude, the greatest rainfall in southwestern Ohio cannot be nearly as heavy as may occur over the south Atlantic and Gulf states. In traveling such long distances over land the air, laden with moisture when it leaves the ocean or gulf, is subject to large variations of temperature, the average of which is gradually decreasing with increasing latitude. This causes the air to lose much of its moisture. The effect of distance of land travel and increasing latitude in decreasing the depth of storm rainfall is plainly evident in all of the investigations described in chapters V to VIII.

Not all the rainfall of the northern interior part of the United States, however, comes directly from the ocean and gulf. A large

part of the rainfall of southwestern Ohio, especially during the summer months, is water that has evaporated from the forests and fields to the south of it. The forests and fields of Missouri and Arkansas, for instance, will evaporate water at the rate of one-eighth of an inch, and perhaps one-fourth of an inch a day, as long as the supply is plentiful. As just stated, this is largely the source of water supply in the frequent thunderstorms of the summer months. Such storms, however, while they may have considerable depths over limited areas, are rarely if ever the cause of serious flood damage in the Miami River. From this it appears that after all, the sources of moisture of destructive storms in the Miami Valley are the ocean and gulf, and the maximum intensity of rainfall in such storms is subject to the limitations imposed by latitude and distance of land travel.

Another geographic feature that tends to reduce the maximum rainstorm which can occur in the Miami Valley is the location of the Appalachian Mountains to the east and southeast. The effect of high mountains in preventing the passage of great quantities of water vapor is discussed in chapter III.

From the foregoing discussion it will be seen that the Miami Valley is located in one of the principal paths of storms. It is so shielded from the two primary sources of moisture, however, that the otherwise possible maximum storm is greatly reduced.

GREAT STORMS OF THE PAST AS APPLIED TO MIAMI VALLEY CONDITIONS

The three factors, time, area, and depth are necessary in determining the absolute and relative sizes of storms. These factors were determined for 33 of the largest and most important storms which have occurred in the eastern part of the United States during the past 75 years, and the results are given and discussed in chapter VIII. In deciding which of these storms are applicable to Miami Valley conditions it is necessary to consider their geographical distribution; and to determine which of those applicable would cause the greatest floods if duplicated in the Miami Valley, it is necessary to consider their seasonal distribution. These subjects are discussed in chapter VII.

Of the 33 great storms for which detail investigations were made, we may at once eliminate from consideration the 16 in the southern group. The investigation of all the factors which influence the size of storms in the northern interior of the United States furnishes conclusive evidence that these southern storms cannot be duplicated in