a single maximum record. This might be indicated in general terms by the statement that any isohyetal which does not enclose at least three rainfall records is of only approximate utility. The greater the area enclosed by an isohyetal, the greater will be the number of stations enclosed within it, and the smaller will be the percentage of probable error in drawing the isohyetal.

ASSEMBLING, COMPUTING, AND PLATTING DATA FOR TIME-AREA-DEPTH CURVES

As previously stated, a map was drawn for each period of maximum precipitation in each of the storms. The number of maps required for a single storm varies from one to five, depending on the number of days the storm lasted. Since each of these maps shows the depth and area of precipitation for a definite period of time, we have the three interdependent factors, time, area, and depth, in a definite measurable form. The data in this form, however, is not easily accessible for direct use, or for comparison with similar data for other storms and other periods of the same storm.

The best method which could be devised for combining the three factors, time, area, and depth, in such a manner as to make them comparable for different storms, and for different periods of the same storm, is to plat the data in the form of curves. The data for an entire storm is a group of curves, each of which gives the time-areadepth relations for one maximum period of the storm. Thus there is a curve for each map. All the curves for one storm are not presented together, however, as it is desirable for comparative purposes and for convenience in publication to have on the same chart a number of curves taken from different storms for the same duration of maximum rainfall. These curves are shown in figures 94 to 103.

Since there is a curve corresponding to each map, for a definite period of maximum precipitation, the element of time remains a fixed quantity for one curve. The varying factor of area is platted as abscissas, and the corresponding average depths as ordinates to the curve.

The steps necessary to take these quantities, area and average depth, from a given map and prepare them for platting involved a considerable amount of work. Table 8 gives the computations for the maximum 3-day period of the storm of July 14-16, 1916, a map of which is shown in figure 105. For convenience in reference a capital letter is placed at each center of precipitation. These, and the order of combining them, are shown in column 1 of table 8. Beginning at the greatest center of precipitation, the isohyetals are planimetered,

and the area in square inches enclosed is set opposite each. This process is continued at the principal center until the last isohyetal is reached which encloses that center alone. Before planimetering and listing the area enclosed by the next lower isohyetal, the one or more additional centers enclosed by it are treated in the same manner as the principal center. The same process is continued until the 2-inch isohyetal is reached. The isohyetals and the area in square inches enclosed by each are shown in columns 2 and 3 of table 8.

The computations for determining the average depth over the area enclosed by each isohyetal are simple, the average depth of precipitation over the area between any two isohyetals, named in column 5, being considered equal to their arithmetical mean. These average depths are given in column 6. The area in square inches enclosed by each isohyetal, column 3, is reduced to square miles and placed in column 4. Column 7 shows the area between isohyetals, obtained by subtracting from the area enclosed by each isohyetal that enclosed by the next higher. The average depth of precipitation over this interspace is given in column 6, and in column 8 the volume in inch-miles obtained by taking the product of the quantities in columns 6 and 7. The total volume of precipitation in inch-miles enclosed by each isohyetal, as shown in column 9, is the sum of the quantity in column 8 and the total in column 9 for the next higher isohyetal. The average depth of precipitation in inches over the entire area enclosed by any isohyetal is, of course, the quotient obtained by dividing the quantity in column 9 by that in column 4. This is given in column 10.

In the appendix of this volume are given in tabular form the essential time-area-depth quantities for the purpose of checking or recomputing the computations, or for reproducing the curves on a larger scale, if it is desired to group them differently for comparative

purposes.

The curve for the maximum 1-day period of storm 157, July 1416, 1916, is a good example of certain peculiarities met in platting the curves for several other storms. For that reason it is shown alone in figure 106. There were three distinct 1-day rainfall peaks of widely differing characteristics. Two of these occurred on July 15, one each in North and South Carolina, and the third occurred on July 16 in North Carolina over an area differing slightly from that covered by the peak of the preceding day. For areas up to 500 square miles, the greatest average depths of precipitation for a 24-hour period occurred in the North Carolina center on July 16; for areas from 500 to 3,000 square miles, in South Carolina on July 15; and for areas greater than 3,000 square miles in North Carolina on July 15.

Table 8.-Form of Time-Area-Depth Computations, Storm of July 14-16, 1916. Maximum 3-day Period, July 14-16

Note.-Blackfaced figures show maximum precipitation at rainfall centers.

It is probable that each curve would suffer some modification if it were possible to free the rainfall observations from the errors arising

5.5

4.5

3.5

2.5

from arbitrary division of time commented on elsewhere in this chapter. For instance, the maximum 24-hour record at Altapass, North Carolina, was 22.22 inches between 2 p. m. of July 15 and 2 p. m. of July 16. But the time-area-depth curve for July 16 shows a maximum, nearly 3 inches smaller, although Altapass was the center of that storm peak. This is due to the fact that the maximum 1-day rainfall at Altapass, based on regular evening readings, is 19.32 inches for July 16, and this, therefore, became the upper limit of the curve.

18

16

14

Greatest Average Depth of 24-Hour Rainfall in Inches

FIG. 106.-TIME-AREA-DEPTH CURVES FOR STORM OF

JULY 14-17, 1916.

This storm occurred over the Carolinas. The curves show the greatest average depth of rainfall during the maximum 1-day period.

To what extent the remainder of the curve is subject to errors from this source can not be ascertained, because of lack of data. The indications are that, as the area increases, the averages obtained from the increased number of station records tends to decrease such errors.

An examination of the three curves referred to shows that no single curve furnishes a complete answer. The curve adopted for the maximum 1-day period, and shown in the group curves, is the

envelope of these three curves. In the group curves, where cases of this kind occur, and the angle between the two curves at the point of intersection is sharp, no attempt is made to join them in a smooth

curve.

A different kind of break in the curves is occasionally caused by a very great increase in the area without a corresponding reduction in average depth of rainfall. This occurs at the point where the base of the greatest storm peak joins the main body of the storm. The curve for storm 10, figure 95, is a good example of such a break. The 6-inch isohyetal, enclosing an area of 1020 square miles over which there was an average rainfall of 7.2 inches, is the lowest which encloses center A alone. The 5-inch isohyetal, enclosing an area of 7460 square miles, over which there was an average depth of rainfall of 6.2 inches, includes centers A to E. Any curved line between these two points is misleading, hence they are connected by a straight dotted line.

The limitations inherent in rainfall data, as described in the preceding pages, together with the manner of compiling the time-areadepth curves, cause the latter to indicate depths of rainfall slightly less than the actual. This is true especially of intense rains occurring over small areas, as illustrated in the case of the July 1916 storm over the Carolinas, but is not so material in storms which have a gradual and even distribution as for instance the March 1913 storm in Ohio.

Continuing this line of reasoning, it follows that errors of this kind are to be looked for principally in the upper portions of the time-area-depth curves, while the lower portions would be little affected. Since the former relate to comparatively small areas of minor interest in connection with flood control problems, such inaccuracies are of little moment.

DEGREE OF ACCURACY ATTAINED

The character of the operations in each step was allowed to govern the extent of detail with which they were checked for accuracy. Assembling the data for platting the maps consisted in listing the stations in the storm area, and placing opposite each the amount of rainfall recorded on the several days of the storm. When ordinary care is exercised but few errors will occur, and each of these will affect only the record at one station for one day of the storm. This would, in general, have a negligible influence on the final maps and curves. For these reasons it was not considered necessary or advisable to check the data completely, as this would have required an additional amount of time equal to about half of that consumed in compiling the data.