EXPERIMENTAL MAPS

Before platting the final maps for the 33 storms selected for that purpose, experimental maps were made in order to learn by what method they could be constructed with the greatest facility and accuracy.

To determine the effect of the several sources of inaccuracy enumerated above, experiments were made with the data for two storms. The storm of October 4-6, 1910, was platted on maps by four different methods, here designated the A, B, C, and D methods. The storm of November 17-21, 1906, was platted by two of these, the A and B methods.

By the A method the morning and evening records taken on the same day were treated as though of equal value and as though they had been taken simultaneously. The depths of rainfall for the different periods of maximum accumulated precipitation at each station. were taken directly from the computations described on page 214. This method is the simplest of the four and would be the natural way of utilizing the data if corrections for the four sources of error described above could readily be made in the original figures. The only inaccuracies that the A method permits to be corrected, however, are those falling in the second class, that is, inaccuracies of reading and recording, and this only when surrounding stations furnish unmistakable evidence as to the nature of the error.

By the B method the evening records were made to control the lines of equal rainfall within the limits imposed by the morning records of the following day. That is, the isohyetals, although drawn with little regard for the morning records of the calendar day, were not drawn through points shown by the records of the following morning to have had less rain than the lines would indicate. The morning records were shown in the form of a fraction, the numerator in black indicating the reading for the current morning and the denominator in red that of the following morning. This method is, therefore, an attempt to adjust inaccuracies due to some readings being taken in the morning. With these adjustments it becomes perhaps slightly easier to form an opinion as to whether or not certain station records were subject to the inaccuracies noted under class 2 above.

The C method was tried with the hope that it might provide a method of compensating for inaccuracies due to variations in time of observation, for those due to arbitrary division of time, and to some extent for those due to inaccuracy of reading and recording, described above under classes 4, 3, and 2, respectively. By this method a definite date was not selected as that of 1-day maximum accumulated

precipitation for all the stations, but the day on which the summation of rainfall for all the stations was greatest (elsewhere considered the date of 1-day maximum accumulated precipitation) was merely taken as a fair basic date, and the 1-day maximum accumulated precipitation allowed, at each particular station, to vary 1 day in either direction from this basic date. Thus, in the storm of October 4 to 6, 1910, the date for which the summation for all the stations is greatest, or the basic date, was October 5; but the 1-day maximum accumulated precipitation at Farmersburg, Ohio, was taken as October 4, because the precipitation at Farmersburg on that date was greater than that on either October 5 or 6; the 1-day maximum at Evansville, Ind., was taken as October 5, because greater at Evansville on that date than on October 4 or 6; the 1-day maximum at Farmland, Ind., was taken as October 6, because greater at Farmland on that date than on October 4 or 5. The dates of maximum accumulated precipitation at each particular station were allowed to include the day either preceding or following the basic period, determined by summing up the precipitations at all the stations, provided this gave a greater maximum for that station. The shapes of the time-area-depth curves obtained by the C method did not seem to justify the latter's use. This is mainly due to the fact that it does not make allowance for the progressive movement of a storm. For instance, if the heaviest rainfall of a given storm extends from May 23 to 25 in southeast Missouri, the heaviest rainfall period in Indiana for the same storm may be, and likely will be, from the 24th to the 26th. By the C method it is made to appear that the rain fell simultaneously in the two states.

In the D method, each successive day's record was platted on a separate map and isohyetal lines drawn. The two successive maximum days were combined by laying one map over the other, noting the points of intersection of the isohyetals, and placing a figure at the point indicating the sum of the two lines. Isohyetals for the 2-day period were then drawn through these points. The map so obtained was combined with the map for the day preceding or following, depending on which was the larger, to get points on the isohyetal lines for the 3-day period, and so on.

This would seem to be the most logical method of the four in that it retains on the map of each successive day certain of the irregularities of storm shape of preceding days, which do not appear when an independent map is platted for each maximum period. By this method, however, it is sometimes possible to build up higher storm centers than seem warranted by the data. This feature, perhaps, has a tendency to minimize inaccuracies introduced by the fixed locations of the stations. One disadvantage is that the method is

very laborious and time consuming. Another is that the A method must be used for platting the precipitation records for each day of the storm, or else it becomes necessary to readjust the morning records arbitrarily.

CONCLUSIONS FROM EXPERIMENTAL MAPS

Time-area-depth curves were drawn for each of the experimental maps constructed by methods A, B, C, and D, for the storm of October 4-6, 1910. There were four distinct but approximately parallel curves for the storm periods of 2 and 3 days; for the maximum 1-day period the maps and curves constructed by methods A and D would have been identical throughout, hence only one set of maps and curves was drawn for this period. The curves by methods A, B, and D for the maximum 2-day and 3-day periods were found to follow each other closely. Similar comparative curves were drawn from the A and B method experimental maps of the storm of November 17-21, 1906. The C and D method maps and curves were not drawn for this storm. The A and B method curves were not as nearly coincident as for the storm of October 4-6, 1910.

The A method was found to be substantially as accurate, and much simpler than any of the other three. It was, therefore, the method finally adopted for use in constructing maps for the 33 great storms.

The B method was found impractical except where the 1-day maximum occurred on the first day of storm, the 2-day maximum on the first and second days of storm, the 3-day maximum on the first, second, and third days of storm, etc., without making arbitrary adjustments of the records. The C method was discarded because, having failed to compensate for inaccuracies due to splitting storms between days, it has no advantages over the other methods. The D method was discarded because of the great amount of labor involved, and the uncertainty attendant on readjusting the morning records. In fact, for the storm of October 4-6, 1910, in which the D method was compared with others, the curves differ by no great amount from those drawn by the A and B methods.

No way could be devised to allow for inaccuracies due to the arbitrary location of observing stations, except to place more dependence on determinations from storms where a great many station records are available than upon those where few are available. If isohyetals for each day could be drawn and the separate days combined with absolute accuracy, the D method would give results identical with the B method. However, owing to the different times of taking the readings, it is impossible to plot a map which represents accurately the rainfall over a large area for any given exact period of

time. This inaccuracy is less for 2 days than for 1 day, less for 3 days than for 2, and so on. Thus in using the D method two maps were combined, the inaccuracy of each of which was as great as that of a single map platted from the combined figures of the two separate maps. The resulting map contains, therefore, not only the errors in its two components, but also the errors in making the combination. Errors of the latter kind were especially introduced when contours did not definitely intersect but lay in the same general direction with a varying distance between them. In such cases it was difficult to determine where to establish points representing their sum. Or, a small peak on one map might lie wholly between two contours on the other map, and it was debatable which of these to add to the peak. As previously stated, after weighing the advantages and disadvantages of each of the four methods, method A was adopted for subsequent use.

CRITICISM OF USING MAXIMUM STORM PERIODS

In passing, attention should be called to the fact that one of the processes in the time-area-depth study is open to an apparent objection. Reference is made to treating separately the maximum 1-day period, the maximum 2-day period, etc., of the storm, without direct reference to the precipitation of preceding and following days in so far as this might affect the runoff and consequent flood damage of the maximum period.

The disadvantages to which this method of treatment gives rise could have been eliminated in the following manner: Instead of platting a separate map and time-area-depth curve for each maximum period of the storm, a separate map and curve might have been constructed for the first day, the first and second days, the first to the third days, inclusive, the first to the fourth days, and the first to the fifth days of the storm. The data as represented by the time-areadepth curves would then be in a form immediately available for runoff computations.

The latter method has the further advantage of tending to correct the inaccuracies previously mentioned under classes 1 and 4, and offers the same facility for correcting the inaccuracy of class 2 as does the method of taking maximum periods. The inaccuracy, class 1, due to arbitrary location of observing stations, is partially corrected by having, for periods of two or more days, the principal storm features of preceding periods as a guide. Usually the first day of an extended storm is not the day on which the rainfall is a maximum, and consequently the error introduced by the arbitrary location of the stations is not of great importance. Inaccuracies of class 4, those due to

variations in time of observation, could be partially corrected by letting the evening records control the lines of equal rainfall within the limits imposed by the morning records of the following day, as described on page 219 for the experimental maps constructed by method B.

In addition to the above advantages, maps for consecutive periods, beginning with the first day of the storm, would show the cumulative depth reached on successive days, and the direction and distance of the storm movement. This information can be ascertained indirectly, of course, from the maps and curves as published.

These objections are not serious, however, and are outweighed by the advantage of having the maximum storm periods the most prominent feature of the results, and the most directly available. This is especially helpful when dealing with small drainage areas, where the runoff collects quickly, and would approximate 100 per cent for the maximum day.

ERRORS DUE TO PERSONAL EQUATION

In platting the isohyetal lines, cases often occur in which either one of two or more courses appears to be correct so far as the available data indicates. The location chosen depends solely upon the judgment of the one doing the platting and may be largely a matter of accident. In order to test the magnitude of this personal equation effect, three maps were platted from the same data by different individuals. The storm of October 20-24, 1908, selected for this trial, shown in figures 76 to 80, was one in which the chance for personal variation was not so great as in some of the others; yet the discrepancy from this source was found to be considerable. The maps were drawn for the total storm rainfall. The relative variation in the small areas around the peak was large, as may be seen from the following table:

The proportional variation is much the greatest for the smallest areas, as might be expected, since the peak is dependent usually upon