Sample Output 4 – Sub 6-Hour Interval Curve

The Sample Output 4 displays the cumulative depth-duration curves for each isohyet. This table is only generated when intervals less than 6 hours are required. The first 6-hour interval from each curve shown in Sample Output 3 is multiplied by the 1:6 hour ratio to obtain the precipitation value for the first hour. This new time-depth value along with a time-depth value of [0, 0] and the original curve are used to generate the points for the cumulative curve. The 1:6 hour ratio is used for all isohyets that are equal to or smaller than the computed optimal storm size. In the example shown, isohyets A through J use the ratio whereas the outer isohyets do not since they are considered residual precipitation. For residual precipitation, the 1-hour precipitation is simply 1/6 of the 6-hour precipitation. The curves are then smoothed. From these smoothed cumulative curves (shown below), each curve is converted back to incremental for the time interval requested. The hyetograph pattern specified in the Computation Options panel is then used to rearrange the ordinals to the requested hyetograph pattern. By convention the intervals from the first 6-hour duration are staggered around the midpoint of the 6 hour interval and the other intervals are placed in declining order moving out from the center.

The output Sample Output 4 displays the cumulative depth-duration curves for each isohyet. This table is only generated when intervals less than 6 hours are required. The initial step is to create cumulative precipitation table starting at time zero, and going out 72 hours, with values at the end of each 6-hour increment. In that table, an ordinate at 1-hour is inserted by multiplying the first 6-hour total by the sum of the of the hyetograph adjustment factor.  See Table 4 and the 1-6 hour ratio for the given isohyet from Figure 39 of the original HMR52 document (National Weather Service, 1982). 

For example, the 1Hour precipitation depth for isohyet A is 5.66=18.22*(.3152+(-.0045)), where 18.22 is the total precipitation for the first 6 hours, .3152 is the 1:6 hour ratio spatially interpolated from Figure 39 of the HMR52 document (National Weather Service, 1982), and -.0045 is the 1:6 hour adjustment factor interpolated from Table 4 for a storm size of 2,109 sq. mi. At this point, the following ordinates are computed: [0hr, 0in], [1hr, 5.66in], [6hr, 18.22in], [12hr, 21.71in], [18hr, 23.2in], [24hr, 24.25in], [30hr, 25.25in], [36hr, 26.19in], [42hr, 27.05in], [48hr, 27.78in], [54hr, 28.34in], [60hr, 28.76in], [66hr, 29.07in], [72hr, 29.32in]. The remaining ordinates in Sample Output 4 are generated through Cubic interpolation. The hyetograph pattern specified in the Computation Options panel is then used to rearrange the ordinals to the requested hyetograph pattern.

For the purposes of illustration, assume that 1-hour hyetographs are required from the analysis. As Sample Output 4 shows, the isohyets A through J are within the optimal storm size of 2109 sq. mi. meaning that the 1:6 hour ratio will be applied resulting in the general pattern as shown in the figure below, Isohyets K though S fall outside the optimal storm size and do not use the 1:6 hour ratio for distributing precipitation and will result in a pattern similar to what is shown in the figure below. For isohyets A through J the 1-hour value is approximately the 1:6 ratio, adjusted using the appropriate ratio adjustment value from the following table, multiplied by the 6-hour value. However, since the curve has been smoothed, the 1-hour values will not be exact. The 1-hour values for isohyets K through S are 1/6 of the 6-hour values.