Stormwater Management Manual

APPENDIX V-B
DESIGN STORM PROCEDURES

Introduction

This appendix describes the procedures used to create a design storm as input to HEC-1 from the data presented in Chapter V and Appendix V-A.

For convenience and reliability, these procedures have been incorporated in a computer program entitled "PDP". PDP runs on personal computers (under DOS) and is available from District staff.

Time Distribution

The design storm is derived from the depth vs duration data for the appropriate recurrence interval and elevation. The maximum depth (the depth for the same duration as the time interval, which is usually 5 minutes) is placed at the center of the distribution. Then, successively lesser incremental depths are computed as the differences in cumulative depths from the depth-duration data for succeedingly longer durations. These incremental depths are positioned alternately after and before the highest (center) intensity.

Example 1-hour, 10 year design storm, 150 foot elevation, 5 minute time step:

Step 1 Compute incremental period depths in order of rank. Cumulative depths are read or interpolated from the tables in Appendix V-A.

Log-log interpolation is used when the depth for a given duration must be interpolated between tabulated depths (those marked below with * ).

Rank	Duration minutes		Cumulative Depth inches	Incremental Depth inches
1	5		0.250	0.250
2	1		0.360	0.110
3	15		0.430	0.070
4	20		0.483*	0.053
5	25		0.529*	0.046
6	30		0.570	0.041
7	35		0.609*	0.039
8	40		0.645*	0.036
9	45		0.679*	0.034
10	50		0.711*	0.032
11	55		0.741*	0.030
12	60		0.770	0.029

The equation for log-log interpolation between successive durations 1 and 2 is:

d = d1 (	t	)k
	t1

where

d = depth, inches

t = duration, minutes

and


Step 2   Reorder the incremental depths with the maximum depth in the center, others alternating after and before the maximum.

Period	Time minutes	Depth inches
1	5	0.03
2	10	0.034
3	15	0.039
4	20	0.046
5	25	0.07
6	30	0.25
7	35	0.11
8	40	0.053
9	45	0.041
10	50	0.036
11	55	0.032
12	60	0.029

Spatial Distribution

When to Use The spatial distribution of the design storm must be taken into account when the area of the overall watershed exceeds significantly the area in Table 5-1 for which the spatial distribution factor is 1.0.

Table 5-1 provides factors to be used for modifying the depths for the most intense 1-hour period within the storm. The factors are constant at the boundary of the ellipse with the area shown in the first column of the table. The major axis of the ellipse is twice the minor axis, and the orientation of the ellipse is taken as the angle of the major axis relative to due north, with a positive angle measured clockwise. The length of the minor and major axes are shown in the last two columns of Table 5-1.

Constant Value for One Watershed - No Subwatersheds In cases where the watershed is not divided into subwatersheds and the area of the watershed is not significantly greater than the area of the ellipse for which the factor is 1.0, the average precipitation for the watershed may be estimated as an area-weighted average considering the procedure described below for a more detailed watershed.

A wide and pronounced variation in the spatial distribution of rainfall over the watershed may require subdivision into smaller watersheds to appropriately reflect the variation.

Divided into Subwatersheds Precipitation for each subwatershed may be reasonably approximated as precipitation at a point near the centroid of the watershed. The procedure below is used.

It is often necessary to repeat the procedure for various centerings and orientations of the ellipse. The elliptical distribution is properly centered and oriented when the maximum flow for the results for the storm recurrence interval. Usually, but not always, this is the centering which produces the highest, area-weighted average factor.

Step 1   Determine the 1-hour factor for the point

The 1-hour factor may be found using a graphical procedure or an analytical one.

Graphical A transparent map overlay is created at the scale of the map with concentric ellipses drawn for appropriate increments of the factors from Table 5-1. For example, ellipses may be drawn for 1.0, 0.9, 0.8, etc. The major and minor axis of the table areas are shown in the far right hand columns in Table 5-1. For other areas, the equations for the minor and major axis are:


b = 2a

where

a = minor axis, miles

b = major axis, miles

A = area, square miles

When the point falls between two of the ellipses on the overlay, the factor for the point is interpolated between the values for the bracketing pair of ellipses.

Analytical The factor associated with the ellipse through the point is computed from position of the point relative to the ellipse, taking into account the angle of the major axis with due north. In the equations below, y is distance north, in miles, from an arbitrary origin, and x is the distance east in miles from the origin. The subscript p refers to the x-y coordinates of the point which is the centroid of the watershed, and the subscript c refers to the x-y coordinates of the center of the storm ellipse. is the angle of the major axis with north in degrees clockwise.






b = 2a



Step 2   Modify the depth-duration relationships using the 1-hour factor.

Look up the 1-hour factor in Table 5-1 corresponding to the ellipse area determined in step 1. The 1-hour depth is modified by simply multiplying it with the factor. Depths for durations of less than one hour are reduced so that the average intensity between any two durations is at least the average intensity between the next longer pair of durations, with the minimum intensity no less than that between the 1-hour and 2-hour durations, and so that the adjusted depths maintain a proportionality among themselves that is reasonably consistent with the proportionality among the unadjusted values.

Example: 100-year event, 1200 feet elevation, 1-hour factor=0.5

Duration		Unadjusted Depth inches		Adjusted Depth inches		Average Intensity inches/hour
0		0		0		---
5m		.41		0.104		1.25
10m		.59		0.174		0.84
15m		.72		0.235		0.73
30m		.98		0.395		0.64
1h		1.36		0.680		0.57
2h		1.91		---		0.55

Step 3  Compute the temporal distribution as described above using the adjusted depth-duration data for durations of one hour and less.

Steps 1-3 are repeated for each subwatershed, then HEC-1 is ran to compute the runoff resulting from that particular centering and orientation of the ellipse. As noted above, it may be necessary to test several centerings to determine the centering which results in the maximum peak flow.