Frequency Storm 3-Day Depth Compute

The Frequency based hypothetical storm creates a balanced storm for a given time interval by performing a linear interpolation on the precipitation-frequency duration and depths in log-log space. Prior to HEC-HMS version 4.10, the 3-day depth was not a depth that users could input, while in HEC-HMS version 4.11 and onward, users are allowed to directly input 3-day depths. Users could experience differences in their balanced hyetograph after migrating their software from 4.10 to a later version of the software.

3-day depth migrating from version 4.10 (or older) to 4.11 (or newer)

The 3-day depth is computed by logging of the 2-day and 4-day depth (blue) before areal reduction due to the storm area and interpolating the 3-day depth (orange) as shown in the Figure below. Converting the logarithm by raising the base value gives you the 3-day depth value added to the component editor.

For example:

Interpolated unreduced 3-day Log Depth = 0.9783 in
Un-log 3-day Depth = 9.5135 in

3-day depth in HEC-HMS 4.10 (and older)

The 3-day depth was not directly computed in the software but could be estimated after the balanced hyetograph is created. To estimate a 3-day depth, the 2-day and 4-day depths are first areally reduced. The figure below shows just the log 2-day and 4-day reduced depths; however, this interpolation is performed from the intensity duration out to the storm duration to build the storm hyetograph.

For a given time increment (defined by the computation time interval), linear interpolation in log-log space is performed at the time interval to estimate the cumulative depths between the 2-day and 4-day durations.

The interpolated log depths are used to compute an incremental depth value. Un-logging the interpolated depth values and sequentially subtracting the cumulative depth by the next cumulative depth gives you the incremental depth value.

For example, for a 15 minute time interval:

Log depth for 2910 min = 0.9260 in
Un-log depth for 2910 min = 8.4333 in
Log depth for 2925 min = 0.9263 in
Un-log depth for 2925 min = 8.4399 in
15 minute increment = 0.0066 in

The increment depths are sorted to by staggering the largest increment depths in the center, and interchanging the next largest depth to the right or left of the largest depth.

The 3-day "reduced" depth can be computed by finding the maximum 3-day depth after sorting the increments.

To obtain the "un-reduced" 3-day depth (backing out of areal reduction), the areal reduction factor needs to be computed. For TP-40 areal reduction, the equation is

$\begin{array}{l}\displaystyle Areal Reduction Factor = 1-factor *(1-e^{-0.015*drainage area}))\end{array}$

The factor is different for each duration. The factor is set to 0.12 for the 3-day reduction curve.

For example:

Reduced 3-day Log Depth = 0.9519 in
Reduced 3-day Depth = 8.9514 in
Reduction Factor (3-day for 254.52 square mile watershed, TP-40): 0.9413
Un-reduced 3-day Depth = 9.5100