The Frequency based hypothetical storm creates a balanced storm for a given time interval by performing a linear interpolation on the precipitationfrequency duration and depths in loglog space. Prior to HECHMS version 4.10, the 3day depth was not a depth that users could input, while in HECHMS version 4.11 and onward, users are allowed to directly input 3day depths. Users could experience differences in their balanced hyetograph after migrating their software from 4.10 to a later version of the software.
3day depth migrating from version 4.10 (or older) to 4.11 (or newer)
The 3day depth is computed by logging of the 2day and 4day depth (blue) before areal reduction due to the storm area and interpolating the 3day depth (orange) as shown in the Figure below. Converting the logarithm by raising the base value gives you the 3day depth value added to the component editor.
For example:
 Interpolated unreduced 3day Log Depth = 0.9783 in
 Unlog 3day Depth = 9.5135 in
3day depth in HECHMS 4.10 (and older)
The 3day depth was not directly computed in the software but could be estimated after the balanced hyetograph is created. To estimate a 3day depth, the 2day and 4day depths are first areally reduced. The figure below shows just the log 2day and 4day 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 loglog space is performed at the time interval to estimate the cumulative depths between the 2day and 4day durations.
The interpolated log depths are used to compute an incremental depth value. Unlogging 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
 Unlog depth for 2910 min = 8.4333 in
 Log depth for 2925 min = 0.9263 in
 Unlog 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 3day "reduced" depth can be computed by finding the maximum 3day depth after sorting the increments.
To obtain the "unreduced" 3day depth (backing out of areal reduction), the areal reduction factor needs to be computed. For TP40 areal reduction, the equation is

Areal Reduction Factor = 1factor *(1e^{0.015*drainage area})) 
The factor is different for each duration. The factor is set to 0.12 for the 3day reduction curve.
For example:
 Reduced 3day Log Depth = 0.9519 in
 Reduced 3day Depth = 8.9514 in
 Reduction Factor (3day for 254.52 square mile watershed, TP40): 0.9413
 Unreduced 3day Depth = 9.5100