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Analyzing the "First Inch"

Runoff or rainfall?

Regulations regarding the "first inch" are a common source of confusion.  First and foremost, you must determine if the regulations address the first inch of runoff or the first inch of rainfall.  When using the SCS runoff equation, the first inch of rainfall will produce little or no runoff, depending on the Curve Number.  Therefore, any "first inch" rule applied to the SCS method should address runoff.

If the regulations address the "first inch" of rainfall, it is likely that the writer was considering only the Rational method, which translates all rainfall into runoff, so the two volumes are always the same.  Unfortunately, it is not uncommon for regulations to contain such inconsistencies.

Note: In recent years it has become more common for stormwater regulations to address the more precise Water Quality Volume instead of just the "first inch".

Determining the event

Next, we must determine if the regulations are requiring that we examine:
    1) An event that produces one inch of runoff, or
    2) The first inch of runoff from some larger event.

In case #1 we must determine the rainfall depth that produces one inch of runoff.  In the case of a homogeneous watershed, this is readily calculated with the SCS runoff equation.  However, since different CN's will produce differing amounts of runoff, the "first inch" from the overall site represents an average from all subcatchments, and is not as easily determined.  One approach is to apply a "first guess" rainfall (perhaps 2-3 inches) and examine the total volume of runoff from the site.  Dividing this by the total area will yield the average runoff depth.  The rainfall depth can now be adjusted until the desired "first inch" of runoff volume is obtained.

Note: To determine accurate hydrograph volumes, it is critical that the proper time span be used.  The span must begin before the earliest runoff, and end after the latest runoff, otherwise the volume will be limited to the flow within the specified time span.  This will typically require a time span of at least 5-25 hours.

Knowing the required rainfall depth, it is now possible to model the implied event and assess specific requirements, such as detention.

Case #2 is somewhat easier, in that the total rainfall depth is directly specified.  In this case, the "first inch" of runoff is readily converted to a volume by multiplying by the total area of the watershed.  Detention or other calculations can now be performed based on this volume.

"Detain the first inch for 24 hours"

Next we must determine the exact detention requirements of the applicable ordinance.  This is sometimes worded as "detain the first inch for 24 hours".  As discussed above, this generally means the first inch of runoff, but exactly how is the 24 hours to be measured?  It makes no sense to measure from the start of a 24-hours SCS storm, since the runoff often doesn't begin until about 10 hours.  Perhaps we should measure from the peak of the pre-development hydrograph?  Again, careful reading and interpretation of the regulations is called for.

Assuming we've determined the start of the 24-hour detention interval (To), what conditions are being required at the end of the interval at To+24 hours?  If the regulations simply require that some discharge be detained until this time, we could detain just enough to supply a 1" pipe, but this clearly would not meet the intent of the regulation!

Hopefully your regulations are more specific in defining these requirements.  If not, don't hesitate to re-read the regulations or ask for clarification.

Measuring time-volume relationships

After sorting out the regulations, your task will probably come down to determining the volume of a hydrograph between specific points in time.  Although HydroCAD calculates only the total volume of a hydrograph, there are several ways to determine the volume between specific points in time.

The most obvious approach is to manually integrate the hydrograph by summing the values over the desired interval and converting the units.  This approach is accurate but time-consuming.

It would also appear possible to restrict the HydroCAD time span to the appropriate interval, and then use the "total" volume that results.  The problem with this approach is that all runoff occurring before the time span will be excluded from the calculation, which in turn will cause the volume within the time span to change!  (As noted above, to get accurate runoff volumes, the time span must start at or before the earliest runoff!)

The recommended solution also involves adjusting the time span, but only the end of the span is adjusted.  The beginning of the time span remains fixed to capture the earliest runoff.  In this approach two HydroCAD runs are performed with different ending times.  Taking the difference between the "total" volume for each run yields the volume between the two desired times.

Other ways to mandate detention

Click for complete self-training materialsAs this discussion makes clear, apparently simple detention regulations can in fact be quite complex to implement, particularly when the analysis is being performed with a full hydrograph routing model, such as HydroCAD.  There is also a risk of differing interpretation and application of the rules.

When the intent is to provide for a specific settling or neutralization time, a better approach is to require a detention time that is based on a numerical analysis of the pond's inflow and outflow hydrographs.  This can be accomplished by using specific detention time calculations.

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