Gamma unit hydrograph in HydroCAD

[pinkpig]

Under Gamma unit hydrograph in HydroCAD, I notice that the Y-coordiante is defined as relative intensity. however, in NEH tables of Appendix 16B, the Y-coordinate is defined as q/q-peak.

thus, in NEH Appendix 16B, the maximum Y is 1.0 (at T=TP, or at dimensionless T=1.0) and in HydroCAD tables, the maximum Y is not 1.0 (varying with different peak rate factors).

I am wondering how HydroCAD developed its Gamma unit hydrograph. I think I can understand the tables NEH tables of Appendix 16B (dimensionless X and Y, corresponding to T/TP and q/q-peak) but I have a hard time to understand the HydroCAD Gamma unit hydrograph.

Thanks.

 

[psmart]

The Gamma UH tables are taken directly from NEH-630. For example:

name=Gamma-400
comment=NEH Part 630, Hydrology, Chapter 16, 2007, Table 16B-5
inten=0.0 0.027 0.1244 0.2732 0.4429 0.6081 0.7517 0.8642 0.9421 0.9863
inten=1.0 0.988 0.9555 0.9076 0.8491 0.7839 0.7155 0.6465 0.579 0.5144
inten=0.4538 0.3977 0.3465 0.3004 0.2591 0.2224 0.1902 0.162 0.1376 0.1164
inten=0.0982 0.0826 0.0693 0.0579 0.0484 0.0403 0.0335 0.0278 0.023 0.019
inten=0.0157 0.0129 0.0106 0.0087 0.0072 0.0059 0.0048 0.0039 0.0032 0.0026
inten=0.0021 0.0017 0.0014 0.0011 0.0009 0.0007 0.0006 0.0005 0.0004 0.0003
inten=0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0

When the curve is displayed in HydroCAD, the Y axis is labeled with the "shape factor" K rather than the original peak of 1. The curve is identical, it's just displayed with a different axis representing the peak factor. This allows you to superimpose and compare different curves. From HydroCAD help:

Shape Factor & Peak Factor

The shape factor (K) is a dimensionless parameter that indicates the peak intensity of the unit hydrograph relative to its volume. This value is often (but not always) the same as the SCS shape factor, which is equal to twice the fraction of the UH volume that occurs before the peak. For comparison, both values are shown on the unit hydrograph selection screen.

For convenience, this characteristic is commonly expressed as a peak factor, given by:
PF = C K
Where C is a combined units conversion factor. For traditional SCS calculations:
C = (5280*5280) / (12*3600) = 645.33
So a K value of 0.75 yields a peak factor of 484.

In the end, the Y axis labeling doesn't matter, because the runoff procedures sets the area under the curve (volume) to the volume of each rainfall burst.




Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[pinkpig]

Thank you Peter. How did you interpret the time interval when you translated Table 16-B of NEH to HydroCAD. It seems the interval is not the same for different Peak rate factor on NEH (for example, Peak rate factor=500, the dimensionless time interval is about 0.1; but for peak factor=200, the time inverval is about 0.2)

 

[psmart]

In the HydroCAD UH report, the peak is automatically positioned at a X value of 1, and the x axis has units of relative Tp (time to peak).

In the actual runoff calculations, the x axis is scaled so that the peak occurs at:
Tp = 2/3 Tc.

For details please read about the SCS UH runoff procedure.

http://www.hydrocad.net/understanding.htm

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[psmart]

The Help context for the UH report also gives a pretty complete explanation:

View|Unit Hydrograph
--------------------------------------------------------------------------------
View UH is used to show detailed information about any unit hydrograph definition. You can also use this form to create your own UH definitions.
....
The time scale (shown at the bottom of the graph and as the first column in the tabular report) is expressed as a fraction of the time-to-peak. All UH definitions are shown with the peak occurring at a time value of 1. During actual runoff calculations, the actual time-to-peak is calculated for each subcatchment as 2/3 Tc. The overall duration of each UH (the time base) is a multiple of the time-to-peak, which will vary depending on the individual UH definition.

The mass report shows the time distribution of the UH as the mass increases from zero to a final value of one. During actual runoff calculations, the actual UH volume is determined by the volume of precipitation excess (runoff) from each burst of rainfall.

The intensity report shows the intensity variation of the UH over time. The maximum intensity is often referred to as the "shape factor" or "K" value. Multiplying this value by a coefficient of 645.33 yields the more common "Peak Factor".

For further details read about unit hydrograph calculations and SCS runoff calculations.


Peter Smart
HydroCAD Software

http://www.hydrocad.net