SCS Dimensionless Unit Hydrograph

Okey, it’s been so long since i didn’t write anything in this “anything” web blog, since i pretty busy on doing anything. I am now living in Japan, by the way. Yea, i think i am kind of adjusting my daily life, due to time difference (that now we’re having night time longer, which means my praying time is also different than it used to be). Ah, by the way, this morning i’d like to talk about hydrology to memorize what I’ve learnt before coming to Japan (I am now studying coastal engineering).

What I’d like to discuss is about SCS Dimensionless Unit Hydrograph, which is one of the approaches to synthesize the hydrograph in a watershed, when there is no information about the discharge in it. The unit hydrograph itself, simply defined by the hydrograph which is resulted from a 1 mm precipitation in 1 hour. Ah, I’ve written about this here.

One of good sources of hydrology online manual is here , in the txdot online manual, the unit hydrograph is defined as:

“A direct runoff hydrograph produced by 1 unit of excess precipitation over a specified duration. For example, a 1-hour unit hydrograph is the direct runoff from one unit of excess precipitation occurring uniformly over one hour.” (source)

The SCS Dimensionless Unit Hydrograph is pretty popular in Indonesia, especially when the discharge data is very limited (well, maybe because in most cases it is limited). Otherwise, another approach, such as HSS Gamma-1 (well-suited in Java island- was developed in Java) will be applied.

Before calculating this dimensionless unit hydrograph, the following parameters need to be obtained:

1. Initial abstraction (Ia), or the losses. to calculate this parameter, we need information about the landscape to define its Curve Number (CN). Here we can find more information about the Curve Number: Engineering. Purdue, this blog, this article, or many other sources. Nevertheless, since hydrology is a “localized natural science”, which is differ due to its natural physical condition, result from a local study might be better to be used. (By the way, this webpage is my favourite explanation about SCS-CN).
2. Hourly rainfall.  This parameter is calculated according to the watershed’s characteristic, and ABM theory can be applied.
3. Effective Rainfall (Peff). As the losses/ initial abstraction (Ia) has been calculated, effective rainfall can be computed using those parameter and the hourly rainfall.

Now, the unit hydrograph can be calculated. There are only two parameters needed:

1. Peak Time, Tp = TL + 0.2TR (Tp = time to peak, TL = lag time, TR = rainfall duration)
2. Peak Discharge, Qp = 0.278. A. Peff/Tp, here, the Peff is the total effective rainfall.

However, these formulas are varied according to its location. It is suggested to look up researches in surrounding area and select the proper formulas based on the similarities in the physical properties of the watershed, such as, the overland slope, the coverage, geological condition, etc.

Here is the simple example of the SCS Dimensionless Unit Hydrograph.

SCS hydrograph (and the table)

Here, is the simple Ms. Excel file for the calculation (download). In the excel file, i used VLOOKUP formula. Nevertheless, it might be better to use the “forecast” formula:

(=FORECAST(NewX,OFFSET(KnownY,MATCH(NewX,KnownX,1)-1,0,2),OFFSET(KnownX,MATCH(NewX,KnownX,1)-1,0,2)))

why? because when the “t/tc” is not exactly as it is in the original table, we can automatically interpolate the value for “q/qp“.

That’s all for today, let’s discuss…!!

がんばりましょ。。。！！！