A Question Regarding Mononobe Rain Intensity Theory 2

[kirei17]

HI!

This is probably just a simple question.

I have a question, i hope someone has the answer quickly
in mononobe rain intensity equation, we have I = R24/24 x (24/t)^ (2/3)
if i take R24= 1 unity, i have an intensity of 0.347 R24 if duration of rain is 1 hour and 0.042 if duration of rain is 24 hr

My question is, how do you understand this?
if this rain extend for 24 hour then the amount of rain is 0.042 x 24 = ~ 1. in my understanding, the rain intensity is linear/ stagnant and the rain last for 24 hour

But if i apply the same logic, if the rain only last for 1 hour, the amount of rain in that hour is only 0.347 or 34.7% from R24 that we usually interpret as daily rainfall for x return period. So where does the rest (0.653 unity) rain go? The rain for that day only last for 1 hour , right?

Is there another 1.88 hour of rain (i get this from 0.653/0.347) that happens in that day that happens in different time? let us say, 1st rain happen during 1 am to 2 am then there are other rain that happen lets say 3 pm to 4 pm and another one at 7 pm to 53 min pass 7 pm (this is 0.88 hour) ? Is this how you interpret the mononobe theory? So what is the concept of t (duration of rain), if the understanding is like above. It means the rain isn't really last for 1 hour. Just the longest duration of the highest peak of rain which is 1 hour. There is assumed to be another one or two hours inn that day in which the rain also happens but perhaps with the same or lower intensity of rain. Does my understanding correct? I don't really get it.

Thanks in advance.

 

[1503-44]

Rain intensity is reduced as the duration increases. It is not linear.

https://iibec.org/rainfall-intensity-changes-over-time-have-the-codes-kept-pace/

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[IRstuff]

Rain isn't exactly a well-defined continuous function, a single equation cannot possibly describe the myriad of potential cloud/rain conditions. The equation is a statistical abstraction, simply saying that a statistically likely 1-hr rainrate can be inferred from the 24-hr rainrate; just consider that the same resultant 1-hr value can be determined from a storm that drops the same rainfall over 12 hr or 24 hr, since that results in the same 24-hr total.

Note that this is all empirical analysis of a chaotic system

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[kirei17]

@1503-44
And? I'm aware of this. Why i said linear comes from the result from Mononobe theory itself. Please read again this passage
"if this rain extend for 24 hour then the amount of rain is 0.042 x 24 = ~ 1".
If 0.042 is a peak value, then the R24 can't be unity (1), it'll fall below that.

@IRstuff
I get what you mean. But what i am trying to confirm is if the duration (1 hr) in Mononobe doesn't really mean as total duration of the rain in that day. Could mean the just the 'storm' duration which is one hour, but the total duration itself is more than 1 hour. But how do you comprehend this with 24 hours duration (t= 24 hours)? Is the storm duration itself is 24 hours? While we know it isn't exactly that big to be called a 'storm' itself.

I may misinterpret what the original founder of the theory (Mononobe) mean, and that is what i am trying to elaborate from those here who understand more about his concept. Despite many nations and regions have developed their own IDF, Mononobe concept, together with others (Sherman, Talbot, Ishiguro), is still a widely used tool to help with areas that has less informative, ready to use, data, especially if what we seek is only the peak intensity value.

Still thanks anyway for your kind input, guys!

 

[IRstuff]

see: Evaluation of Rainfall Temporal Distribution Models with Annual Maximum Rainfall Events in Seoul, Korea

TTFN (ta ta for now)
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[1503-44]

If I plot both your equation and the table values in Excel, trend the lines with a power function and ask for the equations, there isn't much difference.
Your equation: y= 8.3212 x^-0.667
These are for the table values for a 1 Yr return period event and a 2 Yr return period event.
y= 7.211 x^-0.504
y= 8.8319 x^-0.508

We should be on the same page.
Maybe I don't understand your question. Can you rephrase?

My understanding of this is ...
Each event only happens over a stated time. A 15m event only lasts 15min. Then it's done, probably for the rest of the day, maybe for the rest of the week.

The rainfall of a 2 year return freq 15 minute event is 2.81"/hrs, but it only rained 15m. The rain event lasts 15 min. and dumps 2.81"/h x 0.25 h = 0.59" of rain. If that event happens in a day or in a week, it only rains 0.59".

If that event happened twice in one day (it would be unusual), and the total amount of rain for that day would be 0.59 + 0.59 = 1.18".

Are you OK with that explanation?

If you want to know how much it is likely to rain in a day, then we need to find a chart that shows the intensity in inches/hour for a 24 hour event with the return period of interest.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[1503-44]

OK, so I found the data map for a 24h rainfall event with a 100 year return period for Texas.
That's probably for a Category 5 hurricane.

For Houston it is 17" per day. Please note that is total rainfall over 24hrs. It is not rainfall intensity in inches/hrs. If you want to average that you can get an average hourly rainfall intensity of 17"/24h or about 3/4" inches/hr. 0.75 x 24 = 18" of rain in 1 day. But, IMO, you cannot use that average value for anything but useless information. If you have a 1 hr rain spec, you need to find a map of 1-hour rains with the return period of interest.

https://www.noaa.gov/media-release/noaa-updates-texas-rainfall-frequency-values

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[TerryScan]

After a brief search of the Mononobe rain intensity equation, I believe there may be misunderstanding in terminology. One reference refers to "t" in the equation as "lag time of flood" (time of concentration) rather than rainfall duration. This makes sense since intensity (peak flow) is higher for smaller Tc. The overall event volume does not change for the entire event duration.

 

[1503-44]

Time of concentration depends on the stream characteristics of the runoff flow path and has nothing to do with rainfall intensity. It only defines the time that rain runoff water volume arrives at a given point on the flow path. Depending on how far down the path that point lies, it could be days after the rain event has ended.

Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[TerryScan]

Time of concentration depends on the stream characteristics of the runoff flow path and has nothing to do with rainfall intensity. It only defines the time that rain runoff water volume arrives at a given point on the flow path. Depending on how far down the path that point lies, it could be days after the rain event has ended.

Actually, when it comes to hydrology, intensity does refer to rainfall runoff where it collects at a specific location and time of concentration is typically a main component.

From Texas DOT manual on Rational Method (

http://onlinemanuals.txdot.gov/txdotmanuals/hyd/rational_method.htm#MLHHKGHG):

Rainfall Intensity
The rainfall intensity (I) is the average rainfall rate in in./hr. for a specific rainfall duration and a selected frequency. The duration is assumed to be equal to the time of concentration. For drainage areas in Texas, you may compute the rainfall intensity using Equation 4-21, which is known as a rainfall intensity-duration-frequency (IDF) relationship (power-law model).

From article using Mononobe formula (file:///C:/Users/SCAT/Downloads/Utilization_of_a_pond_in_East_Jakarta_for_a_sustai.pdf), section 2.4 (page 3 of PDF):

2.4 Rainfall Intensity Analysis
To determine the planned flood discharge of this reservoir, it is necessary to obtain the bulk intensity
value. Rainfall intensity is the height of rainfall that occurs at a time period where the water is
concentrated [3, 4].)
(see PDF for complete text and formula reference with time of concentration.)

 

[1503-44]

It's still not the same. Refer? " is typically a main component."? "The duration is assumed"?
"You may compute"? What's all that really mean?

Like I said, the formula is
Rainfall intensity X catchment areas X time of concentration X runoff coefficient = runoff volume.

Time of concentration, catchment area, travel time of your flow path (lag time of flood stage), can be 0 to infinity and if the catchment area is larger than your storm size, you will have a bit of trouble with your TX method. That only works for small areas with concentration times less than the rainfall duration.




Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."