# Is there a method to determine the runoff for arid areas in developing countries?

Note: this question was totally rephrased and expanded on, addressing the comments and questions posed to the first version.

The de-facto standard source for runoff calculations in South Africa is the "SANRAL Runoff Manual" (http://www.nra.co.za/content/Drain5.pdf)

I need to design a weir for a small earth dam in an arid area with a small (smaller than 200 ha), fairly flat catchment area in southern Africa. The idea behind the dam is to collect not more than 10 000 cubic metres of water for small stock watering purposes for the immediate time after the rainy season, somewhat reducing the dependency on ground water.

To design the dam wall and the spillway, one needs flow data through the catchment area in question. The rational method provides this formula: $Q=\frac{CIA}{3,6}$              ...(3.8)
where: $Q \hskip{1.5em}=$ peak flow (m3/s)
$C \hskip{1.7em}=$ run-off coeficient (dimensionless)
$I\hskip{2em} =$ average rainfall intensity over catchment (mm/hour)
$A \hskip{1.7em}=$ effective area of catchment (km2)
$3,6\quad =$ conversion factor

In arid areas rainfall events often are thunderstorms of fairly short duration, often less than an hour. These events are separated by long dry periods. Rainfall is generally measured on a daily basis. These recorded values are daily rainfall values, but they say nothing about the duration of the rainfall events.

Rainfall intensity is determined by dividing rainfall by the duration of the rainfall event. Thus, the shorter the rainfall event, the higher the rainfall intensity for the same amount of total rainfall. But since rainfall is not really measured by the second, minute or hour it is impossible to accurately determine rainfall intensity in areas where the rainfall events are short. In fact the margin for error increases tremendously as the duration of rainfall events decreases.

Using rainfall this data (with a large margin of error) for large catchment areas is not recommended, since the rainfall does not have a "temporal distribution for at least a duration equal to the time of Concentration" (page 3.17). Q would be over-estimated and thus dams and spillways would be over-designed.

The opposite is true for small catchment areas, where the time of concentration is less than the duration of a rainfall event. The margin of error in the rainfall intensity calculation will become unacceptably critical. Especially for very small dams they will either be under designed, or they will be financially unfeasible.

Is there an alternative method to determine runoff in arid areas, where rainfall events are of short duration and accurate rainfall data (rainfall and duration of rainfall events) is not available?

• @mart ... your 'cigarette box calculation' is very far from what the hydrological approach is. You did not take into account topography, evaporation, percolation etc. Also, catching the entire rainfall is unfair for downstream communities, thus a percentage must be allowed to pass. Dam design is not that easy :) – NamSandStorm Apr 22 '16 at 10:27
• the problem is that I need to establish the 50 year, 100 year and 150 year floods in a perennial river where there is no data available, except rudimentary daily rainfall and a topographical survey. To design the dam height and spillway, you need the runoff. "The rest" doesn't help me. The rational method for this area gives me excessively high values which don't make any sense. – NamSandStorm Apr 27 '16 at 15:11
• So your problem is the lack of accurate data (50yr, 100yr, 150yr) and not the method used. As @air mentions, you are stating that there is a problem with the method when you aren't sure of your input values. – hazzey Apr 27 '16 at 21:00
• Let me rephrase the question then ... – NamSandStorm Apr 28 '16 at 7:05
• @mart This is already cross-posted on earth science and being on-topic somewhere else does not make it off-topic here. Dam and weir design is very much an engineering concern. – Air Apr 28 '16 at 16:16