# Time of concentration - Difference between large and small basins

I am looking for any academic reference (i.e. articles) regarding the time of concentration for large and small basins.

E.g. I would expect that a large basin (area > 1,500 km^2) will flood (or reach its max peak flow) later in time (e.g. 1-2 days later) when compared to a small basin if the same amount of rain will fall in both of them.

• Assuming any river basin will flood given sufficient rain, it sounds as if you are asking for the 'time of concentration', for which there are many different equations. So the problem boils down to 'what is the time of concentration for a given length of flow, climate, land use and physiography. One might write a book on such a complex problem, but as far as I know, no such book exists. – Gordon Stanger Oct 24 '16 at 8:59
• yes, exactly! :) any particular reference on the matter? – no_one Oct 24 '16 at 9:03

This is a difficult question since time of concentration ($t_c$) can in theory, vary substantially, for two basins of equal size.

Off the top of my head, I can imagine several other variables that would be necessary to determine $t_c$: drainage density, basin relief, basin length, surface roughness (Mannings coefficient), and rainfall statistics. There's certainly others too.

I found a paper titled The characteristic time scale for basin hydrological response using radar data is freely available. There is a discussion of $t_c$ beginning on page 93 at bullet point number 2. They cite other papers in their discussion that would be worth tracking down and reading.

Note they present an empirical equation for $t_c$:

$$t_c=5.4\left(\frac{L}{S^{0.5}}\right)^{0.75}$$

L is basin length, and S is slope/relief. It's weird, yet I'm not surprised since it's empirical. Evidently the 5.4 has dimensions of $time$ and $length^{-0.75}$. It's hard to imagine that this equation would actually be useful.

Unless you're needing specific methods for application purposes, the justification you're providing is clear and wouldn't require a citation. Maybe this is a homework question?

Some rambling thoughts:

Larger watersheds typically have a larger time of concentration. Where things becomes tricky for larger watersheds is that assumptions around rainfall distribution may break down. For example, a really really large watershed may only receive a 100-year storm in the lower or upper reaches of that watershed. So, there's that to consider. If you're looking at a specific watershed, check out some reflectivity data to gauge spatial variability of rainfall .

In the US, you might look for USGS-based studies for your area of interest as a starting point. For a large river with a time of concentration approaching days, many of these are gauged and therefore, you may be able to research that area specifically.

For small, urban time of concentration calculations, some standard references for engineering applications are the National Engineering Handbook, Part 630 for hydrology  , or the NRCS TR 55 text . These types of applications usually calculate time-of-concentration using velocity-based methods, which are tied-to rainfall intensity.