Calculating Discharge, or Hello Rational Method (A Brief Explanation of Simple Hydrology and What It Is Exactly I Do At Work)

My boss came up to me the other day and asked me to help him with a project.  A certain site is having some flooding issues, partially because it was not constructed per recommendations, and now the city is looking to fix it (I think).  Anyway, my boss asks me to calculate the flow at a few different points and how deep the water will be during certain storm situations.  No big deal.

But then, when I start explaining to Keisha about what I'm doing, I realize how complicated things are to someone unfamiliar with hydrology.  It's simple to understand what flow rate, or discharge, or runoff, is: the amount of water (volume, like gallons or feet cubed) flowing over a set point in a given amount of time (seconds, minutes, etc.)  But how does one calculate these flows? 

There are several different methods for calculating discharge, but one of the most commonly used and widely accepted methods is the Rational Method.  The Rational Method is ideal for relatively small drainage areas, under 200 acres.  Stated simply, the flow rate (Q) is equal to the intensity of rainfall (i) times the drainage area (A) times the runoff coefficient (C), or Q=CiA.  And that is the basic formula I use to calculate flows, but coming up with the three variables is sometimes taxing.

The simplest piece of data to calculate is the drainage area.  At the MLC, this is done by using the software MicroStation, a drafting program used for map work.  Land surveyors collect the actual data and give it to a technician that imports it into the program and converts it into maps.  Using the generated contour lines, I then create outlines of the various watersheds, and then it's simply a matter of selecting the watershed to measure the area.  Other methods may require use of aerial photography or USGS quad maps to figure up areas, but more often than not, I can get all I need from the field surveys.

The next piece is the runoff coefficient C.  This value can range from 0 to 1, or from extremely pervious to water-tight.  This number is based on the land types.  For example, if there is a lot of pavement in a drainage area, then the runoff value will be high; conversely, if the site is mostly farmland or fields, the value will be low.  An weighted average C value is chosen for the site based on the total drainage area.

The last thing needed to calculate discharge is the rainfall intensity.  Like there are various methods for calculating runoff, there are many ways to figure up rainfall intensity.  At the MLC, the Intensity Duration Frequency (IDF) curves/equations are used.  Rainfall is not evenly distributed over any area, and this makes getting a reliable i value an odd thing.  For example, it may rain 2" at your house, but where you work there's not a cloud in the sky.  This stochastic characteristic of rain is always fun to deal with.

The IDF method is simple provided you know the time of concentration (the time it takes for the farthest drop of rain, once it hits the watershed, to drain to the outlet, from point 1 to 2 on the map to the left).  However, calculating Tc requires several pieces of information, all of which primarily deal with how the physical properties of the land.  There are two primary types of flow: overland flow (water that doesn't flow in channels), and channel flow.  The overland flow time is pretty easy to calculate, requiring you to know the length of overland flow, the precipitation value for a certain storm, and the slope of the ground.  Using an ugly formula, you can solve the overland flow time, To, quite easily.  If only channel flow time were so.

Channel flow requires much more of the engineer.  Manning's Equation is used to get a velocity of flow going at bankfull.  This is where things get hazy, as bankfull is typically estimated by looking at channel cross-sections in MicroStation.  And some channels may stretch for thousands of feet, changing scores of times from start to the outlet, thus requiring you to come up with an average value to use for the bankfull data.  Once these numbers are known and Manning's Equation is used, the channel travel time, Tt, can be found using a simple formula.  Finally, adding together the overland flow time and the channel time, the time of concentration is solved by Tc = To + Tt.

As stated above, the IDF equation is easy to use, needing only the time of concentration, which is now available.  The equation is i = A0*Tc^(A1+A2*ln(Tc)), where the A values are obtained depending on which zone of influence you are working in, i.e. look these values up in a table.

Finally, now that the three pieces of data are gathered, the discharge can be calculated for the needed storms.  These flow rates are then used to solve the depth of flow by using either Manning's Equation and solving for depth, or in the MLC's case, another computer program, this one DOS based and lacking a GUI.

So there you have it.  Sometimes things get frustrating because I have to "guess" on certain pieces of data, like the channel characteristics, and my confidence in my "guesses" is not always high.  But other than that, it's really not that difficult.  This is just one of the many exciting things I get to do at my job.