River discharge (typically given the variable Q) is defined as volume of water per unit time. The volume component of discharge enables volume calculations, and I wondered if I could easily calculate Tempe Town Lake’s volume from stream gage data. The Lake’s dam ruptured on July 20, 2010, sending the entire contents of the lake down the Salt River as a flash flood. The Priest Drive stream gage is located on the Salt River about a mile downstream of the dam, and data from this gage indirectly provides the total volume of floodwater, and the volume of the lake. The volume of water passing the gage during the flood event should equal the volume of water that drained from the lake.
One could potentially fit a mathematical curve to a hydrograph and calculate the volume of floodwater using calculus, but the margin of error in the stream gauge measurements make such a rigorous analysis unwarranted. Instead, I used a simpler method that involves dividing the flood into time intervals, calculating the volume of floodwater for each interval, and producing a total flood volume by adding the volume for all intervals.
The Priest Drive gage measured river stage every 5, 10, or 15 minutes during the flood event, and converted stage measurements to discharge using a stage-discharge relation curve (I am not sure why the gage did not record at regular intervals during the flood, but perhaps it had to do with the flood event necessitating shorter intervals). I downloaded the discharge data for the Priest Drive gage from the US Geological Survey website for July 20 and 21, 2010, and used those data to calculate the volume of Town Lake.
The discharge during each interval is equal to the average discharge multiplied by the interval length. SInce discharge is only reported every 5-15 minutes, the average discharge for the interval is equal to the sum of the discharges at the beginning and the end of the interval divided by two, or
Q(int) = (Q(begin) + Q(end)/2
Multiplying the average discharge for the interval by the time length of the interval determines the volume of water to pass the stream gage during that interval:
Q(int) * T(int) = V(int).
The total volume of the flood event is the sum of the volumes of the individual intervals, or
V(total) = V(int1)+V(int2)+V(int3)…
Knowing all this, I set up a spreadsheet in Microsoft Excel to calculate the flood volume. First, I needed to know when the dam broke, and when the entire contents of the lake had drained. Local news reported the dam break at approximately 9:45 PM, and this event is apparent in the data as elevated discharge occurred at 9:55 PM. Local news also reported the lake was not completely drained the next morning. At about 3 PM on July 21, the gage reported an increasing discharge, possibly do to a precipitation event. I chose 3 PM on July 21 as the end of the dam burst flood, as this represents the lowest discharge value prior to the onset of increased discharge from another source. At 3pm on July 21, the measured discharge was still slightly higher than just prior to the dam rupture, so it is possible the lake was not completely empty by that time.
I also wanted to eliminate discharge contributions from any other source besides the dam failure. The baseflow of the Salt River prior to the dam break was about 20 cfs, so I subtracted 20 cfs from all discharge measurements. This ensured that I was not adding normal baseflow volume of the river to the total released from the lake.
Calculations from the Priest Drive stream gage measurements reveal the volume of Town Lake is 3,048 acre-feet, or about 133 million cubic feet. This value is extremely close to the 3,065 acre-feet of water reported to initially fill the lake, and the approximately 3000 acre-feet volume reported by the city of Tempe (click links for sources).
Both the hydrograph of the flood and the cumulative volume of water released during the flood are plotted on the same graph. As you can see, almost 75% of the lake water drained in the first two hours after the dam break.
The agreement between the calculated and reported volumes of Town Lake demonstrate this method’s usefulness in calculating flood volume from discharge data. The results also demonstrate the accuracy of the Priest Drive stream gage, and the accuracy of the stage-discharge relation curve.