I performed this calculaton for 30 years while managing the dam safety program for the state of Ok. We used the average end area method when we could find contour maps. Yoyu have to remember that your survey or your input data will determine the accuracy of your study. In the early days of the inventory of dams when we were trying to determine the size of a lake or pond, we would take the depth at the dam, usually the top of the dam because we were trying to clculate max storage times the surface area at the top of the dam and then divide by 3. This turned out to be very accurate when compared to both Federal and state dam projects in Oklahoma. In fact it was prescribed in the early days of the inventory by the Army Corps of Engineers.
I used to perform dam breach analsyses and predicted 2 such later events within .5 ft of the actual flood level. Luckily my calculations were .5 ft higher than the occurrence.
Always remember we engineers work on averages, head in the oven, feet in the freezer, crotch is warm....
Also, you are measuring this with a micrometer, but cutting it with a chainsaw!!!!! Just because we have 5 digits right of the decimal does not mean we have to look further than the first one.
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