Hi,
I am wondering if anyone could me with the topic of 'volume uncertainties'.
Basically, I have computed a relative uncertainty between two DTM surfaces derived from photogrammetry of +/- 0.10m. Now using an area, I can calculate a ‘thickness’ error between the two surfaces to compute a volume uncertainty.
But I have been led to believe as the survey contains thousands of points generated by photogrammetry there is as many points that are +0.10m as there are -0.10m and maybe cancel each other out and approach 0.
Is this where the ‘uncertainty of a mean’ is used? I am confused can someone shed some light on this. I am using approx. 25000 points and a relative uncertainty of +/- 0.10m over and area of approx. 4000m².
Thanks.
Volume calculations are at most an approximate value, to begin with.
The elevations are not exact and no two gatherings to collect the required data will match.
In a nutshell, it is a tool to achieve the best value possible for an amount of dirt or other material that will change in size.
The entire volume is a variable.
Is that 4,000 meters by 4,000 meters (3,950?ñ acres) or 207.5 meters by 207.5 meters (10.6?ñ acres) for us non-metric old fuddy-duddies?
The problem is; there is no?ÿguarantee, the uncertainties, the random errors, will cancel each other out. That's why it's variable; plus or minus.
The report provided, along with volume calculation, should provide the method used to create the surfaces, and the calculations that derived the quantity. Assuring that the reader understands that is a high and low number for the actual size.
This reminds me of a project @Roadhand was working on. A big highway job, somewhere deep in the heart of Texas. He was wondering about the best way to check the accuracy of his equipment. It seems that the Bean Counters figured out that an eighth of an inch of concrete, over the entire project, was worth a million dollars; they wanted someone to provide a quantity, to that accuracy, so that an equitable pay out would be provided. I told him to tell them that a sixteenth of an inch was worth $500,000, why weren't they chasing that? There were some nicer, less condescending answers, that quickly pointed out; it would cost a lot more than 1 million dollars to provide that level of accuracy.?ÿ
Accurate results can be achieved, but it's a tedious, time consuming task and as we all know; time is money.
Yes i agree but im trying to calculate an estimate of uncertainty within the total volume.
right, so you think its fine for me to leave my estimate uncertainty as i have currently calculated +/0.1m?
Why?
Why are you trying to determine this? Is it a part of the deliverable to the client?
I think it should be fine unless the client has stated any other specifications they would like to see.
For a site 40m x 100m, I would just get out the total station and check it. I don't think it is necessary to check it every time but enough to get a good feel for the actual accuracy you are getting.
The thing I have a hard time getting across is the error for each layer compared to the thickness of the volume. If i have 0.10m error in the original layer, then 0.10m error in the final layer, but the vertical difference between the two layers is 10 meters, Then your error estimate would be 2% which is pretty good.
0.2 meter total error when the total average depth of the volume is 1 meter, then your error estimate would be 20%.
?ÿ
Well, 40 meters by 100 meters is about 328 feet by 131 feet, say 43,060± square feet. Not quite an acre.
0.1 meter is about 0.328 feet (4 inches), so ±0.33 feet over that almost-an-acre is 12,920± cubic feet.
That's 478 cubic yards, the usual measure of volume here, or about 50 truckloads.
That close enough for ya?
I'm with JaRo on this one.
SOP for all our photo topo jobs is to check points.
Unless this isn't a job where something is getting built.
?ÿ
To get an accurate check, you need to measure the site with a different procedure and different equipment (our spec's call for equipment 3x more accurate than published accuracy), then calculate the volume with different software and COMPARE results. You will be surprised. I'd expect your quantities to vary by ?ñ4% or more.
At least run the field data through a second software. They all calc volumes slightly different.
I think you should look at your scope of work and reassure yourself that the method used to collect the data and make the calculations meets the expectations of the client.
If it doesn't, maybe you need to rethink your method.
Dougie
Agree with Lee. The only way to get a quantifiable standard error are independent measurements of a higher accuracy, per NSSDA specs.
?ÿ
However, methodology for quantifying the error aside, for the final volume you will be computing the combined error for a sum of quantities.
If there is a 0.1m vertical standard error in two 4000m2 surfaces, that is a 400m3 standard error in volume for each. The difference between them is a sum (subtract one from the other).
The combined error of a sum is the square root of the sum of the squares of the standard errors, which yields approximately 566m3.
