I've got GPS nearshore bathymetry/beach topography sand elevation data from the backbeach out to 8 meters depth, with 1 m spacing in the cross-shore, 100m spacing in the alongshore, and stretching multiple kilometers of coast. I have interpolated the data using a couple different interpolation schemes. We have many many elevation surveys over time (~300 or so), but at the moment I am only interpolating each survey in space. One interpolation method I use is objective mapping (despite the fact that my data set violates many of the assumptions that objective mapping requires - beaches don't have nice statistics!)(adsbygoogle = window.adsbygoogle || []).push({});

ftp://brigus.physics.mun.ca/pub/zedel/P6316/2011/bretherton_davis_fandry.pdf

(objective mapping is similar to kriging)

and the other interpolation method is a scale controlled linear smoother

http://www.sciencedirect.com/science/article/pii/S0025322702004978

Both of these interpolation methods give me an estimate of errors due to the interpolation and GPS RMS errors. We also have GPS bias that we need to account for.

Ultimately I want to use the interpolation maps to estimate a time series of sand volumes on my beaches. The problem is that the errors add up pretty quick in these volume estimates and I have to be really careful when interpreting these curves! I need to do as best I can to estimate the error bars on my volume time series so that I can figure out what is signal and what is noise! (ps- It looks like there are some really interesting long term erosion and accretion trends in my data set. I have many ideas I want to try in order to figure out where the sand is going and come from!)

My question is how do the error estimates from the elevation interpolations add up in a volume estimate?My guess is that a simple sum might overestimate the errors. I also anticipate that I will need to treat the interpolation/measurement RMS errors differently than the measurement bias?

(Real data is not pretty so I will just need to pick the best possible method even though I'm certain it won't describe my data perfectly!) Thanks in advance for the help!

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# Accumulation of errors

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