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I have a dataset of dissolved load (major and trace elements), the associated error is specified as <10% for all the cases, in the same way I have rock analysis (major and trace) with the same analytical error. I applied a very simple model (forward model) in order to apportion the dissolved elements into different sources (basically rain, silicates and carbonates), this model uses the elemental ratios in each source and basic arithmetic operations to sequentially subtract from the river chemistry data the partial contributions from each source.

The results are the specific contributions from each source to the overall river chemistry, for example in my case, the silicates contributed with 65% of the dissolved load, carbonates 30% and rain 5%.

I am looking for a way (method) to express the uncertainty in this analysis, I have checked some basic error propagation equations, but since no function is defined specifically, I have no clue how to propagate the error. Since all the data I am using has the same analytical error: <10%, I will assume 10% for all the samples. How can I proceed?

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    $\begingroup$ I'm a bit confused. If you have a mixing model with elemental ratios from each source and basic arithmetic, doesn't that define your function? $\endgroup$ – haresfur Jul 11 '16 at 0:36
  • $\begingroup$ Indeed, but it does not define a unique function, since I have a sequence of operations, for example I first determine the rain contributions, then the silicate contributions and finally the carbonates contribution. $\endgroup$ – Marlon Calispa Jul 11 '16 at 8:09
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    $\begingroup$ Seems like you should just propogate the errors for each step sequentially. $\endgroup$ – haresfur Jul 12 '16 at 3:06

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