I have a quantity that is calculated with two measurements, but I only have a tabulated standard deviation for one of the measurements. How would I calculate the error on the calculated quantity? The form is as follows: $\frac{a - b}{b}$. I have an std on $b$.
The problem is that I'm not sure how the standard deviation of $b$ is calculated. Both $a$ and $b$ are ozone measurements, but one is done with a ground-based instrument and the other is done with a satellite. The ground-based data has a cataloged std. These measurements are daily. The satellite data does not have an error estimate. I wonder if I should calculate my own estimate of the error on the satellite data or only use the cataloged std for the combination (relative difference) of $a$ and $b$? Because of seasonal variations in the data, I don't think I can just use all the data (or even one year) to estimate a standard deviation.
The ultimate goal is to put a $\sigma$ error bar on the relative difference of $a$ and $b$. Right now I'm just using the given std as an error bar and the results look okay, but I can't justify this approach. To give you an idea, my error bars are shown below. I find similar figures in this validation report, but the errors are not discussed in depth.
Any tips are greatly appreciated!