IsoReduce and isotope reduction - UofU-Cryosphere/IsoReduce GitHub Wiki

This wiki explains the basic theory behind the reduction of raw Picarro isotope data in the IsoReduce software. It further provides the documentation and best practices for how to operate and use the software in your research. Note that the equations in this wiki are rendered using the Code Cogs website.

Principle of isotope reduction

The main idea behind isotope reduction is to take all the measurements from a sample (multiple measurements per injections, multiple injections per sample, etc.) and reduce those into a single measurement per sample. This involves a number of error corrections which must be accounted for to generate unbiased results. IsoReduce corrects for inter-injection memory, intra-run measurement drift, and systemic isotope biases using in-lab isotope standards. Another advantage of the data reduction and corrections in IsoReduce is the ability to use fewer injections while still generating accurate and precise results. Using this software, you can use 5-6 injections with what would sometimes take double that with the default Picarro settings (i.e. simply throwing out the first 3-6 injections and averaging the remaining ones). I will briefly describe the theory behind each of the three injection corrections in IsoReduce.

Memory correction

Due to the nature of cavity ringdown spectroscopy, a given injection's value will be influenced by the preceding injection values. IsoReduce uses two methods to correct for this. The first is a geometric mixing model. This assumes that the current injection's measured value \delta_i is a geometrically-weighted sum of the sample's true value \delta_T and it's previous injections.

\delta_i = \frac{1}{\mathcal{F_N}} \left( \delta_T + \sum_{k=1}^n r^k \delta_{i-k} \right)

where r is the decay rate of the memory effect, k is the number of components in the mixing model, and \mathcal{F_N} is a normalizing factor based on the number of injections

\mathcal{F_N} = \sum_{k=0}^n r^k

The equation for the true isotopic value therefore simplifies to

\delta_T = \delta_i \sum_{k=0}^n r^k - \sum_{k=1}^n \delta_{i-k}

The current version of IsoReduce assumes a 3-component mixing (the true injection value and the 2 preceding values so k=3) and a decay ratio (r) of (1/2).

This geometric mixing model works best for situations where the isotopic values between nearby injections do not vary substantially. If the maximum difference between isotopes is sufficiently large, IsoReduce switches to a power-series curve-fitting routine to perform memory correction. This method benefits from the large spread in isotopic values to produce more accurate results than the mixing model on injections with a predictable

Drift correction

Over time, CRDS instruments values can drift away from previously measured values, even if the true values remain unchanged. This usually has to do with minor differences in the reference laser wavelength or current output. Although one of the primary advantages of the Picarro instruments over other CRDS competitors is the relatively low drift, we still provide corrections for any residual deviations. We do this by comparing the starting, stopping and (if present) intra-run isotope standard values for changes in measured value throughout the run. We then remove the time-interpolated drift effect from all sample injections.

Measurement bias

In most cases, a measurement bias is introduced in isotope value estimates, where the measured values systemically differ from the true values. This is true even when the measurements are sufficiently precise and properly corrected for memory effects and drift effects. We therefore use the measured values of our known isotope standards to standardize the measured values of isotope samples to their true values, relative to the standards used.

This is a test

\delta_T = \delta_i \sum_{k=0}^n r^k - \sum_{k=1}^n \delta_{i-k}