## EXTENDING MINIMUM DETECTABLE FLUX TO HIGH-FREQUENCY MEASUREMENTS

As discussed previously, the MDF metric provides a useful experimental design and quality control criteria for flux measurements. However, it can be extended from the original formulation to show more clearly how increased measurement frequency, as provided by laser-based analyzers, like the Picarro G2508, can further lower the minimum detectable flux.

In their paper, Christiansen et al. (2015) use the raw noise (no time averaging) of the Picarro G2058 instrument as the estimate of the analytical uncertainty. However, this uncertainty metric is not fully-descriptive for instruments that provide high-frequency measurements of gas concentration. In this case, it is arguable that the raw noise should be replaced with a measure similar to the statistical standard error (assuming the noise is approximately normally distributed):

where A_{SE} is a modification to A_{A} in the original MDF calculation (Equation 1) and n is the number of measurements of the gas concentration during the chamber closure period. Note that this standard error approach is a first order approximation for the MDF from high-frequency measurements and that the “true” MDF is a function of the chamber time series fit type as well (i.e. Linear, exponential, quadratic).

where p_{s} is the sampling periodicity (i.e. every 10 s) in hours. This MDF_{SE} metric is equally applicable to instruments such as the GC, as long as multiple samples are drawn during the chamber closure period; however when using these manual sampling approaches the reduction of the MDF is typically significantly less than when using instruments that make measurements with periods on the order of seconds.

Using this new MDF_{SE} approximation, the increased temporal resolution of measurements in laser-based analyzers means that the analytical uncertainty of a GC or similar lab-based measurement devices would need to be better by a factor of about √n in order to yield the same MDF_{SE}, given the same chamber system and deployment period.

Since it is not desirable to deploy chambers for a long period of time due to the disturbance they cause on the soil gas diffusion profile (as mentioned by Christiansen et al.), it is also useful to turn this new MDF_{SE} metric around to show that chambers that are coupled to high-frequency concentration analyzers can be deployed for a factor of √n less time and yield the same data quality as a chamber that is being measured using the traditional techniques (i.e. Gas Chromatography). The other benefit this offers is that users can measure √n more frequently – whether this is more measurements of fluxes across space, or measurements of the temporal dynamics at a single location.

As a more concrete example of the benefits, take the case of deploying a chamber of 0.5 m effective height (effective height is equal to volume divided by surface area) to measure methane fluxes. Assume that is is necessary to measure fluxes of 0.1 umol/m^{2}/s and above for the purposes of the example. From Figure 1, the CRDS system (which measures concentrations about once every 10 seconds) requires a closure of about 15-17 minutes to stay above the prescribed MDF limit for our hypothetical study. The same chamber sampled every 5 minutes (300 s) for GC based analysis (assuming the GC has the same analytical accuracy as the CRDS) needs to be deployed for more than an hour and sampled 12 times during that period to achieve an above MDF_{SE} limit flux measurement.

**Figure 1.** Calculated MDF for a laser-based instrument (i.e. Picarro G2508 CRDS) and MDF curves for GC based analysis with the same precision as the CRDS, but varying frequency of gas concentration sampling (see legend).

From this example it is easy to see that users with high-frequency measurement instruments could either measure more sites in the approximate 45 minutes of time saved by using the CRDS, or alternatively measure the flux at the same position 3 more times to get a better idea of the variability or trend over time.

#### Conclusions

The Minimum Detectable Flux metric, as proposed by Christiansen et al. (2015)and the modifications that have been made in this article offer chamber users a new method to ensure experimental design and quality control criteria are met during greenhouse gas flux measurement campaigns. The MDF and work of Christiansen et al. (2015) also clearly demonstrates the utility of the relatively new high-resolution, in situ greenhouse gas analysis systems in accurately monitoring greenhouse gas emissions from a variety of environments and across a large range in efflux rates.

#### References

Christiansen, J.R., Outhwaite, J., Smukler, S.M., 2015. Comparison of CO2, CH4, and N2O soil-atmosphere exchange measured in static chambers with cavity ring-down spectroscopy and gas chromatography. Agricult Forest Meterol 211(2015): 48-57, doi: 10.1016/j.agrformet.2015.06.004

1. https://www.picarro.com/company/technology/crds

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