NOAA Global Monitoring Division, Boulder CO, USA

Transcription

1 Efforts to separately report random and systematic measurement uncertainty for continuous measurements in the NOAA Global Greenhouse Gas Reference Network Arlyn Andrews 1, Michael Trudeau 1,2, Jonathan Kofler 1,2, Anna Karion 3, Kirk Thoning 1, Pieter Tans 1, Colm Sweeney 1,2, Kathryn McKain 1,2, Edward Dlugokencky 1 1 NOAA Global Monitoring Division, Boulder CO, USA 2 Cooperative Institute for Research in Environmental Sciences, U of CO, Boulder, CO, USA National Institute of Standards and Technology, Gaithersburg, MD, USA Goal: Develop an objective and flexible framework to fully describe measurement uncertainty, including time-dependence, suitable for application to multiple species and types of analyzers.

2 SPO in Situ Analysis System: Standard Deviation and Standard Error Std error = on 5 minute average (reference gases) Std error = on 20 minute average (air samples) Standard deviation only slightly higher for air samples than for cylinders. Standard Deviation Measurement Uncertainty

3 Atmospheric Carbon Dioxide Dry Air Mole Fractions from the NOAA GMD Tower Network, Version: Sample README Field 12: [MEASURED VALUE] The dry air mole fraction. Missing values are denoted by [9]. Field 13: [MEASUREMENT UNCERTAINTY] The measurement uncertainty estimate (see Section 7). Missing values are denoted by [9]. Field 14: [SYSTEMATIC UNCERTAINTY] The non-random component of measurement uncertainty (see Section 7). Missing values are denoted by [9]. Field 15: [RANDOM UNCERTAINTY] The random component of measurement uncertainty (i.e., analyzer precision; see Section 7). Missing values are denoted by [9]. Field 16: [STANDARD DEVIATION] The standard deviation corresponding to the reported measured value (see Section 7). Missing values are denoted by [9]. Field 17: [SCALE UNCERTAINTY] The scale uncertainty estimate (see Section 7). Missing values are denoted by [9]. Field 18: [ANALYSIS FLAG] A three-character field indicating the results of our data rejection and selection process, described in section 7.4.

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5 Douglas Skoog: Stanford University Professor of Chemistry He wrote the book(s)

6 Douglas Skoog: Stanford University Professor of Chemistry He wrote the book(s) Various editions of the three books were translated into several languages including German, French, Italian, Portuguese, Russian, Croatian, Turkish, Chinese and Korean, and are used throughout the world.

7 Confidence interval represents only the uncertainty of the fit coefficients, so that if the experiment were to be run repeatedly the specified percentage of the resulting curves would fall within the confidence interval se fit = standard error of the fit (i.e. of the calibration curve) The prediction interval describes the range of values encompassing a specified percentage of individual measurements, provided that the measurements have the same statistical uncertainty as the calibration standards (represented by σ y ). σ y = standard error of the fit residuals

8 Confidence interval represents only the uncertainty of the fit coefficients, so that if the experiment were to be run repeatedly the specified percentage of the resulting curves would fall within the confidence interval se fit = standard error of the fit (i.e. of the calibration curve) Implies that error characteristics of unknown samples are same as for standards used to calibrate the sensor

9 Prediction interval versus confidence interval: Regression 95% Confidence 95% Prediction Prediction bands encompass 95% of data (samples and new unknown standards). Confidence bands reflect uncertainty in the curve fit directly related to propagation of errors for fit coefficients

10 Typical regression analysis assumes no error in the independent variable x. This is not hard to deal with. I follow the convention of Skoog and set x = assigned values of standards.

11 Sample application to real world measurements: Implies that error characteristics of unknown samples are same as for standards used to calibrate the sensor

12 Sample application to real world measurements: Implies that error characteristics of unknown samples are same as for standards used to calibrate the sensor Replace with a more general description of the sample uncertainty

13 Model of sample uncertainty: precision baseline extrapolation standard equilibration water vapor

14 + u sens 2 + u nonlinearity 2 + precision baseline drift extrapolation standard equilibration water vapor A more complete model of sensor drift would account for additional terms such as sensitivity (gain) drift and change in response curve (nonlinearity).

15 Reported measurement uncertainty is largest of: Fit residuals minus contribution from uncertainty in assigned values of the standards 67 th percentile of the absolute difference between measured and assigned target values Reproducibility of assigned standard values

16 u tgt, bottom up u M from larger of 9a & 9b

17 Tall Tower Measurement Uncertainty: measurement_uncertainty random_uncertainty standard_deviation scale_uncertainty n_samples u measurement2 = u random2 + u nonrandom 2 u random2 = u p2 + u baseline_random 2 u p = precision u baseline_random = portion of baseline unc that is random over timescales of seconds to minutes

18 Standard Deviation and Atmospheric Variability: Atmospheric variability AV is given by: If the atmospheric variability is not detectable above the random uncertainty (i.e. if SD M < u R ), then AV is undefined.

19 Atmospheric variability: signal in the noise Summer and Winter Hourly Variability at Park Falls, WI January July Sampling Height, m Sampling Height, m Typical tower licor random uncertainty < 0.01 ppm Hourly standard deviation is related to surface flux.

20 Application to historical records: South Pole

21 Case SPO: July 2017 Voltage for each reference gas before and after gain & baseline drift correction Blue = T Black = W1 Red = W2 Green = W3 g & b computed using W1 & W3

22 Here W2 is treated as an unknown: 67.5% of W2 within ppm W1, W3, T & W2 used to generate daily response curves (after adjusting voltage for g & b) Closest response curve in time is used to calculate DMF for each sample and standard W2 is treated like an unknown sample in between response curves Case SPO: July 2017 Continued

23 First attempt at SPO formal error propagation (only for response curve, not for g & b): Estimated measurement uncertainty for one response curve PI = z * sqrt(se fit2 + σ y2 ) Minimum value = First day s response curve has residual standard error: on 12 degrees of freedom --Should it really be 12 degrees of freedom due to multiple runs of cylinders? Case SPO: July 2017 Continued

24 PSA SYO HBA High Southern Hemisphere gradients suggest likely issues in late 1980s and early 1990s: PSA, HBA, SYO minus SPO in situ

25 SPO Next Steps: Work backward in time toward more complicated cases. Target tanks added: Prior to that, mix of on-site standards and working tanks, Boulder laboratory cals and spo on-site cals sometimes inconsistent. Steel tanks required drift corrections and were used into late 1980 s or early 1990 s uncertainty of drift corrections? Earliest spo reference gases were synthetic air, and blend of O2, N2, Ar not always reliable. Pressure broadening corrections were necessary. uncertainty of pressure broadening corrections? If response curve can be shown to be relatively stable, it may be possible to identify problematic tanks more confidently. Possible special issue paper on uncertainty of historical records?

26 Newer technologies next steps: Multi-point calibration for Earth Networks systems (A. Karion, work in progress) Improved estimate of uncertainty in water correction needed (multiple groups)

27 Take home messages: Measurement uncertainty is more than standard deviation. There is signal in the noise. Separation of random and non-random uncertainty is necessary. Measurement uncertainty is not constant over time. Simple algorithms can provide very useful information for future users. Work is underway to characterize uncertainty for modern analysis systems. K. Verhulst, A. Karion, J. Kim et al., ACP, 2017 F. Reum, ACPD, Picarro water correction analysis. Work is needed to document uncertainty for historical records. Inverse modelers need this information (even if they don t know how to use it yet!). Detailed uncertainty quantification is required for confident interpretation of trends and spatial gradients and cannot be neglected in the context of emissions/sink verification such as to support the Paris Agreement.

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32 Mean = , median = , sd Range = to SPO alternative processing, difference from database values.