Recently reported trends of carbon dioxide uptake pose the question of whether trends may be the result of the limited digitalization of gas analysers and sonic anemometers used in the 1990s. Modifying a 12 bit digitalization and the instrument error reported for the Gill R2 and R3 sonic anemometers found elsewhere, the influence of these deficits in comparison to the now commonly used 16 bit digitalization were quantified. Both issues have an effect only on trace gas fluxes of small magnitude, mainly for the carbon dioxide rather than for the water vapour fluxes. The influence on the annual net ecosystem exchange is negligible, because other errors resulting from gap filling routines, for example, are much larger.
Nowadays, data sets from FLUXNET sites are available and many papers have
been published which analyse and compare these data and link them to
ecosystems, phenology, regions, and climate (Baldocchi, 2008; Williams et
al., 2012; Keenan et al., 2013, 2014; Kutsch and Kolari, 2015; Baldocchi et
al., 2016; Babel et al., 2017). Among the factors, which possibly influence
the resulting budgets, is the quantification (digitalization) error (Ifeachor
and Jervis, 2002), arising from the use of a limited 12 bit digitalization of
turbulence data which was the state of the art about 15–20 years ago
(Vickers and Mahrt, 1997). This error could introduce spurious trends (Foken,
2017a) and has, up to now, not been investigated thoroughly. The influence of
the digitalization error on flux calculations is the topic of this short
note. An impact similar to the effect of the digitalization error could have
been caused by the instrument error reported for the formerly used Gill R2
and R3 sonic anemometers (now Gill Instruments Ltd, Lymington, UK) before
the year 2003 (Foken et al., 2004, found by Christoph Thomas, University of
Bayreuth, 2002). The problem was identified when deploying these sonic
anemometers for a relaxed eddy accumulation (REA) system, where the vertical
wind velocity close to 0.00 m s
Carbon dioxide concentration on 2 August 2012 measured with the
LiCor 7500 (orig.) and reduced to 12 bit resolution. The difference between
both signals is shown in
The data used in this study were collected at the FLUXNET site (DE-Bay)
Waldstein-Weidenbrunnen (50
The instrumentation not only at the Waldstein-Weidenbrunnen site, but at all FLUXNET sites, has changed dramatically starting around the year 2000. At this time, the first commercial open-path instruments for carbon dioxide and water vapour concentration measurements became available. Before 2000 only the LiCor 6262 closed-path instruments mainly in combination with Gill R2 and later R3 sonic anemometers (Moncrieff et al., 1997) were used, which only offered a 12 bit signal digitalization, while later devices featured 16 bit digitalization or higher. The digital signal of the LiCor 6262 can be connected to the serial input of a PC or the analog output of the LiCor 6262 can be connected to the input multiplexer of a sonic anemometer (at this time sonic anemometer had a 12 bit digitalization). The latter version was used by Moncrieff et al. (1997) and a simplified electronic circuit is shown therein. The comprehensive electronic circuit of a multiplexer system is shown, for example, in Foken (2017b) and Harrison (2015). The signal resolution of both systems is identical.
Quadrant (hole) analysis of all data points (20 Hz sampling rate)
of the vertical wind velocity and the carbon dioxide concentration for 1 h
(summer at noon) with 16 bit digitalization
The root mean square noise (possible resolution) of the carbon dioxide channel of LiCor 6262 is about 0.2 ppm and the digitalization step for 12 bit digitalization is much larger with 0.73 ppm (see Table 1). The calculations in this table were done for the full range of the measurement signal which is equivalent to 0–5 V. A reduction in the measurement range could reduce possible errors; however, for some very stable atmospheric stratifications very high carbon dioxide concentrations are possible that can only be measured if the full range is available. For the more modern LiCor 7500 instrument the 16 bit digitalization step is equal to 0.046 ppm (see Table 1), which is only about half of the root mean square noise of about 0.1 ppm. Therefore the digitalization has had no influence on the data since the year 2000.
Characteristic resolutions for water vapour and carbon dioxide concentrations with 12 bit and 16 bit digitalization. Data in italics were used for the calculation. Parts per thousand is denoted by “ppt”.
1 year of measurements collected during 2012 from the METEK sonic anemometer USA-1 (METEK GmbH Elmshorn, Germany) and the LiCor 7500 gas analyser were used for this study. Turbulent fluxes of carbon dioxide and water vapour were calculated using the internationally tested software package TK3 (Mauder et al., 2008; Fratini and Mauder, 2014; Mauder and Foken, 2015). All necessary corrections and quality checks were applied according to micrometeorological standards (Foken et al., 2012). Coordinate rotation was carried out using the planar-fit method (Wilczak et al., 2001) for each month separately following (Siebicke et al., 2012). The net ecosystem exchange (NEE) is defined as the sum of the vertical eddy-covariance carbon dioxide flux and the change in storage term of the air column below the sensor.
Probability density plot of the vertical wind velocity for 1 h (summer at noon) with the manipulated instrumental error of the R2 sonic anemometer.
The effect of limited amplitude resolution of fluxes of small magnitude was already discussed by Vickers and Mahrt (1997) and is illustrated in a time series of the carbon dioxide concentration in Fig. 1.
Comparison of the original NEE measurements at
Waldstein-Weidenbrunnen site in 2012 (original 16 bit digitalization) with
calculations using data with 12 bit resolution for the gas analyser in summer
(July,
Comparison of the original NEE measurements at the
Waldstein-Weidenbrunnen site in December 2012 (original
16 bit digitalization) with synthetic data with 12 bit digitalization for the
gas analyser and the instrument error (
The typical characteristics of 12 bit and 16 bit digitalization are shown in
Table 1. The problem is more significant for carbon dioxide than for water
vapour because the magnitude of carbon dioxide fluctuations is much smaller
in relation to measurement ranges than those of water vapour. The output
resolution of all current sonic anemometers equal to least 0.01 m s
Up to the year 2003 the Gill R2 and R3 sonic anemometers suffered from
instrument error (Foken et al., 2004): in the case of R2, the instrument
would not output vertical wind velocities of
From a theoretical point of view the digitalization error should only impact
small magnitude fluxes found mainly in winter due to small magnitude of
perturbations. If the fluctuations are on the order of the digitalization
step the signal becomes constant or changes are limited to a few decimal
places only. In Fig. 4 only fluxes smaller than
The original data of the vertical wind velocity collected from the USA-1
sonic anemometer not suffering from errors were replaced by data simulating
the instrument error of the R2 sonic anemometer. The simulated errors had no
significant impact on the results (Fig. 5a, compare with Fig. 4b).
To isolate the effect of the coordinate rotation from that of the instrument
error on to the fluxes the analysis was repeated with unrotated data in which
the digitalization step 0.00 m s
To investigate the influence of digitalization errors on annual sums of the
NEE the data of 2012 were analysed and the results are shown in Table 2. The
time series was not gap-filled, and therefore respiration data are partly missing
and NEE is larger than expected for this ecosystem. The simulated
12 bit digitalization error has no significant impact on the annual carbon
budget, except for the impact described above resulting in a reduction in the
respiration for fluxes smaller
Annual sum of NEE with 12 bit and 16 bit digitalization and with and without R2 instrumental error (the data were not gap-filled, and therefore the sum is larger than expected; relevant differences are in italics).
Since long time series of carbon exchange may contain important information about ecosystem dynamics, investigations of older data sets should be undertaken with care since the results could possibly suffer from artifacts resulting from changes in instrumentation and data handling. The present study showed that the impacts of the limited 12 bit digitalization of the gas analyser LiCor 6262 and that of the instrument error of the sonic anemometers R2 and R3 have negligible effects on summer and annual carbon budgets. Only data of small magnitude fluxes show increased scatter and deviations of approximately 5 % due to the digitalization error – mainly in wintertime. The effect of the R2 and R3 instrument error was negligible. Measured low fluxes and fluxes in wintertime are often discarded by quality routines and subsequently gap-filled. Because of general low wintertime fluxes across ecosystems, the findings can be universally applied to carbon flux measurement sites. In comparison, errors resulting from the gap filling (Moffat et al., 2007) are much larger than the errors reported here.
An overview of the instrumentation and important
measurement data at the Waldstein-Weidenbrunnen sites is provided by T.
Foken, available at
Concept and first draft were created by TF. CT discovered hardware digitalization defects and computed first statistics. All calculations and figures were done by WB. After the discussion of the results, TF, WB, and CT completed the paper.
The authors declare that they have no conflict of interest.
This publication was funded by the German Research Foundation (DFG) and the University of Bayreuth in the funding programme Open Access Publishing. Edited by: Ad Stoffelen Reviewed by: two anonymous referees