A fault-tolerant eddy covariance systemfor measuring CH4 fluxes

Werner Eugster and Peter Pluss

Institute of Plant, Animal and Agroecosystem Sciences, ETH Zurich, Universitatsstrasse 2, CH–8092 Zurich,Switzerland

Manuscript accepted by Agricultural and ForestMeteorologySpecial issue on CH4 and N2O fluxes.

Preprint version (published version will havedoi:10.1016/j.agrformet.2009.12.008)

Corresponding author

Werner EugsterETH ZurichLFW C55.2Universitatsstrasse 2CH–8092 ZurichSwitzerland

e-mail: eugsterw@ethz.chphone: +41 44 632 6847fax: +41 44 632 1153

Abstract

Eddy covariance flux measurements ofmethane, other trace gases, and fog dropletsoften involve modern analyzers that use digitalsignal processing. This allows to eliminateseveral potential sources of noise by usingthe digital signal directly in combination witha digital sonic anemometer. Some specificknowledge on timing issues and fault tol-erance of such a digital data acquisition ishowever needed. Here we show how such asystem works successfully with a modern cavityringdown spectrometer measuring CH4 concen-trations. This system has evolved over the past10 years and has successfully been used foreddy covariance flux measurements with othersensors as well. In a field deployment duringfive days in July 2008 we measured methanefluxes from a sealed landfill (Lindestock nearLiestal, Switzerland) that contains organicsubstances that lead to event-driven effluxes ofmethane at relatively low rates. During fourdays mostly net CH4 emissions were measuredwith daily median values between 1.6 and11.0 µg CH4 m–2 s–1, whereas during one day

primarily uptake (methane oxidation) wasmeasured with a median flux of –0.62 µg CH4m–2 s–1. Detailed analyses indicate that thisnew CH4 flux system is able to measure thismagnitude of fluxes. The performance of theoff-axis integrated-cavity output spectrometerwas quantified at 0.35 ppb at optimum inte-gration time, with a white-noise level of 1.5ppb Hz–1/2, which corresponds to a precisionof ±0.08% of the background concentration at1-Hz resolution. Depending on the samplingrate of the chemical analyzer in comparisonto the sampling rate of the sonic anemometerit was found that the variance measured byoversampling the digital signal is as goodor even better than the downsampling withrespect to an ideal sensor. It is thereforeconcluded that switching from partial digitalor analog data acquisition to fully digital dataacquisition is highly recommended for eddycovariance flux measurements with moderninstrumentation.

Keywords: Digital data acquisition; Noiseelimination; Methane analyzer; Landfill ef-fluxes; Off-axis integrated-cavity output spec-trometer; Switzerland

1 Introduction

Eddy covariance flux measurements are car-ried out with a wide variety of data acquisi-tion systems. Whereas sonic anemometers andchemical analyzers were analog instruments inthe very beginning of such flux measurements,newer equipment is entirely based on digitalsignal processing. This opens new possibili-ties for data acquisition, but also poses newproblems to those new to the field of eddy co-variance flux measurements. Here we discussthe problems of eddy covariance data acquisi-tion for methane flux measurements with a cav-ity ringdown laser spectrometer (Los Gatos Re-search DLT-100). Although this is a new instru-ment, the overall data acquisition concept pre-sented here is based on experience gained dur-

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ing the past ten years using other analog anddigital analyzers in combination with a digitalsonic anemometer. The underlying concept ofeddy covariance flux measurements of CH4 isnot discussed here, but all relevant information,including the strengths and weaknesses of eddycovariance in this field of application can easilybe found in Denmead (2008).

During the early days of CO2 flux mea-surements, the standard instrumen-tal set-up of Euroflux and follow-upprojects often used the EdiSol software(http://www.geos.ed.ac.uk/abs/research/micromet/edisol/) with a digital three-axis ul-trasonic anemometer-thermometer (Gill SolentR2, Solent, U.K.) with five analog inputs wherefast chemical analyzers can be attached. In thestandard set-up this was a closed-path infraredgas analyzer (IRGA), most commonly a Licor6262 CO2 and H2O analyzer (Licor, Lincoln NE,U.S.A.). The digital signal of the instrumentwas converted to an analog voltage whichcould then be connected via an analog data lineto the analog inputs of the sonic anemometer.This instrument digitized the analog voltagesto digital values that were directly mergedwith the digital information from the sonicanemometer (e.g. Corradi et al. 2005, Kolleand Rebmann 2007). The whole data streamwas then transferred via an RS-232 or RS-422serial digital data line to a serial port of a laptopor other computer (Figure 1a or b, dependingon analyzer). This concept has also beensuccessfully used for CH4 flux measurementswith a tunable diode laser system (e.g. Edwardset al. 1994, Edwards et al. 2003, Hargreaveset al. 2001, Heikkinen et al. 2002, Pattey et al.2006, Wille et al. 2008, Sachs et al. 2008),and with a cavity ringdown analyzer (Hendrikset al. 2008) of the same manufacturer as weused.

Such a set-up however does not take full benefitof the digital signals of the analyzer attached tothe sonic anemometer, and thus we—and sev-eral others—changed the data acquisition con-cept when the open-path Licor 7500 instrumentbecame available. With such instruments, it ispossible to connect the analyzer directly to oneserial port of a computer (Fig. 1c) and the sonicanemometer to another independent serial port.With adequate commercial or self-written soft-ware the two data streams are merged onlineon the computer in a loss-less way (e.g. Laurila

et al. 2005 and Rinne et al. 2007 use such aconcept). Here, our goal is to make our knowl-edge about using this new concept available toothers. We focus on CH4 flux measurements andshow results from a first field test on a landfillsite in Switzerland as a proof of concept.

2 Background

With the older Euroflux concept three unneces-sary sources of noise and uncertainty are intro-duced: (1) the conversion from digital to analogsignals normally involves some filtering to pro-vide smooth signals; (2) the analog data linealso acts as a radio antenna, attracting addi-tional noise (which can be greatly reduced butnot entirely eliminated by correctly groundedshielding wires around the signal leads); and(3) the back-conversion from analog to digitalsignals again involves filtering to avoid alias-ing of quick changes of analog signals, andthe rate of conversion may not perfectly matchthe data rate of the sonic anemometer. More-over, lightning protection filters add additionalnoise. With two serial data lines these prob-lems are entirely eliminated from the data ac-quisition. Also the lightning protection is solvedin a noiseless manner, typically by optically iso-lated circuits that separate the signal lines onthe outside of the data acquisition system fromthe inside. However, new issues about tim-ing and data merging appear which require acertain level of fault tolerance of the system.This paper suggests a solution using the exam-ple of methane flux measurements with a LosGatos Research (LGR) DLT-100 fast methaneanalyzer and a Solent R2A anemometer (seeSection 3.1). Similar set-ups were realizedwith newer Solent anemometers (Gill, Lyming-ton, U.K., models R3-100, R3-50, HS-100) andCampbell Scientific (Logan, UT, U.S.A.) CSAT-3 anemometers which were combined with aLicor 7500 (e.g. Rogiers et al. 2005, Rogierset al. 2008), a Droplet Measurement Technol-ogy (Boulder, CO, U.S.A.) FM-100 fog dropletspectrometer (Burkard et al. 2002, Burkardet al. 2003, Eugster et al. 2006), or an Aero-dyne (Billerica, MA, U.S.A.) QCLAS for N2O(Eugster et al. 2007) or stable isotope flux mea-surements (Zeeman 2008).

An alternative would be to use a data log-

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ger that attempts to solve the problem in adifferent way, which is however difficult toimplement with instruments that are sendingdata without the possibility to poll or trigger themeasurement, as for example the instrumentused in this study. The first problem to besolved is that of timing of data acquisition. Itis well-known that general-purpose operatingsystems on computers (e.g. Windows, Linux,MacOS X, Solaris) have great advantage overspecial-purpose operating systems, but they arenot true real-time operating systems. That is, itis unpredictable what the computer does at agiven time, only a probability information canbe provided. Whereas there are possibilitiesto use a variant of Linux which has an elab-orate real-time scheduling system (RT-Linux,e.g. http://www.tldp.org/HOWTO/RTLinux-HOWTO.html, http://www.fsmlabs.com/products/openrtlinux/), this generally requiresfine-tuned software code that is not portable toother systems anymore and may need a lot ofservicing as both computer hardware and oper-ating systems evolve. Some scientists thus stilldecide to use the DOS operating system fromthe pioneering times of personal computing.This is a real-time operating system if—andonly if—it is run on very old computers witha processor that provides a real-time mode.Newer personal computer processing units(CPUs) however are no longer offering such areal-time mode, and thus DOS does not appearto be an option for newer systems. Actually, afully-fledged real-time operating system is noteven needed for an application such as eddycovariance flux measurements. This task differsclearly from what is required for example inan aircraft flight control system (where a crashwould be the unacceptable result of a failureto respond in real-time), or for space flight,which is considered the ultimate challenge forreal-time operating systems.

For eddy covariance flux measurements near-real-time performance as it can be achievedby standard computer hardware and general-purpose operating systems is sufficient. Oneprerequisite is however to use continuous datamode of the sonic anemometer under use.These instruments that we have worked withso far provide equally spaced data records thatcan be considered the reference timing standardeven on non-real-time systems.

Our concept is thus to merge each arriving

data record from the sonic anemometer withthe most recent data record that arrived fromone or more additional digital analyzers thatare each attached to their specific individual se-rial port on the data acquisition computer. Al-though this appears to be a simple task there areseveral issues that need to be considered andwhich will be discussed in detail in the follow-ing: (1) How can this be achieved with min-imum uncertainty in timing? (2) How can thesystem work with different data rates from sonicanemometer and digital analyzers? (3) Howcan we assess the overall performance of, forexample, the methane flux system mentionedabove?

3 Methods

3.1 Instrumentation

The specific instrumentation used for CH4flux measurements consists of a DLT-100 fastmethane analyzer (Los Gatos Research, Inc.,Mountain View, CA, U.S.A., model 908-0001-0002, serial number 07-0055, manufactured12/07) and a Solent R2A ultrasonic anemome-ter (Gill Instruments Ltd., Lymington, U.K.)which are combined in a field-deployable con-figuration as shown in Figure 2. The DLT-100 is a cavity ringdown spectrometer and wasalready described in more detail by Hendrikset al. (2008). The intake hose was a 6.7 mlong Synflex-1300 tubing (Eaton PerformancePlastics, Cleveland, OH, U.S.A.) with 10 mmouter diameter (8 mm inner diameter). To pro-tect the CH4 analyzer from dust, insects andoccasional water droplets during fog and rainevents, the intake hose was connected to thesensor inlet via a combined water trap (SMC,Japan, model AFD30-F03 with 0.3 µm filter;http://www.smcworld.com). An external vac-uum pump (BOC Edwards XDS-35i) was usedfor eddy covariance flux measurements. In thefinal configuration the median flow rate at am-bient pressure (as determined from the time lagbetween the CH4 concentration signal and thevertical wind speed) was 26.3 L min–1. This cor-responds to 140 L min–1 at a nominal cell pres-sure of 190 hPa (142.5 Torr). Thus, the cell vol-ume of 0.408 L is refreshed approximately 5.7times per second (newer instruments are now

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allowing 2× this refreshment rate; D. Baer, pers.comm.). Ideal would be if a complete renewalof the sample cell could be achieved for eachsingle measurement at 20 Hz. Incomplete re-freshment of the cell volume results in signaldamping as has been described in detail (Moore1986, Eugster and Senn 1995, Horst 2000). Inmost applications this is only a small concernfor the quality of flux measurements, as will beshown later.

There was no access to mains power at the land-fill site, which required the use of a power gen-erator running on gasoline. The critical issuewas to start the strong dry scroll pump, whichunder operation requires less than 800 W at230 V AC, but consumes a startup current be-tween 13 and 15 A. Using the well-establishedtrial and error concept we were successful tostart the pump and thus the whole system witha Geko 6501 ED-AA/HHBA (MetallwarenfabrikGemmingen GmbH & Co., Gemmingen, Ger-many) generator rated at 22.6 A or 5.2 kVA at230 V AC. Smaller devices were unable to de-liver the initial current for the external pump,but were well able to start the system with theinternal pump of the DLT-100.

3.2 Field site

Field tests with the CH4 flux system describedhere were carried out on five days in July 2008at the Lindestock landfill site (47◦29′41.41′′

N / 7◦45′04.15′′ E, 570 m a.s.l.) near Li-estal, Switzerland. Sensor height was 1.6 mabove ground level (1.3 m above displacementheight). The local surface area covered by theeddy covariance flux measurements during thatperiod is shown in Figure 3. We installed theCH4 flux system near the top of the landfill hillin such a way that the expected footprint areawould have a relatively modest slope angle.This was the case with wind directions rangingbetween 190◦ and 0◦ (westerly winds).

We are only aware of two other studies (Hovdeet al. 1995, Laurila et al. 2005) that success-fully tried to measure methane fluxes from alandfill site directly by eddy covariance. Thelandfill site in Switzerland is very different fromthe Finnish site (Laurila et al. 2005) in thatit should actually not show relevant methanelosses. Hence, the short field campaign that

we carried out did not yet aim at quantifyingthe annual CH4 losses, but only should pro-vide a proof of concept that the eddy covariancemethod with a DLT-100 analyzer should be ableto resolve the CH4 fluxes from such a landfill.In Switzerland, municipal waste is typically in-cinerated, not put into landfills. However, thereare older landfill sites where no strict separationof inert material (e.g. rubble) and organic wastewas made. Such landfills should by definition becovered in such a way that no greenhouse gasescan escape in an uncontrolled way.

3.3 Data acquisition and data merg-ing

Data acquisition was carried out with an in-dustry grade embedded box computer (Advan-tech ARK-3381, Taipei, Taiwan) with seven se-rial ports. Earlier systems used standard laptopswith Quatech Inc. (Hudson, OH, U.S.A.) four-port PCMCIA serial cards. In all cases we usedLinux as the operating system. The same con-cept however also works with any other Unixvariant such as MacOS X or Solaris with stan-dard Unix System V inter-process communica-tion (IPC) capability. This allows one program(or process) to exchange data with a secondprogram.

The main process for data acquisition reads theserial port where the sonic anemometer is at-tached to. The sonic anemometer is config-ured in continuous mode and thus sends itsdata records at regular intervals. For each addi-tional analyzer a separate data acquisition pro-gram is running. In the case of the DLT-100CH4 analyzer this program just receives arrivingdata from the instrument. For other instrumentssuch as the Licor 7500 CO2 and H2O infraredgas analyzer, the program also interacts with theinstrument, configures it according to the spec-ifications defined in a specific set-up file, andretrieves all information about the instrumentitself (serial number, firmware version, dates oflast calibrations and internal coefficients of thecalibrations) which are saved in the log file. Ar-riving data are then prepared and sent to an IPCmessage queue at full temporal resolution. Inaddition to this, one record per second is sentto a second IPC message queue where it can beused for controlling the proper operation of thedata acquisition.

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For each arriving data record from the sonicanemometer, the most recently arrived recordfrom the CH4 analyzer (and potentially all sub-sequent analyzers) are merged with the sonicdata, giving it the flag 0. If no new record ar-rived since the last anemometer record arrived,the previous CH4 record is replicated, giving itthe flag 1. If a certain number of replicationsis reached, the missing data flag is saved inplace of the CH4 record. The threshold whenthis should happen is defined according to theperformance of the instrument. For example, ifan instrument delivers data at a rate fluctuatingbetween 3 and 5 Hz, but the sonic anemome-ter is running with 20 Hz resolution, then upto six replications would indicate normal con-ditions which should not produce warnings orerror messages. More details are given below inSection 3.5.

In such a way we obtain a robust and fault tol-erant data acquisition system, that: (a) doesnot fail if we decide that the sonic anemome-ter should run at a lower sampling rate thanthe gas analyzer; (b) does not fail if the sonicanemometer runs at a higher sampling rate thanthe gas analyzer; (c) does not fail if the datarecords delivered by the gas analyzer are notperfectly sent at regular intervals. The only fail-ure is the case, where the sonic anemometerstops to work, which is the least probable failurein the typical eddy covariance system accordingto our experience.

3.4 Timing issues in data acquisi-tion

The sonic anemometers are configured to sendbinary data, which allows to read the incomingdata stream in raw mode (Sweet 1999). Thatallows one to get full control over the behaviorof the computer program, when data bytes ar-rive at the serial port.

As a quick estimate of the order of magnitude ofthe delays we consider that data are sent at, forexample, 38,600 baud (that is, 38,600 bits persecond). Each byte of binary data is sent withone start bit, one stop bit, and no parity bits.Thus, each byte of data is actually composed of10 bits that need to travel along the serial datacommunication line. Thus, 2 bytes take roughly20/38,600 seconds (518 µs) between a sonic

anemometer and the computer’s serial port. Al-though this is quite fast in the understanding ofan eddy covariance experimentalist, for a mod-ern computer this delay is extremely long. Amodern 1 GHz processor can carry out morethan half a million simple integer operations insuch a time. Thus, if a general purpose operat-ing system is used (instead of a real-time oper-ating system), the problem needs to be solved,how to guarantee that the computer program isactually ready to accept the arriving data aftersuch a long wait since the last data word ar-rived. This can be done (a) with two specificprogramming techniques, (b) by avoiding largesystem loads on the computer during data ac-quisition (e.g. not using a graphical interfacewhich consumes most of the processor time insuch a setting), or (c) using specific hardwarethat has a much better data throughput conceptthan a standard personal computer.

Under Linux we successfully used the variant(a) with memory locking via the mlockall()system function (to prevent unexpected delaysin response to our incoming data), and usingthe near-real-time Round Robin scheduler witha very high system priority for the data acqui-sition process via the setpriority() systemfunction.

The typical delay times of a full data record sentby a CSAT-3 or a Gill/Solent sonic anemometeruntil they are available at our data acquisitionsystem are around 10 ms. For example, CSAT-3sonics send records with 10 bytes (5 words) at abaud rate that is fixed at 9,600. Thus, this takes1/96 second or 10.4 ms.

3.5 Strategy to cope with differ-ent sampling rates of instru-ments

Our considerations in the previous section al-ready indicate the relevance for the user, whohas the choice of different sonic anemometertypes that can run at different baud rates. Simi-larly, the gas analyzers provide an additional setof possible modes and configurations. This eas-ily confounds the user. Even more so, if suchan instrument needs to be combined with an-other instrument that basically is subject to ex-actly the same timing issues.

Thus, it is not surprising, that often the tech-

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nologically old-fashioned concept is used thatconverts a digital signal of a modern gas ana-lyzer back to analog voltage, which later on isagain digitized for data acquisition (Figure 1a).In such a way one only has to tackle the tim-ing issues of acquiring the data from a sonicanemometer. This is however done at the ex-pense of increased system noise levels, as isschematically shown in Figure 1. Contrastingly,a fault-tolerant system that is able to use dig-ital signals from digital analyzers without theneed for conversion, must be able to cope withanalyzers that provide their data at a differentsampling rate than the sonic anemometer, andpossibly even with variable spacing betweenrecords.

This is needed when working with a DLT-100CH4 gas analyzer. Figure 4 shows the typicalexperience that we and others make: The nom-inal sampling rates that the user can select viathe system software is not perfectly matchingthe true sampling rate under typical field con-ditions. This is of no concern if one has an ad-equate data acquisition system, but can lead toproblems when the data acquisition is not fault-tolerant.

In the special case of the DLT-100 CH4 gas ana-lyzer we distinguish between the “normal” caseduring 23.81 hours of the day in the exam-ple shown in Figure 4, and a short period of11.5 minutes (0.19 hours) starting at 0402 localtime, when the system does its special house-keeping cleanup.

We cannot and do not want to change the soft-ware running on the system purchased from asupplier, but what we can do is to consider aspecific strategy to cope with such effects, whichare also seen with most other modern gas an-alyzers (the only exception the authors haveexperienced so far are the Licor gas analyzersfor CO2 and H2O where nominal and actualdata rates agree very well). As already men-tioned, our concept is thus to merge each arriv-ing data record from the sonic anemometer withthe most recent data record that arrived fromone or more additional digital analyzers that areeach attached to their specific individual serialport on the data acquisition computer. This ofcourse adds some digital noise at the very end ofthe pipeline, as shown in Figure 1c. We will ad-dress this type of noise in detail and show thatthis noise is small compared to the signal from

the CH4 analyzer under use, and that this con-cept is providing defensible time series data foreddy covariance flux analysis.

3.6 Flux computations

After data have been acquired the off-line pro-cessing in general follows standard procedures:(1) The 3-dimensional wind vector data weresubjected to a coordinate rotation procedurethat aligned the u-component with the localstreamlines (which are along the prevailingwind direction) for each 30-minute interval (thefirst two rotation steps of McMillen 1988), andwhich forced the lateral v and surface-normal wcomponents to be zero on average (i.e. v = 0and w = 0). (2) To determine the lag timebetween CH4 and w we performed a cross-correlation computation with w and CH4 con-centration time series, then shifted the CH4 timeseries relative to the wind speed series to elim-inate possible time delays caused by the lengthof the intake tube, the DLT-100 data process-ing and delivery system, and also to account forpossible effects of sensor separation. All thesecomputations are analogous to standard eddycovariance flux measurements of trace gases(see e.g. Baldocchi 2003, Mauder et al. 2008).No detrending and no autoregressive filteringwere used in the computation, and fluxes werecomputed as block averages for each 30-minuteinterval.

4 Results

4.1 Performance of a CH4 ana-lyzer

Before deploying our fast CH4 analyzer in thefield we tested its performance under labora-tory conditions. Figure 5 shows the Allan vari-ance plot with laboratory background air (allsinks in the laboratory were re-filled with freshwater) early in the morning well before peoplestart their work. This assessment suggests thatthe precision of this analyzer, if averaged overthe typical time period of ≈1 minute is on theorder of 0.35 ppb CH4 with a precision of the1-Hz signal around 1.5 ppb. Against a back-ground concentration of 1.87 ppm this indicates

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a precision of ±0.08% at the 1-Hz resolution,which by itself indicates the high potential ofthis instrument for eddy covariance flux mea-surements.

4.2 The effect of oversampling thedigital CH4 signal

Despite its good performance, the varying sam-pling rate as shown in Figure 4 is of some con-cern. With our concept we solved this issue byoversampling the digital signal. To show thepotential effects that the non-random noise in-troduced by oversampling a digital signal mighthave, we used existing data of vertical windspeed fluctuations and produced artificial timeseries where we ignored every second record,4 out of 5 records, and 14 out of 15 records.This corresponds to the typical ranges found inthe DLT-100 analyzer at 20 Hz resolution (Fig-ure 4). Since we just replicate the previous datarecord received from the analyzer, we basicallyproduce a rectangular signal of the time spacingprescribed by the sonic anemometer.

We then performed a spectral analysis of theresulting time series (Figure 6) using a FastFourier Transformation (FFT) of the R softwarepackage (R Development Core Team 2008). Fig-ure 6a shows the original unmodified spectrumand the spectra of the three artificially pro-duced oversampled variants. Figure 6b providesa close-up of the high-frequency range wherethe effect of oversampling is clearly seen. Thevertical lines show the Nyquist frequencies ofthe respective signals, and the broken curves tothe right of each Nyquist frequency are only in-cluded in the graph to show the effect of over-sampling. In reality, it is of course clear thatthe resolved frequency of the instrument is re-lated to the sampling rate of the instrument,and not to the data acquisition rate, which couldbe in oversampling mode. Nevertheless, the un-resolved variance that is found in higher, unre-solved frequency ranges is folded into the lowerfrequency ranges due to aliasing of the data ac-quisition system (see Stull (1988) and Kaimaland Finnigan (1994) for more details on alias-ing).

Figure 6c clearly shows that both the oversam-pling technique described here (solid lines) andthe potential downsampling technique (sym-

bols) deviate from the perfect 1:1 ratio. Inthe extreme case of using only 1 out of 15data records, the oversampling technique leadsto roughly 20% overestimation of the varianceclose to the Nyquist frequency, whereas thedownsampling technique underestimates by asimilar percentage. Figure 6 suggests that over-sampling of the digital signal yields a frequencyresponse that is closer to ideal conditions athigh frequencies near the Nyquist frequencythan downsampling. This, however, does notautomatically translate also to cospectra (Fig-ure 7), as will be elaborated in more detail inSection 4.3.

4.3 The spectral and cospectralshapes of an oversampled digi-tal CH4 signal

A rectangular signal with constant amplitude Acan be written in a mathematical way as

y(t) = A·∑ (

sinωt +13

sin 3ωt +15

sin 5ωt . . .

),

(1)with t being time (s) and ω the frequency in ra-dians per second. Thus, our type of oversam-pling produces non-random noise with such arectangular shaped curve that contains all oddmultiples of the base frequency. If we performan FFT on such an artificial time series, we yielda spectrum of the type shown in Figure 8 with aclear difference of the discrete spectral densitiesat 1, 3, 5 etc. multiples of the base frequency,and a many orders of magnitude lower randomwhite-noise component.

While the discrete spectral peaks in this artifi-cial rectangular time series with constant ampli-tude are very narrow, it is important to note thatthese spectral peaks can broaden considerablywhen a strong signal is added to this rectangu-lar noise as was done in Figure 6a/b: the bro-ken line that relates to the 1/15 nominal sam-pling rate yields a theoretical Nyquist frequencyof 20.83/30 = 0.7 Hz. Its odd harmonics arethus: 2.1 Hz, 3.5 Hz, 4.9 Hz, 6.2 Hz. Hence,what appears to be narrow peaks in the wrongdirection are the lack of variance between theodd multiples of the base frequency of the rect-angular signal in Figure 6b.

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In contrast, if the rectangular noise is present ina spectral area where the signal is absent, thesame structure as in Figure 8 can be found inreal measured data. This happens for exampleif the CH4 analyzer is operated with the slowinternal pump (Figure 9), for which the systemsoftware of the analyzer only provides a max-imum 1 Hz data output rate. The 1-Hz cutoffin this setting is clearly seen as the first dis-crete maximum in the high-frequency range ofthe oversampled signal (Fig. 9, bottom right).Since the Nyquist frequency is 0.5 Hz in thiscase, we plotted the random white-noise slope,which follows the f+1 line in Figure 9, with re-spect to the spectral density under the assump-tion that the signal-to-noise ratio at 0.5 Hz iszero. This is a conservative assumption and onecould also argue that the spectral densities ob-served between the discrete spectral peaks orig-inating from oversampling should be taken asthe random noise level of the analyzer. This ishowever of no importance for eddy covarianceflux measurements.

More important is the fact that measurementswith the internal pump lack the adequate f–2/3

response expected in the inertial subrange. Par-tially, the observed spectra follow the typicalfirst-order damping slope of f–8/3 as describedby Eugster and Senn (1995) and others, butare damped much more in the frequency range0.05–0.2 Hz in Figure 9. This indicates that thetype of damping is different from the conven-tional first-order damping.

To overcome this issue, the CH4 analyzer comeswith a strong external pump for eddy covari-ance flux measurements. Figure 10 clearlyshows an improvement in spectral response ofthe analyzer. The inertial subrange nicely fol-lows the f–2/3 up to roughly 0.5 Hz, then fol-lows the typical damped spectrum along thef–8/3 slope, until the curvature changes towardsthe f+1 white noise slope.

Typically, scientists use spectral analysis to as-sess the quality of a new sensor or one, thatis unknown to them. One prerequisit for suchan analysis is the equally spaced time step inthe time series, which is not yet the standardwith CH4 and N2O analysers. Oversamplingas proposed here, combined with the neces-sary knowledge, how to interpret the spectra,can thus help to gain confidence in the instru-ments.

However, a word of caution is required withrespect to flux assessments where the cospec-trum between vertical wind speed w and con-centration c is analysed. The oversamplingtechnique proposed here improves the low-frequency agreement of cospectra with the ref-erence curve and reduce the aliasing of unre-solved high frequency contributions (Fig. 7).This can be useful to distinguish a nicely-working system with imperfect time spacing ofdata delivery from one that might suffer fromtechnical problems. However, oversamplingtends to reduce the covariances computed overa given time interval, and thus for CH4 flux com-putations, a standard processing of data (thatis, only using records with flag 0) is still recom-mended.

4.4 CH4 fluxes

A gas analyzer with the precision of the CH4 an-alyzer used here is thus in principle well suitedfor eddy covariance flux measurements. Still,a word of caution based on own experienceshould clarify that there can be important differ-ences between eddy covariance CH4 flux mea-surements and the more wide-spread CO2 fluxmeasurements that most experimentalists arefamiliar with. The example from a landfill siteshown in Figures 11–12 illustrates this point,although we do not have concurrent CO2 fluxmeasurements: the temporal variation in CH4concentrations at this site (Figure 11a) showsrather episodic bursts of higher concentrations,such as one expects from a process that is notperfectly continuous, but event-driven. Thiscontrasts with typical CO2 flux measurementsover vegetated ecosystems where variations ofCO2 concentrations are less asymmetrically dis-tributed around their temporal mean, which is aconsequence of the continuous processes of res-piration and assimilation. On a landfill, how-ever, it is expected that some hotspots releaseCH4 in higher quantities during specific events,e.g. when wind picks up and dynamic pressurein the atmosphere drops.

This leads to the effect that the conventionalcross-correlation procedure that can be used todetermine the actual time lag between verti-cal wind speed data and the CH4 concentration(Figure 12c) is often not as clearly seen as thisis normally the case with CO2. The example

8

shown in Figure 12c is a nice case where thelocal peak of the cross-correlation function isclearly seen and corresponds with the approxi-mate estimate of the time delays associated withthe length of intake hose, hose diameter, andpump flow rate. However, the search windowfor finding this peak had to be narrowed in quitestrongly to be able to locate this peak even incases where episodic plumes of CH4 in the timeseries led to much stronger cross-correlationsthan that of the time delay between verticalwind speed data and the CH4 concentration. Toreduce the probability to use a physically unre-alistic time lag we had to narrow in the searchwindow to the range 0.24 to 1.44 s (verticallines in Figure 12c).

At our landfill site, the fluxes varied consider-ably among the five field days (Figure 14). Dur-ing four days, we found a net efflux with me-dian values ranging from 1.6 to 11.0 µg m–2

s–1, which is at the low end of the range ob-served over the Finnish landfill site (Laurilaet al. 2005). One day even showed a net oxida-tion of CH4 (downward fluxes on 10 July 2008),which is the condition one would expect hadthis Swiss landfill site been perfectly sealed asexpected (Gomez et al. 2008).

5 Discussion

The white noise level of 1.5 ppb Hz–1/2 as deter-mined from the Allan variance plot (Figure 5) isslightly below that of 2.9 ppb Hz–1/2 found fora QCL system (Kroon et al. 2007) and is clearlybelow the minimum performance for CH4 fluxmeasurements that Kroon et al. (2007) suggestto be around 4 ppb Hz–1/2.

Hendriks et al. (2008) provided an in-depth as-sessment of an earlier version of the CH4 an-alyzer from the same manufacturer. In theirassessment, the Allan variance plot did not re-veal the typical behavior of such an instrument.Normally, the Allan variance follows the whitenoise slope, similar to what Kroon et al. (2007)found with a QCL analyzer measuring CH4 andN2O, and which is also seen with other sim-ilar QCL-based instruments (see Tuzson et al.2008a, Tuzson et al. 2008b). An almost per-fect response was shown by Werle and Kormann(2001) for a TDL system, were sensor drift waseliminated by a filtering procedure before com-

puting fluxes. Contrastingly, Hendriks et al.(2008) show an Allan variance plot that directlylinks high-frequency noise with low-frequencysensor drift in an almost horizontal line withno apparent local minimum in Allan variance.Nevertheless, they quantify the short-term pre-cision (white noise level) of their analyzer at7.8·10–3 ppb Hz–1/2, which appears three or-ders of magnitude better than our instrument,but which must be questioned with respect toour results and those obtained by Kroon et al.(2007).

With respect to sensor drift we see a need formore detailed investigations to clarify the dif-ference between undesired sensor drift, whichneeds to be corrected for (Werle and Kor-mann 2001), and true signal of low-frequencyfluxes (and thus variations in concentration)that would be arbitrarily removed from the timeseries by using a filter such as the one usedwith TDL instruments. Our present, still verylimited experience with the DLT-100 analyzersuggests that drift is not as severe as in olderTDL analyzers. Still, Figure 12b indicates thatthere is unexpected high variance at frequen-cies below 0.005 Hz, which is less apparent inthe spectrum of w in Figure 12a. On the otherhand one should recall that natural frequencies≤0.005 Hz are covered by less than 10 datapoints in a 30-minute time series, and henceare associated with high statistical uncertain-ties, irrespective of filtering. Nevertheless, thetime course of the CH4 concentration (Figure11a) clearly suggests that such low-frequencyvariations are real, most likely associated withthe event-driven kind of CH4 flux process ofsuch a landfill, and not at all a sign of signaldrift.

This episodic nature of CH4 effluxes from ourlandfill site also explains the less smooth cospec-tra of the CH4 flux (Figures 12d and 13) thanwhat the experienced scientist would expectfrom a CO2 flux cospectrum obtained over greenvegetation under stationary atmospheric condi-tions, or what Laurila et al. (2005) showed fromtheir landfill site with strong fluxes. Thus, de-pending on the type of flux process that one in-tends to investigate, and the magnitude of thefluxes the analysis of cospectra will rather in-dicate the time scales (and thus spatial scales,based on the time-for-space substitution madeby Taylor’s frozen turbulence field hypothesis,Taylor 1938) of the process under investigation.

9

Consequently, cospectra of CH4 flux should notbe expected to primarily provide informationon whether the overall eddy covariance set-upsucceeded in measuring the flux. The spectraof CH4 variance, however, provide clear evi-dence that the instrumentation worked at high-est quality levels, even though cospectra are notalways easy to interpret.

6 Conclusions

Eddy covariance flux measurements ofmethane, other trace gases, and fog dropletsoften involve modern analyzers that use digitalsignal processing. This allows to eliminateseveral potential sources of noise by usingthe digital signal directly in combination witha digital sonic anemometer. Some specificknowledge on timing issues and fault toleranceof such a digital data acquisition is howeverneeded. We were able to show that the conceptwe use works successfully with a modernintegrated-cavity output spectrometer measur-ing CH4 concentrations, and with other sensorsthat the authors have been using in the past 10years.

The advantage of avoiding analog noise by afully digital system has the disadvantage of in-troducing a new non-random noise componentfrom oversampling of digital signals. We wereable to show that the concept we are using isperforming in a predictable way, and that theresolved variance from that oversampling tech-nique is at least as good as the approach usingdownsampling (to cope with imperfect instru-ments in a fault-tolerant way). However, thisshould not be confounded with the need to onlyuse really measured concentration records forthe computation of the CH4 fluxes.

In a field application on a landfill site in Switzer-land, where partially organic waste should besealed from the atmosphere, it could be shownthat the CH4 flux system used here is well ca-pable of resolving these relatively small CH4fluxes. The rather event-driven nature of theseeffluxes from the landfill clearly shape thecospectra of the fluxes in a way that is moredifficult to interpret than cospectra from fluxesthat originate from continuous processes suchas photosynthesis and soil respiration. Thespectra of CH4 concentration time series nev-

ertheless clearly indicate an excellent perfor-mance of the cavity ringdown spectrometer,which is comparable to a quantum cascade laserabsorption spectrometer system.

The main goal of this paper was however tostrongly encourage experimentalists working inthe field of eddy covariance flux measurementsto switch to fully digital data acquisition, if theyhave not yet started to do so.

Acknowledgments

We thank the team of scientists that organizedthe Lindestock landfill campaign and helped inthe field, namely Katherine E. Gomez-Holmes,Martin H. Schroth, Susanne Liebner, PascalA. Niklaus, Josef Zeyer (ETH Zurich) and Pe-ter Oester (Messtechnik Thun, Switzerland).Roland A. Werner (ETH Zurich) helped strongly(in a literal sense) to move and install all equip-ment.

The DLT-100 analyzer was purchased fromfunds received from ETH Scientific Equipmentgrant 0-43350-07 to Werner Eugster and JosefZeyer, and by funds from Alfred Wuest andCarsten Schubert (EAWAG Kastanienbaum).Nina Buchmann (ETH Zurich) is acknowledgedfor her continued support and the substantialfunds she has provided for all the adaptationsand construction work that were necessary tomake the CH4 flux system field-deployable. Thiswork is also a contribution to the ETH Com-petence Center Environment and Sustainability(CCES), project MAIOLICA.

10

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Heikkinen, J. E. P., Maljanen, M., Aurela, M.,Hargreaves, K. J., and Martikainen, P. J.,2002. Carbon dioxide and methane dy-namics in a sub-Arctic peatland in northernFinland. Polar Research 21, 49–62.

Hendriks, D. M. D., Dolman, A. J., van derMolen, M. K., and van Huissteden, J.,2008. A compact and stable eddy covari-ance set-up for methane measurementsusing off-axis integrated cavity output

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spectroscopy. Atmospheric Chemistry andPhysics 8, 431–443.

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Taylor, G. I., 1938. The Spectrum of Turbulence.Proc. R. Soc. London Ser. A 164, 476–490.

Tuzson, B., Mohn, J., Zeeman, M. J., Werner,R. A., Eugster, W., Zahniser, M. S., Nel-son, D. D., McManus, J. B., and Emmeneg-ger, L., 2008a. High precision and continu-ous field measurements of δ13C and δ18Oin carbon dioxide with a cryogenic freeQCLAS. Applied Physics B. Lasers and Op-tics 92(3), 451–458.

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13

Analoganalyzer DigitalanalyzerFilter*

Filter*AnalogoutputAnalogoutput

D-Aconverter

Antialiasingfilter* AntialiasingfilterA-Dconverter A-Dconverter

Data acquisition(computer, logger)

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line

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data l

ine(se

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e, no n

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£AIR

£AIR

£AIR

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*Signal smoothing and lightning protection filter

(a) (b) (c)

Figure 1: Schematic data flow from gas analyzer (top) to data acquisition system (bottom) in atypical eddy covariance set-up, and the potential sources of additional noise in the data time series.For older analog analyzers (a) the typical configuration uses a analog-to-digital (A-D) convertereither in the sonic anemometer or in the computer or logger data acquisition system. The sameis still possible with newer digital sensors (b), but many of the potential sources of noise can beeliminated by directly using the digital data without conversion (c). The symbol for noise does notindicate the strength of the noise or its relevance. Conceptual idea taken from Clark and Whitfield(1994).

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ÄnderungenDatumName gez.:

gepr.:

DatumName Bezeichnung

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Blatt

von

A B C D E F

1

2

3

41

1Norm:

Dateiname: methanlaser1.spl

Prinzipschemaportable Methanlaser-anlage mit Sonic Anemometer

Peter Plüss 24.11.2008

Weatherproof instrument housing

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Ventilation (IP55)

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12V Charger

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EmbeddedComputerARK–3381

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eter

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all complying with IP68

Los GatosFast MethaneAnalyzer

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ith5 µm

filter cylinder

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Figure 2: Design scheme of the field-deployable set-up including the fast methane analyzer anda high-performance dry scroll vacuum pump which are placed in separate weatherproof housings(dashed rectangles).

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Figure 3: Aerial photograph of landfill site with flux footprint area obtained during five field days(a) using the Kljun et al. (2004) footprint model, and close-up with 1-m contour intervals (b).The isolines of the footprint area denote equal percentage of flux footprint weight with respectto the point of maximum contribution. The position of the eddy covariance system is shown as ablack cross with white outline. Aerial photograph c© 2009 swisstopo (JD082776), contour linescourtesy of Peter Oester.

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Figure 4: Effective sampling rates during a typical 24-hour period in the field (24 June 2008) atthe CH4 analyzer’s nominal 20 Hz measurement frequency. The fraction of records denotes thefraction equal or above the frequency value shown by the bold lines. Under normal conditionssampling rate fluctuates between 18.5 and 11.8 Hz (black line), whereas during 0.19 hours of theday the instrument is in a special housekeeping cleanup mode and sampling rate can drop to 1.4Hz (gray line), but even in the worst-case conditions, 97.5% of all measurements are delivered at12.7 Hz or better. The horizontal broken line shows the median value, which is the same for bothtime periods.

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Figure 5: Allan variance plot from one hour of data obtained in the laboratory (2 February 2008,05:15–06:15 CET) with background air from which no net CH4 flux is expected, using the internalpump at 1 Hz data delivery rate. The two broken lines show the white noise slope (left) and theslope of the signal drift (right). The white noise slope is found at a level of 1.5 ppb Hz–1/2. Theplot follows the concept by Werle et al. (1993) which is based on original ideas by Allan (1966).

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Figure 6: Effect of reduced data supply rate on variance spectra of an eddy covariance system: (a)example of vertical wind variance spectra over 52.4 minutes at 20.83 Hz (216 records); (b) close-up of high-frequency conditions; and (c) frequency-dependent ratio of variance with respect to thevariance at full time resolution. The thin horizontal line is the reference, whereas gray lines andsymbols show three examples of reduced data supply rates. Point symbols show results obtainedby disjunct eddy covariance data selection, and lines show conditions obtained via oversamplingof available data as described here. Broken lines show the noise from the rectangular signalgenerated by the oversampling procedure. At frequencies below the respective Nyquist frequency(vertical lines with numbers) the latter method yields results that are closer to the true referencevariance spectrum.

19

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0.30 Reference1/5 subsamped1/10 subsampled1/20 subsampled1/5 oversampled1/10 oversampled1/20 oversampled

Figure 7: Simulation of the effect of subsampling and oversampling of a digital concentrationsignal on normalized cospectra. The reference cospectrum and flux represents 52.4 minutes (216

records) of sensible heat flux measured at the Lindestock site on 2008-07-17 starting 11:30 CET(thick gray curve). All cospectra were bin-averaged to 100 frequency bins with equal width on thelogarithmic axis, followed by a 17-point Gaussian filter. At the high-frequency end the bin-averageswere added for this display. While subsampling (solid lines with symbols) approximates the overallmean flux w′c′ref better than oversampling (broken lines), the latter shows better agreement withthe reference at low frequencies and reduces the variability and lack of information at the high-frequency end.

Frequency (Hz)

0.1 1 10

1e−15

1e−11

1e−07

1e−03

1e+01Rectangular Signal Spectrum

f Sx(f

)

13 5 7 9

Figure 8: Spectral analysis of a theoretical rectangular signal of 1 Hz, sampled at 20 Hz shows thebase frequency with its odd harmonics. The spectral densities of the harmonics follow an empiricalf –5/3 rule (upper gray line), which is orders of magnitudes above the white noise level (lower grayline).

20

Frequency (Hz)

f Sw(f)

/w'2

0.001 0.01 0.1 1 10

0.00

001

0.00

10.

11

Spectrum w'

Frequency (Hz)

f Sc(f

)/c'2

0.001 0.01 0.1 1 10

0.00

001

0.01

1

Spectrum CH4'

Frequency (Hz)

f Sw(f)

/w'2

0.001 0.01 0.1 1 10

0.00

010.

001

0.01

0.1

Spectrum w'

Frequency (Hz)

f Sc(f

)/c'2

0.001 0.01 0.1 1 10

0.00

001

0.00

10.

1

Spectrum CH4'

f +1

f –2/3

f –8/31

35 79

(a) (b)

(c) (d)

Figure 9: Normalized power spectra of w (a, c) and CH4 concentration (b, d) during a 30-minuteperiod measured at a landfill site (4 July 2008, 11:00–11:30 CET). Top panels show the fullspectral resolution, bottom panels the same spectra after bandwidth averaging in 100 bands ofequal size on the logarithmic frequency scale.

21

Frequency (Hz)

f Sw(f)

/w'2

0.001 0.01 0.1 1 10

0.00

001

0.00

10.

11

Spectrum w'

Frequency (Hz)

f Sc(f

)/c'2

0.001 0.01 0.1 1 10

0.00

001

0.01

Spectrum CH4'

Frequency (Hz)

f Sw(f)

/w'2

0.001 0.01 0.1 1 10

0.00

010.

001

0.01

0.1

Spectrum w'

Frequency (Hz)

f Sc(f

)/c'2

0.001 0.01 0.1 1 10

0.00

010.

001

0.01

0.1

Spectrum CH4'

f –2/3

f –8/3

f +1

(a) (b)

(c) (d)

Figure 10: Same as in Figure 9 but using the high-flow dry scroll pump for eddy covariance fluxmeasurements, 4 July 2008, 13:30–14:00 CET.

22

1.8

2.2

2.6

CH

4 (pp

m)

CH4 Concentration14

3.6

144.

0

Cel

l P (T

orr)

Cell Pressure

37.8

38.1

Cel

l T (°

C)

Cell Temperature

10.1

910

.21

Rin

gdow

n Ti

me

(µs)

13:00 13:05 13:10 13:15 13:20 13:25 13:30

Mirror Ringdown Time

13:00 13:05 13:10 13:15 13:20 13:25 13:30

13:00 13:05 13:10 13:15 13:20 13:25 13:30

13:00 13:05 13:10 13:15 13:20 13:25 13:30

(a)

(b)

(c)

(d)

Figure 11: Example time series of (a) CH4 concentration, (b) cell pressure, (c) cell temperatureand (d) cavity mirror ringdown time during a 30-minute interval at a landfill site (10 July 2008,1300–1330 CET) at full temporal resolution.

23

Frequency (Hz)

f Sw(f)

/w'2

0.001 0.01 0.1 1 10

0.00

10.

1

Spectrum w'

Frequency (Hz)

f Sc(f

)/c'2

0.001 0.01 0.1 1 10

0.00

10.

1

Spectrum CH4'

−15 −10 −5 0 5 10 15

−0.0

40.

00

Time Lag (s)

r(ch4

,w)

Cross−Correlation Function

Frequency (Hz)

f Co w

,CH

4(f)

/ w'C

H4'

0.001 0.01 0.1 1 10

−1.0

0.5

1.5

Cospectrum w'CH4'

f –2/3

f+1

Frequency (Hz)

Frequency (Hz)

Lag (s)

(a)

(b)

(c)

(d)

Figure 12: Normalized spectra of (a) w and (b) CH4 concentration time series as a function of nat-ural frequency (Hz), (c) lagged cross-correlation between w and CH4 signals, and (d) cospectrumof turbulent flux after shifting the time series by 5 records. The time period covers that shown inFigure 11. The lines given in panel (b) are the inertial subrange slope (f –2/3) and the white noiseslope (f +1). The vertical lines in panel (c) show the search window for the time lag with highestlinear correlation, and best lag (middle line).

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Frequency (Hz)

| f C

o w,c

(f)/

w'c'

|

0.0001 0.001 0.01 0.1 1 10

0.0001

0.001

0.01

0.1

1

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f−4/3

●

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> 0< 0idealized

Figure 13: Normalized cospectra of CH4 flux (absolute values) of the time period shown in Figures11 and 12. The idealized cospectrum was taken from Kaimal et al. (1972).

25

04.07.2008 08.07.2008 10.07.2008 15.07.2008 17.07.2008

−10

−5

0

5

10

15

20

Date of Field Work

CH

4 Flu

x (μμ

g m

−−2s−−1

) 11.0(–0.14 ... 15.5)

1.6(0.28 ... 2.9)

–0.62(–1.4 ... –0.11)

1.7(1.4 ... 2.0)

8.0(4.6 ... 10.2)

Figure 14: Boxplots of 30-minute averaged CH4 fluxes from the Lindestock landfill site, Switzer-land, during five days in July 2008. Measurements were only accepted if wind direction wasbetween 190◦ and 0◦ (from the west) and if momentum flux was directed toward the surface.Boxes show the median flux (bold line, bold numbers) and the interquartile range (25% to 75%interval, gray box and range given in brackets). Whiskers denote the full range of all values (n ≤9, depending on date).

26