George G. Burba, Dayle K. McDermitt, and Dan J. Anderson. Open-path infrared gas analyzers are widely used around the world for measuring CO 2

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1 1 Influence of instrument surface heat exchange on CO 2 flux from oen-ath gas analyzers George G. Burba, Dayle K. McDermitt, an Dan J. Anerson LI-COR Biosciences, 4421 Suerior Street, Lincoln, Nebraska 6854, USA (george.burba@licor.com) 1. Introuction Oen-ath infrare gas analyzers are wiely use aroun the worl for measuring CO 2 exchange. There have been many comarisons between oen-ath an close-ath sensors emonstrating substantially similar CO 2 flux measurements. However, there is growing evience that shows ifferences between oen-ath an close-ath measurements, esecially in the form of aarent off-season CO 2 utake when it is hysiologically unreasonable to exect it. Measurements mae with close-ath analyzers, chambers, an graient methos have consistently shown small releases of CO 2. To aress this issue, a series of laboratory an fiel exeriments were conucte to examine the influence of instrument surface temerature an heat exchange on the oen-ath CO 2 fluxes. The following concetual framework (Burba et al. 25a,b; 26 a,b) was use: if the instrument surface temerature is ifferent from the ambient temerature (i.e., measure outsie the instrument oen ath), it coul cause sensible heat fluxes insie the oen-ath cell to be ifferent from the ambient, thus affecting CO 2 ensities. This henomenon shoul be accounte for in Webb-Peraman-Leuning term (WPL, Webb et al. 198). With these issues in min, this investigation focuse on the following secific questions: i) Is the instrument surface temerature significantly warmer or coler as comare to the ambient air?

2 2 ii) Does the resulting instrument surface heat exchange correlate with the vertical win see to rouce a sensible heat flux insie the ath which is ifferent from the ambient sensible heat flux? iii) Can the effect of this heat exchange be eliminate by enclosing an oen-ath gas analyzer? iv) Can a sensible heat flux measure irectly insie the ath be use in WPL to correct unreasonable oen-ath fluxes to match close-ath fluxes? v) Can the instrument surface heat exchange be estimate from co-locate meteorological ata to correct reviously measure oen-ath fluxes? vi) What are the consequences of assuming the instrument surface heating effect is negligible? 2. Theoretical Consierations The imact of instrument surface heating on air ensity in the otical ath of an oenath instrument (Burba et al. 25a, b; 26a, b) can be escribe using the Webb-Pearman- Leuning ensity formulation (WPL, Webb et al. 198), which can be written in the following form for CO 2 flux: E ρc S ρc Fc = F + µ + ρ ρ v ρc Ta 1+ µ ρ (1) an for water vaor flux: ρ S v ρ v E = ( 1+ µ )( E + ) (2) ρ ρc Ta where F c is WPL-correcte CO 2 flux (kg m -2 s -1 ); E is WPL-correcte H 2 O flux (kg m -2 s -1 ); F o is initial CO 2 flux, not correcte for WPL (kg m -2 s -1 ); E o is initial H 2 O flux, not correcte for WPL

3 3 (kg m -2 s -1 ); µ is ratio of molar masses of air to water (µ=1.677); ρ is mean ry air ensity (kg m -3 ); ρ v is mean water vaor ensity (kg m -3 ); ρ c is mean ambient CO 2 ensity (kg m -3 ); ρ is mean total air mass ensity (kg m -3 ); S is sensible heat flux (W m -2 ); C is secific heat of air (J kg -1 K -1 ); T a is ambient air temerature (K). Traitionally, S has been measure outsie the gas analyzer oen ath by sonic anemometry, or with the hel of a fine-wire thermocoule installe near or in the sonic ath. If warm instrument surfaces aroun the oen ath heat air in the ath, then there may be nonnegligible ifferences between sensible heat flux insie the oen ath of the gas analyzer an that in ambient air, such that measure or estimate sensible heat flux insie the oen ath shoul be use in the WPL term instea of S measure in ambient air (Burba et al. 25a, b; 26, a, b). T a is affecte in a similar manner as S, but since it is in o K, its effect on the WPL term is small (Eqs. 1 an 2). The concet of using heat flux measure in the otical ath was confirme in a stuy by Grelle an Burba (27), where S an T a were measure insie the instrument oen ath using a fine-wire thermometer uring normal oeration, an uring a regime in which the instrument was heate by an external heater. In both cases, S measure insie the oen ath was substantially ifferent from ambient. Also, in both cases, CO 2 fluxes ajuste using a WPL term with S measure insie the oen ath i not exhibit the unreasonable off-season an nighttime utakes observe when using ambient S, an they closely matche the reference flux measure with a LI Here we escribe, test, an comare several techniques for ealing with S insie the oen-ath volume, as summarize in Table I. These techniques inclue: 1) the traitional aroach (S is measure in the ambient air using sonic anemometry); 2) an enclose LI-75 technique (S is effectively eliminate by a temerature attenuation in the intake tube of the

4 4 enclose analyzer); 3) a fine-wire PRT technique (S is measure irectly insie the oen ath; Grelle an Burba 27); an 4) an estimate heating correction technique, which can be alie to reviously collecte oen-ath ata (S for the WPL term is comute by aing estimate sensible heat fluxes from key instrument surfaces to the ambient sensible heat flux; Burba et al. 26 a, b). In all cases, CO 2 fluxes from close-ath systems (e.g., LI-6262 an LI-7) are use as references, because high-frequency temerature fluctuations are attenuate in such systems by long intake tubes, thus greatly minimizing or eliminating S insie the analyzer cell. Further etails on theoretical an exerimental aroaches can be foun in Burba et. al. (28) 3. Results an Discussion Instrument surface heating an its effect on oen-ath CO 2 fluxes were teste over four ecosystems: ryegrass, forest clear-cut, maize, an soybean. The surface temeratures of the oenath infrare gas analyzer ajacent to the samling volume were u to 6 o C warmer than the ambient air uring aytime ue to heating from the sensor hea electronics an solar loaing. The heat exchange insie the ath was correlate with vertical win see. This rouce sensible heat fluxes that were on average 14% larger than in the ambient air, at mil air temeratures. This ercentage increase further with coler air temeratures an associate increase in sensor hea instrument heating by on-boar thermoelectric evices. Figure 1 shows cumulative fluxes measure in four exeriments with the close ath LI-6262 an with the oen ath LI-75, which was either enclose or correcte for the heat exchange, using the methos escribe in Table I. Summary of the integrate CO 2 flux values is rovie in Table II. In all exeriments, use of solely ambient sensible heat flux in the WPL term (Metho 1) causes CO 2 flux integrations to be biase towars the CO 2 utake as comare to close-ath references. During 4 weeks in winter over ormant ryegrass (Fig 1 A), flux

5 5 measurements mae with the oen-ath LI-75 an correcte using Metho 1 uner-estimate CO 2 release by 12 g C m -2 (33%; Table II) as comare to the close ath reference. In contrast, using an enclose LI-75 (Metho 2) resulte in a nearly erfect match with the reference LI- 7, with an error of.3%. When a heating correction was comute from instrument surface temeratures (Metho 4) that were estimate from T a by linear regression, the error was reuce from 12 to 2 g C m -2 (from 33% to 5%; Table II). This was not as goo as an enclose LI-75, but was consierably better than ignoring the instrument surface heat exchange. In the fine-wire PRT exeriment (Figure 1B), use of traitional Metho 1 le to a 3 g C m -2 (19%) unerestimate of CO 2 release uring two weeks in October. Meanwhile, the PRT technique (Metho 3) an estimate heating correction from T s comute via linear regression with T a (Metho 4) le to a consierably better match with close-ath references to within 1 g C m -2 (Table II). Remaining iscreancies between Methos 3 an 4 may be ue to unaccounte heat fluxes cause by nearby structures, since the LI-75 was mounte close to the base of the sonic anemometer. Figures 1C an 1D show cumulative yearly CO 2 fluxes etermine in the Mea, NE exeriment from maize an soybean, resectively. During the off-season erio (October-May) traitionally correcte oen-ath fluxes were 39 to 66 g C m -2 (75-81%) lower than the closeath flux because of the systematic unerestimation of CO 2 loss ue to instrument surface heating (Table II). Consistent unerestimation of CO 2 flux by the traitional technique has resulte in a consierable overestimation of the yearly CO 2 utake at both sites by 92-1 g C m -2 (14-16%) as comare to close-ath fluxes. In contrast, cumulative fluxes from an oenath sensor correcte using Metho 4 from T s estimate via both linear an multile regressions were consistently similar to close-ath fluxes throughout the entire year (Figures 1 C,D). On an integrate basis over the off-season, the multile regression technique resulte in a larger error in

6 6 Maize (-1% vs. -4% for linear regression with T a ), but was better in Soybean (4% vs. 7% for linear regression with T a ). On a yearly basis both regressions gave goo results, with the LI-75 CO 2 flux matching the close-ath reference within 1%. Overall, on a seasonal basis, any technique accounting for instrument surface heating (Methos 2-4) resulte in a significant imrovement in CO 2 flux estimates comare with the traitional aroach, which uses only ambient sensible heat flux in WPL term (Metho 1). The most significant imrovements were observe when the effect of instrument surface heat exchange was eliminate by enclosing the LI-75 (CO 2 flux error of.3%), followe by measuring sensible heat flux in the oen ath using the fine-wire PRT technique (CO 2 flux error of -4%; Grelle an Burba 27). Estimating the instrument surface heat exchange (Burba et al. 26b) using measure T s reuce the CO 2 flux error to -6%, while estimating T s by linear regression with T a reuce the error to -6 to 7%; estimating T s by multile regression with weather variables reuce CO 2 flux error to -1% to 4%. By contrast, in the ecosystems stuie, neglecting the instrument surface heat exchange an using only ambient sensible heat flux in the WPL term (Metho 1), rouce unerestimates of CO 2 release ranging from 14 to 81% (Table II). 4. Conclusions Among the teste techniques the best erformance was yiele by an enclose LI-75 (Metho 2), followe by the fine-wire PRT technique (Metho 3), an by the estimate heating correction technique which utilizes measure T s, an T s evaluate by linear regression with T a, or by a multile regression with weather variables (Metho 4). The least successful erformance was yiele by a traitional aroach (Metho 1) that uses solely ambient sensible heat flux in WPL term, resulting in a significant unerestimate of long-term CO 2 release in all conucte

7 7 exeriments. Further etails on results from this stuy, as well as on concetual an methoological consierations, can be foun in Burba et. al. (28). These results may have imortant imlications for global carbon cycle research an climate moeling. Systematic unerestimation of the CO 2 release uring off-season erios by oen-ath sensors woul likely be biase towars col-climate ecosystems. As a result, longer an coler off-season erios woul have greater unerestimates of CO 2 release. Yearly estimates of net ecosystem exchange then may be significantly biase towar CO 2 utake in such col-climate ecosystems, an may nee to be revise in some cases. Warm-climate ecosystems are less likely to be strongly affecte, esecially when air temeratures o not ro below freezing an when CO 2 fluxes stay large throughout the year. Oen-ath CO 2 fluxes calculate with the traitionally comute WPL term were not correcte for this reviously unknown instrument surface heat exchange effect, so it is likely that biases alreay exist in ata from coler ecosystems, an have affecte a number of stuies, their conclusions, an resulting moels. Aitional research is require to evaluate the otential imact of such bias, an to evelo a strategy to correct the large volume of reviously collecte oen-ath ata, incluing further investigation an valiation of the roose techniques for correction of instrument surface heat exchange in a wie range of ecosystems an exerimental settings.

8 8 References Balocchi DD, Hincks BB, Meyers TP (1988) Measuring Bioshere-Atmoshere Exchanges of Biologically Relate Gases with Micrometeorological Methos. Ecology, 69 (5), Burba GG, Anerson DJ., Xu L, McDermitt DK (25a) Solving the off-season utake roblem: correcting fluxes measure with the LI-75 for the effects of instrument surface heating. Progress reort of the ongoing stuy. PARTI: THEORY. Poster. AmeriFlux 25 Annual Meeting, Bouler, Colorao. Burba GG, Anerson DJ., Xu L, McDermitt DK (25b) Solving the off-season utake roblem: correcting fluxes measure with the LI-75 for the effects of instrument surface heating. Progress reort of the ongoing stuy. PARTII: RESULTS. Poster. AmeriFlux 25 Annual Meeting, Bouler, Colorao. Burba GG, Anerson DJ., Xu L, McDermitt DK (26a) Correcting aarent off-season CO2 utake ue to surface heating of an oen-ath gas analyzer: rogress reort of an ongoing exeriment. Proceeings of 27th Annual Conference of Agricultural an Forest Meteorology, San Diego, California, 13. Burba GG, Anerson DJ., Xu L, McDermitt DK (26b) Aitional Term in the Webb- Pearman-Leuning Correction ue to Surface Heating From an Oen-Path Gas Analyzer, EOS Trans. AGU, 87(52). Burba GG, McDermitt DK, Grelle A, Anerson DJ, Xu L (28) Aressing the influence of instrument surface heat exchange on the measurements of CO2 flux from oen-ath gas analyzers. Global Change Biology. Accete. Grelle A, Burba GG (27) Fine-wire thermometer to correct CO2 fluxes by oen-ath analyzers for artificial ensity fluctuations. Agricultural an Forest Meteorology, 147(1-2): Nobel PS (1983) Biohysical Plant Physiology. W.H. Freeman an Comany, San Francisco: 488. Webb EK, Pearman GI, Leuning R (198) Correction of flux measurements for ensity effects ue to heat an water vaour transfer. Quart. J. R. Met. Soc., 16: 85-1

9 9 Table I. Techniques for correcting oen-ath fluxes for the effect of instrument surface heat exchange (Burba et.al, 28) General Equations General equation for the gas flux (F c ) over a homogenous horizontal lain for steay state conitions incluing WPL term (Webb et al, 198) F c = E ρ c S F + µ + ρ ρ v 1 + µ ρc ρ ρ c T a General equation for the water vaor flux (E ) over a homogenous horizontal lain for steay state conitions incluing WPL term (Webb et al, 198) ρ S v E = ( 1 + µ )( E + ρ ρc ρ v ) T a Sensible Heat Flux, S, for General Equations Traitional WPL correction technique. Sensible heat flux is comute in the ambient air from sonic temerature or from a fine-wire thermocoule in the oen air (Balocchi et al., 1988) S = ρ C w ' T a ' Metho 1 Enclose LI-75 technique. Sensible heat flux has been eliminate by attenuating temerature fluctuations in the long intake tube. Same rincile is use in the reference close-ath measurements (LI-6262 or LI-7) S = Metho 2 Fine-wire PRT technique. Sensible heat flux insie the oen ath is measure irectly by fine-wire PRT an use instea of ambient sensible heat flux measure in the oen air (Grelle an Burba, 27) Estimate heating correction technique. Total sensible heat flux for WPL term is comute by aing estimate sensible heat fluxes from key instrument surfaces (bottom winow, to winow an ) aroun the oen-ath to the ambient sensible heat flux (Burba, 26b). S = ρc w ' TPRT bot to S = ρc wt ' a' + S + S +. 15S ' Metho 3 Metho 4 Surface Sensible Heat Fluxes for Nobel Formulation use in Metho 4 Nobel (1983) formulation for S bot,s to an S. T s can be measure, or estimate via linear regression with Ta (Table III) or via multile regression with key weather variables (Table II). to δ S S to S bot = k = k bot δ = k bot air ( Ts bot δ Ta) to to to air ( r + δ )( Ts Ta) to to air r r ( Ts r ln( l bot δ Ta) + δ r = U l to = / U +.45 U ) δ =.58 l U w is vertical win see (m s -1 ); T a is ambient air temerature ( o K); T PRT is temerature measure insie the oen ath with fine-wire PRT ( o K); S bot, S to,s - sensible heat fluxes from key instrument surfaces of bottom winow, to winow an, resectively (W m -2 ); T s is the mean surface temerature of the bottom winow (T bot s ), to winow (T to s )an(t s )( o K); δ is average thickness of the bounary layer above the bottom winow, to winow, an (m); r to is the raius of the shere (.225 m); r is the raius of the cyliner (.25 m); l bot is iameter of the source housing treate as a lane (.65 m),.4 m is ae to comensate for the 2 o angle of the shoulers in relation to the horizontal bottom winow; l to is the iameter of the etector housing treate as a shere (.45 m),,.45 m is ae to comensate for the non-sherical surface of the to winow; l is the iameter of the s treate as cyliners (.5 m); k air is the thermal conuctivity coefficient of air (W m -1 o K -1 ); U is mean horizontal win see (m s -1 ). Other terms are efine in the text.

10 1 Table II. Comarison of the integrate CO 2 release measure in three ifferent fiel exeriments with four ifferent techniques for comuting WPL term. All tables an lots inclue only hours with comlete ata, i.e. when actual reaings from the LI- 62/7, LI-75, an other instruments use in the roose corrections were available. Non-stationary conitions, rain, snow, instrument malfunctions an other fille-in erios were exclue to assure roer comarison between LI-75 F c an LI-6262/7 F c. The error in F c calculate by these techniques is comute using close-ath LI-6262 or LI-7 as reference such that % error=1*(f 75 -F 6262/7 )/F 6262/7. Off-season erios are consiere to be erios without green foliage area. In all three exeriments, use traitionally comute WPL term with oen-ath LI-75 (Metho 1) leas to significant unerestimates of CO 2 release or overestimates of CO 2 utake, while LI-75 flux correcte for surface heating by either of three roose alternative methos is close to reference close-ath LI-6262/7 flux which is not affecte by heating roblem (Burba et.al, 28) Reference Metho 4 Metho 3 Metho 2 Metho 1 Technique Units Enclose LI-75 Fine-Wire PRT Stuy at Mea Essence of Technique Nebraska Sween Nebraska Dec-Jan October Off-season Off-season Year Year Ryegrass Forest clear-cut Maize fallow Soy fallow Maize Soybean Close-ath Fc: LI or LI-7 (use as reference) Fc from oen-ath LI-75 with traitionally comute WPL (Webb et al., 198) Fc from an enclose LI-75 Fc from oen-ath LI-75 with finewire PRT correction (Grelle an Burba, 27) Fc from oen-ath LI-75 with estimate heating correction (Burba et. al., 26b): Ts is measure Fc from oen-ath LI-75 with estimate heating correction (Burba et. al., 26b): Ts is estimate from linear regression with Ta Fc from oen-ath LI-75 with estimate heating correction (Burba et. al., 26b): Ts is estimate from multile regression from Table II Exeriments g C g C % error g C % error g C % error g C % error g C % error g C % error Heat exchange effect is minimize by attenuation of high frequency temerature fluctuations in intake tube. Only latent heat flux ortion is use in the WPL term Ambient sensible heat flux measure outsie the oen ath is use in the WPL term Heat exchange effect is minimize by high frequency temerature attenuation in intake tube. Only latent heat flux ortion is use in the WPL term Sensible heat flux measure using fine-wire PRT in the oen ath is use instea of the ambient sensible heat flux in the WPL term Aitional sensible heat flux in the oen ath is comute from instrument surface temerature, T s, using the formulation by Nobel (1983), an then ae to ambient sensible heat flux in the WPL term. Ts can be measure irectly near to an bottom winows an on s, or estimate from air temerature, or multile regression with key weather variables.

11 11 A Cumulative Fc, g C m Winter: ormant ryegrass B Cumulative Fc, g C m -2 D C 2 Year: Maize Cumulative Fc, g C m -2 12/19/6 12/28/6 1/7/7 1/16/7 15 Fall: clear-cut 1 5 make it in grams of C an change lines 1/8/26 1/2/ D Cumulative Fc, g C m -2-8 Oct-2 Nov-2 Jan-3 Mar-3 May-3 Jul-3 Se-3 2 Year: Soybean Oct-2 Nov-2 Jan-3 Mar-3 May-3 Jul-3 Se-3 Reference LI-6262 LI-75 with traitionally comute WPL (Metho 1) Enclose LI-75 (Metho 2) LI-75 with heat correction comute via fine-wire PRT (Metho 3) LI-75 with estimate heating correction (Metho 4): Ts is estimate via linear regression with Ta Ts is estimate via multile regression from Table II Ts is measure Figure 1. Cumulative lot of hourly Fc values (in g C m -2 ) in four ecosystems. (A) enclose LI-75 exeriment over ormant ryegrass; (B) fine-wire PRT exeriment; an stuy an Mea, NE: (C) maize, an (B) soybean. In all cases ata were use only when actual reaings from the LI-62/7, LI-75, an other instruments use in the roose corrections were available. Non-stationary conitions, rain, snow, instrument malfunctions, an other fille-in erios, were exclue to assure roer comarison between LI-75 an LI-6262/7. In all exeriments, use of traitionally comute WPL term (Metho 1) with the oen-ath LI-75 leas to unerestimates of CO 2 release, an overestimates of CO 2 utake, while LI-75 flux correcte for surface heating by any of the roose methos is quite similar to the reference close-ath LI-6262/7 flux (Burba et.al, 28)