the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Air-parcel residence times in a mature forest: observational evidence from a free-air CO2 enrichment experiment
- 1Birmingham Institute of Forest Research, University of Birmingham, Edgbaston, Birmingham, United Kingdom
- 2Department of Civil Engineering, University of Birmingham, Edgbaston, Birmingham, United Kingdom
- 3Department of Geography, Earth, and Environmental Sciences, University of Birmingham, Edgbaston, Birmingham, United Kingdom
- retired
- 1Birmingham Institute of Forest Research, University of Birmingham, Edgbaston, Birmingham, United Kingdom
- 2Department of Civil Engineering, University of Birmingham, Edgbaston, Birmingham, United Kingdom
- 3Department of Geography, Earth, and Environmental Sciences, University of Birmingham, Edgbaston, Birmingham, United Kingdom
- retired
Abstract. In forests, air-parcel residence times – the inverse of first-order exchange rates – influence in-canopy chemistry and the exchanges of momentum, energy, and mass with the surrounding atmosphere. Accurate estimates are needed for chemical investigations of reactive trace species, such as volatile organic compounds, some of whose chemical lifetimes are in the order of average residence times. However, very few observational residence-time estimates have been reported. Little is known about even the basic statistics of real-world residence times or how they are influenced by meteorological variables such as turbulence or atmospheric stability. Here, we report opportunistic investigations of air-parcel residence times in a free-air carbon dioxide enrichment (FACE) facility in a mature, broadleaf deciduous forest with canopy height hc ≈ 25 m. Using nearly 50 million FACE observations, we find that median daytime residence times in the tree crowns range from around 70 s when the trees are in leaf to just over 34 s when they are not. Air-parcel residence times increase with increasing atmospheric stability, as does the dispersion around their central value. Residence times scale approximately with the reciprocal of the friction velocity, u*. During some calm evenings in the growing season, we observe distinctly different behaviour: pooled air being sporadically and unpredictably vented – evidenced by sustained increases in CO2 concentration – when intermittent turbulence penetrates the canopy. In these conditions, the concept of a residence time is less clearly defined. Parameterisations available in the literature underestimate turbulent exchange in the upper half of forest crowns and overestimate the frequency of long residence times. Robust parametrisations of air-parcel residence times (or, equivalently, fractions of emissions escaping the canopy) may be generated from inverse gamma distributions, with the parameters 1.4 ≤ α ≤ 1.8 and β = hc / u* estimated from widely measured flow variables. In this case, the mean value for τ becomes formally defined as 𝜏̅ = β / (α−1). For species released in the canopy during the daytime, chemical transformations are unlikely unless the reaction time scale is in the order of a few minutes or less.
Edward J. Bannister et al.
Status: final response (author comments only)
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RC1: 'Comment on acp-2022-318', Tobias Gerken, 23 Jun 2022
The authors present an observational study of air residence times generated from CO2 data during a FACE experiment and use these to investigate impacts of environmental conditions on air residence times. Inspired by a previous paper (Gerken et al. 2017, GCF17) that sought to describe the probability density function (PDF) of air parcel residence times, the authors note a generally similar behavior to GCF17 of their data and use the data to fit an inverse gamma distribution to their calculated air residence times. In general, I find the paper to be interesting especially given that air residence time is a fundamentally unsolved problem, which may be of some importance for modeling air chemistry of BVOCs. At the same time, I have several comments that should be addressed before publication.
As a side note, I am the first author of GCF17 and it is nice to see that this paper is being used as a basis for discussion.
General comments:
- Eulerian vs. Lagrangian approach: The authors' approach is in essence a Eulerian approach to calculating a mean air residence time, while Gerken et al. 2017 (GCF17) applies a Lagragian model within an LES to generate a PDF of air parcel residence times, which is used to then estimate the parameters of a first passage process (Schrödinger 1915). It appears that the main difference between the PDF of CO2 residence times generated in this work and in GCF17 is that GCF17 predicts a heaver tail of long residence times, which is not found in the data for this manuscript and the authors attribute this to limitations of the eddy diffusivity approach and the homogeneity assumption embedded in GCF17 (I hope that this is a fair reading). First of all, I don't want to dismiss these explanations, given that GFC17 was developed using LES data rather than direct observations of air parcel residence times, which cannot be observed in the field. At the same time, I am wondering about whether there is a mismatch between the Eulerien approach in this manuscript and the Langrangian approach in GFC17. It is my understanding that the approach employed in this manuscript and represented by eq. 5 of this manuscript provides a singled mean air residence time for the entire air volume within the control volume (sorry for the wordy description of this). I believe that this is not directly comparable to the air parcel residence time as defined in GCF17, which arises from tracking of individual Lagrangian particles that are thought to represent a hypothetical air parcel. So in my view the air residence time (tau) calculated in this manuscript might be more akin to the mean of the air parcel residence time distribution from GCF17. In this view each calculated \tau would be another sample of the mean air parcel residence time rather for a given instance of turbulent conditions rather than the residence time of an air parcel that together make up the PDF that are used to fit equation 1 in GCF17. In other words, the tau values in this work might represent a multitude of air parcels over a given averaging length (5 minutes in this case). This interpretation would account for the fact that tau values found in this work lack the heavy tail found in GCF17. I would appreciate additional discussion of this.
At this point I would like to reiterate that, it might very well be true that GCF17 overestimates the heavy tail of the tau PDF, but at least for the LES applied in GCF17 we did not find this to be true (see Figure 5b in GCF17).
This is also not to say that the analysis done in this work is not useful on the path to develop air residence time parameterizations and I certainly find the discovered gamma distribution fit (eq. 7 and Fig 9) a valuable contribution.
- Advection: If I understand correctly, the authors assume that advection and therefore losses to the side of the control volume are negligible. Given the setup of the FACE (and admitting that I am not very familiar with it), I am wondering to what extent this would be true given the open sides and the fact that the FACE experiment enriches CO2 inside the control volume, thus producing an artificial horizontal CO2 gradient. I would appreciate additional discussion on this and potentially some evidence that advection or horizontal loss of CO2 is indeed neglegible.
- Role of LAI: Generally speaking, it might make sense in the introduction and discussion to reference LAI and leaf area density profiles more frequently since the interaction between leaf drag and turbulence penetration into the canopy are likely one of the main reasons for widely varying estimated residence times.
Specific comments:
Title: In the light of my general comment 1, it might be better to remove the 'parcel' from the title.
L 67: "Gerken et al. (2017) (hereafter GCF17) offer ..." > I suggest to also reference Katul et al. 2005 in this context, since their model was used as a starting point and includes similar assumptions. One should also note that this formulation was only proposed for neutral conditions.
L 87: "In an LES investigation of flow over forested hills, residence times of Lagrangian air parcels emitted in the lower part of the canopy were shorter than those moving over flat terrain (Chen et al., 2019)." > I suggest to expand on this since the impacts of terrain are very important for real world applications and there is ample evidence (albeit andecdotal) for preferential venting due to terrain
L90: "Researchers have also used Eulerian frameworks to investigate residence times in forests." > It might be good in this context to discuss some of the limitations on Eulerian vs. Lagrangian methods regarding their implications for air chemistry. This also goes along with my general comment on the comparability of Lagrangian and Eulerian approaches. Given that aur parcel residence time is a fundamentally Lagrangian process, the Eulerian description has some limitations such as that it is in my mind a mean air residence time, which can underestimate the tail ends, which might be important for air chemistry.
L200: "because broadleaf forests uptake little carbon below this threshold" > this sounds off. 'because carbon uptake is negligible' (?)
Section 2.3: What is the time scale of the \tau calculation? (P.S. I see that this is answered in the data processing section. I suggest to move this forward). Additionally and given the importance of release height pointed out in Gerken et al. 2017, it would also be good to hear more about at what heights CO2 is being releases. I
L 237-240" "Therefore, rather than trying to assign a numerical value to ð¹ðð¢ð¡(âðð) , we identify meteorological conditions under which ð¹ðð¢ð¡(ð¡ðð) â« ð¹ðð¢ð¡(âðð) , and therefore ð = ðð¶ð2 /ð¹ðð ≈ ðð¶ð2 /ð¹ðð¢ð¡(ð¡ðð) . Figure 3 presents probability density functions of ð during the lowest 50% of wind speeds of the leaf-on period (solid black), during the highest 25% of wind speeds of the leaf-on period (dashed),... " > This seems like an abrupt transition. It might be good to give provide a sentence or two on who these are related to advection. On a broader note, I appreciate the advection problem in the sense that this is something that has been challenging in high vegetation with CO2 accumulation within the canopy airspace.
L 241" zrel > I am wondering whether it would make sense to adjust z_rel, given that it is not clear to me what the real release height of the CO2 is would be to minimize the difference between the observational results and the theoretical result by adjusting z_rel.
Figure 3a: It seems to me that all the curves in Figure 3 should have the same integral. Could you confirm this and check whether all curves are properly normalized, since it seems (by eyeballing) that the GCF17 might not have the same area under the curve.
Figure 6 should have a colorbar and possibly a trendline to better gauge the underlying density distribution
The stability classes in Section 3.3.2 should probably be moved to methods section.
L 384: "The distributions of ð remain positively skewed for each stability class (e.g., the right whiskers are longer than the left in Figure 7a)." > It might be a good idea, here and in general to report the skewness.
Section 3.4.: I am not sure how informative this section and the associated figure is. I think that it is important to discuss the edge effect and impacts of heterogeneity, but I am not sure whether this section currently does this in the optimal way. Especially since I think that Figure 8 is pretty hard to read. What dominates the differences in the different wind sectors. Is it heterogeneity or some other influence such as time of day coupled with stability?
L445: "However, although GCF17’s model generates modal values similar to those we observed, it appears to overpredict the
likelihood of long residence times in the upper canopy." > this might be true, but also there might be the issue of comparing an essentially Eulerian and Lagrangian method (see general comments).L463: "These eddies create significant turbulent transport, meaning that the eddy-diffusivity model underestimates turbulent forest-atmosphere exchange in the upper canopy and therefore overestimates residence times." > Turbulent diffusivity approaches do have issues within forest canopies. One thing to note about GCF17 is the fact eddy diffusivities are estimated from the LES and adjusted for the release height by taken the mean modeled diffusivity (either arithmetic or geometric mean) between release height and canopy top. It is not clear to me that this would lead to an effective underestimation of turbulent transport. Some additional thoughts by the authors would be appreciated.
Section 3.7: This section seems a bit tacked on in the sense that it is not clear how it relates to the previous section of the model, especially given that the main conclusion from the previous section seemed to point to an overestimation of residence times in GCF17. While the information presented here is an interesting case study, it might make sense to either tie this directly to the analysis before or to remove/ move to an appendix. On a side not and also with respect to long residence times. The original GFC17 study was motivated by air exchange within Amazon rainforest canopies with large LAI and limited penetration of turbulent eddies into the lower half of the canopy. Evidence for the limited coupling of canopy airspace to the above canopy air can be for example found in Freire et al. (2017).
References:
Freire, L. S., T. Gerken, J. Ruiz-Plancarte, D. Wei, J. D. Fuentes, G. G. Katul, N. L. Dias, O. C. Acevedo, and M. Chamecki (2017), Turbulent mixing and removal of ozone
within an Amazon rainforest canopy, J. Geophys. Res. Atmos., 122, 2791–2811, doi:10.1002/2016JD026009.Katul GG, Poporato A, Nathan R, Siqueira M, Soons M, Poggi D, Horn H, Levin S (2005) Mechanistic
analytical models for long-distance seed dispersal by wind. Am Natural 166(3):368–381Schrödinger E (1915) Zur Theorie der Fall- und Steigversuche an Teilchen mit Brownscher Bewegung. Physikal
Z 16:289–295 -
RC2: 'Comment on acp-2022-318', Anonymous Referee #2, 12 Sep 2022
Review of the manuscript “Air parcel residence time in a mature forest: observational evidence from a free-air CO2 enrichment experiment”
General comments
This study analyses an extensive dataset from a FACE facility in the UK with the objective to quantify the air parcel residence time a mature broadleaf deciduous forest ecosystem. The manuscript is generally very well written and clearly structured. All figures are well designed and very instructive. The introduction covers the relevant literature well, identifying the knowledge gaps, clearly state the objective. The methods section is a pleasure to read and provides all relevant details on the site, the study period, the instrumentation and the data processing. The presentation of the results is informative and addresses the objectives defined by the authors. This section is accompanied by a critical discussion of the results with important notes on further analysis using LES or physical models. The conclusions are meaningful and drawn correctly. Overall, this is an excellent manuscript and it was a pleasure to read it. I just have one suggestion: conclusion 2 could be substantiated by calculating the Damköhler number, which relates the chemical reaction timescale to the transport timescale, as in, e.g. Karl et al. (2013). Therefore, I recommend this article for publication after minor revisions.
Karl, T., Misztal, P. K., Jonsson, H. H., Shertz, S., Goldstein, A. H., & Guenther, A. B. (2013). Airborne flux measurements of BVOCs above Californian oak forests: experimental investigation of surface and entrainment fluxes, OH densities, and Damköhler numbers. Journal of the Atmospheric Sciences, 70(10), 3277–3287. https://doi.org/10.1175/jas-d-13-054.1
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AC1: 'Comment on acp-2022-318', Ed Bannister, 02 Nov 2022
The authors thank Tobias Gerken (RC1) and the anonymous reviewer (RC2) for their thoughtful comments on our manuscript. We found the comments valuable, and they helped us refine and present the ideas in our manuscript.
We include detailed responses to RC1’s comments below. These are preceded with ‘>>>’ in case the bold formatting is stripped in the online version.
As a summary of the main changes to the manuscript, we have:
- Clarified our definition of a ‘residence time’ of air in a forest canopy. We now use ‘air-parcel residence times’ only in the context of Lagrangian investigations, and ‘residence time of air’ in the context of our results (which are derived using a Eulerian mass-balance approach). This change allows a more balanced comparison of our results and those in earlier papers (most notably, to GCF17).
- Included more discussion of the limitations in our method, such as the possibility of non-negligible advection from the control volumes within which the residence times are calculated.
- Included an illustrative example, using the reaction timescale of isoprene, of the influence of short residence times on Damköhler numbers (and how they may respond to changes in atmospheric stability).
- Improving several of the figures, and making the figure captions stand alone, so that the key information can be found by readers skim-reading the paper.
- Including more detail on the complexity of density and morphology in real forest canopies. The effect of canopy structure on residence times has not been tested in the field, but we include references to investigations in idealised numerical models (lines 83–95: all line numbers in this comment refer to those in the revised manuscript).
- Changed references to statistical ‘dispersion’, which could potentially be confusing in this context, to ‘spread’ or ‘variability’.
- Included a short introduction to the strengths and weaknesses of the three methods of statistical variability used in this manuscript.
Specific comments:
Title: In the light of my general comment 1, it might be better to remove the 'parcel' from the title.
>>> This a fair comment and we have adjusted the title of the manuscript.
L 67: "Gerken et al. (2017) (hereafter GCF17) offer ..." > I suggest to also reference Katul et al. (2005) in this context, since their model was used as a starting point and includes similar assumptions. One should also note that this formulation was only proposed for neutral conditions.
>>> We have included this reference at lines 64–65, thank you.
L 87: "In an LES investigation of flow over forested hills, residence times of Lagrangian air parcels emitted in the lower part of the canopy were shorter than those moving over flat terrain (Chen et al., 2019)." > I suggest to expand on this since the impacts of terrain are very important for real world applications and there is ample evidence (albeit anecdotal) for preferential venting due to terrain.
>>> We have expanded this section, including references to relevant observational and modelling studies (lines 97–106). However, a detailed discussion of the various flow phenomena that occur in hilly terrain is out of scope of this study (see the included references for further detail).
L90: "Researchers have also used Eulerian frameworks to investigate residence times in forests." > It might be good in this context to discuss some of the limitations on Eulerian vs. Lagrangian methods regarding their implications for air chemistry. This also goes along with my general comment on the comparability of Lagrangian and Eulerian approaches. Given that our parcel residence time is a fundamentally Lagrangian process, the Eulerian description has some limitations such as that it is in my mind a mean air-residence time, which can underestimate the tail ends, which might be important for air chemistry.
>>> This is an important point. We have included some discussion of the strengths and weaknesses of the two approaches at 111–124. We have also adjusted the wording of the manuscript to refer to ‘air-parcel residence times’ only in the context of Lagrangian investigations, and ‘residence time of air’ in the context of our results (which are derived using a Eulerian mass-balance approach).
L200: "because broadleaf forests uptake little carbon below this threshold" > this sounds off. 'because carbon uptake is negligible' (?)
>>> We have clarified this statement, as suggested, at lines 232–233.
Section 2.3: What is the time scale of the \tau calculation? (P.S. I see that this is answered in the data processing section. I suggest to move this forward). Additionally, and given the importance of release height pointed out in GCF17, it would also be good to hear more about at what heights CO2 is being releases.
>>> We have moved the timescale of the residence calculation to section 2.3, as suggested (lines 281–288). We have also provided a little more background on the heights of the fumigation at BIFoR FACE in sections 2.3 and 2.4 (lines 277–279 and 321–325).
L 237-240" "Therefore, rather than trying to assign a numerical value to F_out(hor), we identify meteorological conditions under which F_out(top) >> F_out(hor), and therefore tau = M_CO2/F_in ~ M_CO2/F_out(top). Figure 3 presents probability density functions of during the lowest 50% of wind speeds of the leaf-on period (solid black), during the highest 25% of wind speeds of the leaf-on period (dashed),... " > This seems like an abrupt transition. It might be good to give provide a sentence or two on how these are related to advection. On a broader note, I appreciate the advection problem in the sense that this is something that has been challenging in high vegetation with CO2 accumulation within the canopy airspace.
>>> The mean wind speeds at z = 25 m are no more than around 2 m/s for the lower 50% of our observations, on which we derived the residence time. Because the wind speed decays exponentially with height within forest canopies, the speed at the height of the release (around 15 m, see comment below) is likely to be very low. On this basis, advection will of course be non-zero, but is likely to be small (see lines 264–276). Unfortunately, we do not have a direct measure of advective fluxes at the BIFoR FACE facility, and such measurements have proved to be very difficult even with dense networks of sensors (Aubinet et al., 2010). We therefore cannot make this point unequivocally. However, we are further comforted by long-term analysis of the BIFoR FACE observations, which suggest that contamination events between the arrays are rare— i.e., passage of CO2-rich air from the fumigation arrays to the control arrays (Hart et al., 2020).
L 241" zrel > I am wondering whether it would make sense to adjust z_rel, given that it is not clear to me what the real release height of the CO2 is would be to minimize the difference between the observational results and the theoretical result by adjusting z_rel.
>>> We tested a range of values for z_rel, and obtained the best fit between our data and GCF17 using z_rel = 15 m. However, see our comments as to the fumigation heights at BIFoR FACE (lines 277–279 and 321–325)—a single value for z_rel is more difficult to define for our observations than for the Lagrangian parcels in GCF17’s model.
Figure 3a: It seems to me that all the curves in Figure 3 should have the same integral. Could you confirm this and check whether all curves are properly normalized, since it seems (by eyeballing) that the GCF17 might not have the same area under the curve.
>>> Thank you. We have checked, and confirm the normalisation of the PDFs in Figure 3 is correct (as for the PDFs elsewhere in the paper). We agree the left tail of the GCF17 in Figure 3 looks slightly odd, particularly on the log axes. This is caused by the smoothing algorithm in the kernel density estimation for very small values of , but does not affect the conclusions in this paper.
Figure 6 should have a colorbar and possibly a trendline to better gauge the underlying density distribution.
>>> We have updated Figure 6, using filled contour lines rather than hexagons to display the 2D density plots. We have included a colour scale, as you correctly suggest.
The stability classes in Section 3.3.2 should probably be moved to methods section.
>>> Thank you for this suggestion. We have moved the definitions of the stability classes to the new section 2.6, and have updated the cross references.
L 384: "The distributions of remain positively skewed for each stability class (e.g., the right whiskers are longer than the left in Figure 7a)." > It might be a good idea, here and in general to report the skewness.
>>> Good idea. We now report the skewness of the distributions in Table 2.
Section 3.4.: I am not sure how informative this section and the associated figure is. I think that it is important to discuss the edge effect and impacts of heterogeneity, but I am not sure whether this section currently does this in the optimal way. Especially since I think that Figure 8 is pretty hard to read. What dominates the differences in the different wind sectors. Is it heterogeneity or some other influence such as time of day coupled with stability?
>>> We have clarified the caption to Figure 8, to make the plot easier to interpret. Edge effects are important for both the flow and for forest ecology. However, their effects on residence times are difficult to generalise because they are very site specific, save for very general comments, such as regions of high turbulence (e.g., upwind edges or clearings) having shorter residence times. Our findings in section 3.4 did not materially vary with time of day or stability—see (bearing in mind that we are considering only daytime residence times).
L445: "However, although GCF17’s model generates modal values similar to those we observed, it appears to overpredict the likelihood of long residence times in the upper canopy." > this might be true, but also there might be the issue of comparing an essentially Eulerian and Lagrangian method (see general comments).
>>> This is a fair comment. We have qualified our findings (see 517–541), including noting that the comparison is not completely like-for-like (i.e., Lagrangian air parcels in GCF17 and, in our study, a mean (five-min) residence time of air in a control volume)
L463: "These eddies create significant turbulent transport, meaning that the eddy-diffusivity model underestimates turbulent forest-atmosphere exchange in the upper canopy and therefore overestimates residence times." > Turbulent diffusivity approaches do have issues within forest canopies. One thing to note about GCF17 is the fact eddy diffusivities are estimated from the LES and adjusted for the release height by taken the mean modeled diffusivity (either arithmetic or geometric mean) between release height and canopy top. It is not clear to me that this would lead to an effective under estimation of turbulent transport. Some additional thoughts by the authors would be appreciated.
>>> We agree that the use of LES (as in GCF17) navigates some of the issues with earlier Lagrangian stochastic models, such as the need to specify a priori profiles of turbulence statistics, which are usually not realistic. LES remains the best method for turbulence-resolving models of exchange in forest canopies—at least for studies on the scale of metres to km, and seconds to hours—and GCF17 is an example of the technique being used well.
However, LES is by no means perfect—e.g., it requires a sub-grid parametrisation scheme, which are seldom tuned to flows in vegetation, and may under-simulate certain aspects of the flow in forests, such as the penetration of sweeps and gusts, or the boundary-layer TKE above the canopy. Further, most LES models of forests (including that in GCF17) do not resolve the inherent patchiness found in reality (gaps, clearings, roads, different-aged trees etc.), let alone landscape fragmentation. These features would likely reduce the probability of long residence times of air in forests, relative to homogeneous models, because turbulent mixing would be stronger in reality than in the models. However, to our knowledge, this has not been tested directly. See lines 533–541.
Section 3.7: This section seems a bit tacked on in the sense that it is not clear how it relates to the previous section of the model, especially given that the main conclusion from the previous section seemed to point to an overestimation of residence times in GCF17. While the information presented here is an interesting case study, it might make sense to either tie this directly to the analysis before or to remove/ move to an appendix.
>>> We agree that the manuscript is more reader-friendly by focussing on the residence-time analysis. However, we consider that the case study that was previously in section 3.7—an unusual example of a microfront causing venting of the canopy airspace—could be valuable to the community. We have therefore retained the case study, but have moved it to a new Appendix C (renumbering Figure 11 to Figure A2, and updating the supporting text).
On a side note, and also with respect to long residence times: the original GFC17 study was motivated by air exchange within Amazon rainforest canopies with large LAI and limited penetration of turbulent eddies into the lower half of the canopy. Evidence for the limited coupling of canopy airspace to the above canopy air can be for example found in Freire et al. (2017).
>>> Noted with thanks.
Edward J. Bannister et al.
Data sets
Raw FACE observational data sets BIFoR FACE https://doi.org/10.25500/edata.bham.00000564
Model code and software
Processing and visualisation code supporting this manuscript Edward J. Bannister https://doi.org/10.25500/edata.bham.00000836
Edward J. Bannister et al.
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