Changes of the aerodynamic characteristics of a flux site after an extensive windthrow

. A maritime pine plantation in Central Portugal that has been continuously monitored using the eddy-covariance technique for carbon fluxes since a wildfire in 2017 was significantly affected by two storms during December 2019 that resulted in a large-scale windthrow. This study analyses the impacts of this windthrow on the aerodynamic characteristics of zero-plane displacement and roughness length, and, ultimately, their implications for the turbulent fluxes. The turbulent fluxes were only affected to a minor degree by the windthrow, but the footprint area of the flux tower changed markedly, so 15 that the target area of the measurements had to be re-determined .

that fluxes were estimated using complicated approximation approaches (Kader and Perepelkin, 1984). In recent times, by contrast, profile measurements are typically missing so that they are replaced by reasoned inferences on profile 40 characteristics. In a strict sense, zero-plane displacement and roughness length can only be assumed uniform across homogeneous surfaces. Recent attempts have tried to incorporate stand structure into empirical relationships for determining zero-plane displacement and roughness length (Nakai et al., 2008;Raupach, 1994), especially by deriving stand structure from remote sensing data, based on the paper by Thom (1971). Maurer et al. (2015) carried out a large-eddy simulation to compare various approaches to estimating aerodynamic characteristics, and confirmed a near-linear relationship between 45 canopy height and zero-plane displacement.
The post-wildfire flux site in Vila de Rei, central Portugal (Oliveira et al., 2021) offered an opportunity to study the impacts of an abrupt change in aerodynamic characteristics, following a windthrow caused by two consecutive storms Elsa and Fabien, without an apparent concomitant change in stand heterogeneity, virtually like a laboratory experiment.
Namely, the storms caused an extensive windthrow of the -dead -burnt maritime pine trees between 19 and 21 of 50 December 2019, 28 months after the wildfire, while the tumbled trees remained on the ground afterwards ( Figure 1). Still, the two storms did not throw over the -living -eucalypt trees, i.e. neither the individual eucalypt trees along the pine plantation nor those of the eucalypt plantations adjacent to it. These individual eucalypt trees expectedly have an influence on the aerodynamic characteristics (Jegede and Foken, 1999). This prompted us to examine the changes in the roughness length assuming a linear dependence of zero-plane displacement on stand height before and after windthrow. Furthermore,

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we decided to analyse if the changes in these two aerodynamic characteristics also affected carbon dioxide fluxes. This question, however, is difficult to answer in this particular case. Roughly two years after the wildfire, the pine ecosystem was still in its initial phase of post-fire vegetation recovery, so that an increase in CO2 uptake is to be expected between the period before and the period after the windthrow, regardless of the aerodynamic changes. Nevertheless, a change in zeroplane displacement can have a significant impact on the Obukhov-Lettau stability parameter (z-d)/L (z: measurement 60 height, d: zero-plane displacement, L: Obukhov length, Foken and Börngen, 2021), which, in turn, is crucial to the correction and assessment of carbon dioxide fluxes.

Measurement site and measurements
The measurement area, instrumentation, and data processing were comprehensively described by Oliveira et al. (2021), so only the details essential for this study are given below.
The study area is located 8 km to the southwest of the Vila de Rei municipality, N39⁰ 37' W08⁰ 06', in a Mediterranean climate zone. The wildfire affecting the area burned 1250 ha of woodlands. The measurement site included a plateau of 70 sedimentary sandstone deposits, located at an elevation of 250 m a.s.l. and with slopes of up to 5 o over an extension of roughly 10 ha. The crowns of the bulk of the burned maritime pine (Pinus pinaster Ait.) were fully consumed by the fire but their trunks of approximately 8 m height remained standing. This canopy height and a zero-plane displacement of 3.8 m were used in all calculations before windthrow in Oliveira et al. (2021). While the eucalypts plantations were hardly affected by the windthrow, the maritime pine area following the windthrow was a mixture of dead pine trunks fallen on the soil 75 surface or on the recovering vegetation with an estimated canopy height of 2-3 m. The vegetation mainly consisted of shrubs, locally intermixed with 2-3 year old pine seedlings and a few individual, resprouting eucalypt treelets. The localized patches of burned eucalypt trees and stands had a canopy height of approximately 4 m.
In the relatively open part of the pine area, a 12m-high slim tower was installed at the end of September 2017 and equipped with an eddy-covariance system at 11.8 m, including a sonic anemometer CSAT3 (Campbell Sci. Inc.) and a LI-7500A gas 80 analyzer (Licor Biosciences), see Figure 1. The fluxes of momentum, sensible heat, latent heat, and carbon dioxide were analyzed with the eddy-covariance method (Aubinet et al., 2012). The data of the eddy-covariance system were calculated with the Campbell Sci. Inc. EasyFlux DL software for a quick inspection in the field, while all further calculations were done with the software package TK3 (Mauder and Foken, 2015). The processing of the turbulence data is described in full detail in an extensive supplement (https://bg.copernicus.org/articles/18/285/2021/bg-18-285-2021-supplement.pdf) in 85 Oliveira et al. (2021). Special note should be made of the use of the double rotation (Kaimal and Finnigan, 1994) and that no gap filling was applied. The analysis of the aerodynamic characteristics was done for two 9-month periods from 22 Dec.

Aerodynamic characteristics
The starting point for the analysis of the aerodynamic conditions was the logarithmic wind profile. In order to exclude influences due to the stability of the stratification, the analysis was limited to neutral cases (-0.05 ≤ z/L ≤ 0.1). The profile 100 equation contains the measured quantities wind speed u and friction velocity * and the two unknowns of zero-plane displacement d and roughness length 0 (Arya, 2001;Foken, 2017;Stull, 1988) with the von Kármán constant = 0.4. If wind speeds are measured at different heights, both unknowns can be determined iteratively. In the present case, however, measurements were only available at 11.8 m height, so one of the two parameters 105 must be estimated. It is common in such cases to estimate the zero-plane displacement, in particular as equal to two-thirds of the stand height ( = 0.666 ), as is implemented in calculation programs for eddy-covariance measurements. In reality, however, this multiplication factor varies in the range from 0.5 to 0.8, depending on stand structure and, hence, on plant development over the course of a year (Maurer et al., 2015) as well as wind speed (Marunitsch, 1971). Often the value attributed to this factor depends strongly on the experience of the observer. Oliveira et al. (2021) used as canopy height zc 110 =7.6 m, as zero-plane displacement d = 3.8 m = 0.5 zc, and as roughness length z0 = 0.4 m for the period before the windthrow.
This determination was made because of the sparse canopy with charred trunks without leaves. For the investigations after the windthrow a canopy height zc = 2.7 m and a zero-plane displacement d = 1.8 m = 0.666 zc were assumed. This relationship between canopy height and zero-plane displacement corresponds to the classical approach from hydrodynamics. The application of this approach is comprehensively described in Foken (2017, Sect. 3.1.1 and 3.1.2). More recent canopy 115 structure dependent approaches (Nakai et al., 2008;Raupach, 1994) lack input parameters for the highly disturbed surface.
The roughness length and the dimensionless wind profile ( − ) * � are typically used as measures of the roughness of surface and the friction on the surface. In addition, it is useful to determine the so-called integral turbulence characteristic from the standard deviation of the vertical wind velocity and friction velocity * � , which has a value of about 1.25 in the neutral case (Foken, 2017;Garratt, 1992) and of 1.1 for measurements close above the canopy (Finnigan et al., 2009). It can, 120 however, attain higher values under the influence of high roughness (Foken and Leclerc, 2004).
Roughness length can be determined by two methods that are nearly independent. The first method is through Eq. (1) for a given − : The second method is based on the following relation (Panofsky, 1984), with * � = 1.25: From Eq. (3), roughness length then follows as:

Influence of the changes in aerodynamic characteristics on carbon dioxide fluxes
All relevant software packages for the calculation of the carbon dioxide fluxes use, besides measurement height, canopy height and zero-plane displacement as input parameters. These parameters are mainly needed to determine the Obukhov-Lettau stability parameter ( − )/ , with the Obukhov length: with the gravity accelaration g, the temperature T, the sensible heat flux QH, the air density , and the specific heat for constant pressure cp.
The Obukhov-Lettau stability parameter, in turn, is crucial for: (i) spectral correction in the high-frequency spectrum (Garratt et al., 2020;Moore, 1986); (ii) stability-dependent turbulence characteristics in quality control (Foken and Wichura, 1996); and (iii) determination of the footprint (Leclerc and Foken, 2014). Therefore, this study also addresses the implications of 140 the windthrow-induced changes in aerodynamics for these three aspects.
The model spectra for frequency correction (e.g. Kaimal et al., 1972) are stability dependent (i), and the integral characteristics used for data quality analysis (if not limited to the neutral case as in Eq. (3)), are also stability dependent (ii), e.g. according to Panofsky et al. (1977) To determine the source area of CO2-flux measurements, footprint models (iii) are used, and the input parameters are mainly wind speed, roughness length and stability. In the present case, the widely used model according to Kormann and Meixner (2001) was applied.
Further explanations of the corresponding equations and models shall be omitted since they are described comprehensively in the literature (Foken et al., 2012;Mauder et al., 2021). Furthermore, supplementary information was provided in the prior 150 publication (Oliveira et al., 2021).

Aerodynamic characteristics
A climatology of the wind field would require a minimum of 10 years of data, even if a period of 30 years is the standard.

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In other words, changes in the wind field before and after the windthrow could simply reflect the inter-annual variation.
Nevertheless, it was striking that the median wind speed was higher after than before the windthrow in eight of the twelve wind sectors (Figure 2), suggesting that the windthrow provoked a generalized decrease in zero-plane displacement.

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According to Table 1, the ratio ( − ) * � before and after the windthrow changed roughly from 5-6 to 8-9, corresponding to about 60% increase. In the NE sector, the change was smaller but the ratio was already comparatively high before the windthrow. Assuming a value for z -d of 8 m before and 10 m after the windthrow, the effective measuring heights were 8 m and 10 m, respectively.
The roughness length showed a decrease after the windthrow (Table 2). Especially after the windthrow, the roughness lengths 165 agreed relatively well between the two methods. Generally, the roughness length was greatest in the SE sector.
The ratio * ⁄ showed the expected values (Table 3). The values were slightly lower before than after the windthrow, in line with the smaller distance between measurement height and the top of the canopy. The NE and the W-NW sectors revealed comparatively large roughnesses both before and after the windthrow. The wind sectors highlighted in Tables 1-3 are illustrated in Figure 3.

Influence on Carbon dioxide fluxes
Carbon dioxide fluxes were evaluated for the months of May to August 2019 and 2020 to investigate the impacts of the windthrow-induced changes in the stability parameter. This was done without gap-filling. Of course, the comparison between 190 before-and after-windthrow fluxes is not straightforward, because of the differences in weather conditions as well as in postfire ecosystem recovery between the two periods. Therefore, the spectral correction and data quality analysis were only done for the 2020 data set, assuming two different zero-plane displacements.
Examination of the ratio * � showed minor and not relevant differences for z -d = 8 m before the windthrow and z-d = 10 m after the windthrow. The median differed by only 0.4 % and, hence, did not affect the quality flagging. Also, the 195 difference with and without spectral correction was reduced, even if slightly over 1 %.
A similar result was obtained for the CO2 and net ecosystem exchange (NEE) fluxes. As shown in Figure 4, the differences in NEE fluxes with and without stratification-dependent spectral correction was about 1% for the two different effective measurement heights 8 m and 10 m. The median values of the spectrally corrected fluxes differed less than 0.5 % between both measurement heights. Furthermore, the scatter around these median values was reduced.

Aerodynamic characteristics
Before the windthrow, the wind profile was lifted up by the displacement height. After the windthrow, the roughness of the pine stands was determined by the vegetation that had recovered after the fire (mainly consisting of shrubs, locally intermixed 230 with 2-3 year old pine seedlings) and the dead pine trunks that had fallen on top of this vegetation or on the soil surface.
The two determination methods produced consistent results. Worth stressing is that the two methods (Eq. 2 and 4) are not completely independent, because they can be transformed into each other.
The 120°-150° sector had a comparatively high roughness both before and after the windthrow. This was probably due to the greater slope angle or the influence of the tower. By contrast, the 30°-60° and 270°-300° sectors were affected by 235 additional mechanical turbulence, as was also found by Oliveira et al. (2021) for the first post-fire year. This is illustrated in Figure 6, using Eq.
(1), and shows the dimensionless wind profile as a function of z -d for different roughness lengths. Also the median values for the 30° sectors were included in the plot. Because of the physical correlation between all quantities, the plot cannot be used to determine the zero-plane displacement (as referred earlier) but it does indicate the sectors where the assumed parameter values seem appropriate.

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The ratio * ⁄ was largely constant at neutral stratification and only revealed a small stability dependence. This parameter can be used to detect obstacles at larger distances (Foken and Leclerc, 2004) or near the anemometer, for example. Even single standing trees can generate noticeable mechanical turbulence (Jegede and Foken, 1999). In the 60°-90° sector, the mechanical turbulence was probably due to eucalypt trees, whose crowns were quickly re-established after the wildfire by resprouting. The increased values in the 270°-330° sector can only be explained by slope parallel flow, see Oliveira et al.
Evaluation of both dimensionless parameters, together with an assessment of terrain and post-fire vegetation recovery, suggested that the assumptions in (Oliveira et al., 2021) of z -d = 8 m and z0 = 0.4 m were adequate for most wind sectors for the post-fire and pre-windthrow period. However, a value for z0 = 0.7 m would have more appropriate for the calculation of the footprint. Likewise, the assumptions of z -d = 10 m and z0 = 0.3 m were appropriate for most wind sectors for the 255 post-windthrow period. These assumptions, however, were less approriate for three sectors highlighted in Table 3, most notably after the windthrow, where no increase in the wind speed ( Figure 2) could be detected. The greater variability in roughness after the windthrow can be explained by the higher wind speeds which, in turn, were due to the increase in effective measurement height resulting from the larger distance to the canopy height.
Before the windthrow, a very low roughness height of z0 = 0.4 m = 0.05 zc was assumed because of the very wind-permeable 260 nature of the martime stands which, in turn, reflected the fact that the fire had consumed the complete crowns of the bulk of the pine trees. This very low roughness height could not be confirmed by eitherthe calculations using Eqs. 2 and 4 or Figure 6.
The obtained value of z0 = 0.7 m agreed with the simple relationship of z0 = 0.1 zc (Foken, 2017;Monteith and Unsworth, 2013) but not that of z0 = 0.2 zc (Kaimal and Finnigan, 1994). The same applied, mutatis mutandis, after the windthrow. By contrast, the assumed values for the ratio d/zc of 0.5 before the windthrow and 0.666 after the windthrow were confirmed by 265 the observations. These findings further confirmed a linear relationship between d and zc, in line what was found using approaches that explicitly consider parameters describing stand structure (Maurer et al., 2015).

Influence on Carbon-dioxide fluxes
The investigations carried out clearly showed that due to the different values of the effective measurement height z -d before and after the wind break in the determination of the Obukhov-Lettau stability parameter, no influence on the quality flags 270 and the measurement of the net ecosytem exchange could be detected that would have even come close to the typical error range.
By contrast, however, the footprint area increased markedly due to the change in roughness and possibly also wind speed.
The difference would probably not have been as large if a slightly better value of z0=0.7 m had been assumed before the windthrow. The increase in footprint area also implied a decrease of the target areas in the footprint. In case target areas 275 differ markedly from non-target areas in terms of carbon dioxide fluxes, the change in aerodynamic conditions would substantially affect flux measurements. At the present study site, this is probably not the case, as the non-target areas mainly differ from the target areas by their greater slope angles and not the burned forest. A reduction of the footprint through a reduction of the measurement height is usually not possible with long-term measurement programmes with a permanently installed mast, because reduction of the measurement height will then typically produce flow distortion problems due to the 280 mast. Hydraulic lifted masts are hardly ever used in such programmes (Kolle et al., 2021).

Conclusions
The windthrow at the end of 2019 had a significant impact on the aerodynamics of the study area. The present analysis addressed dimensionless turbulence characteristics and focused on the parameters of roughness length and zero-plane 285 displacement. Since both parameters are not independent, either the zero-plane displacement or the roughness length must be specified a priori. For the first post-fire year, Oliveira et al. (2021)  The initial assumption of this study of z -d = 10 m and a roughness length of z0 = 0.3 m for the post-windthrow period 290 continues to seem reasonable as well. This implied that the windthrow drastically changed aerodynamic site conditions. The increase in * � provided a clear indication that the distance between measurement height and canopy height had increased significantly after the windthrow.
The present study confirmed the disturbances in specific wind sectors signalled by Oliveira et al. (2021). The disturbances in the NE and NW sectors could be assigned to terrain characteristics. According to Figure 6, a change in zero-plane 295 displacement in this sector would not result in an improvement. If coordinate rotation is performed by means of double rotation (Kaimal and Finnigan, 1994), the problem is hardly relevant for the measurements; however, if the authors would have done it by means of planar fit rotation (Wilczak et al., 2001), the disturbed sector would have to be rotated separately.
The change in aerodynamic conditions due to the windthrow did not have marked impacts on the calculation of the carbon dioxide fluxes, but it did substantially increase the footprint area. In the present case, this increase in footprint area implied 300 the inclusion of sloping terrain but with essentially the same pre-and post-fire vegetation cover as the realtively flat target area, so that the implications are expected to be minor. The present windthrow occurred at a relative early stage of post-fire ecosystem recovery, so that a direct comparison of pre-and post-windthrow carbon dioxide fluxes was considered unwarranted.
Based on the investigation carried out, we generally recommend determining the effective measurement height and the 305 roughness length as precisely as possible when aerodynamic conditions change in order to be able to determine changes in the footprint area. Since areas outside the target area may have an influence on the fluxes, the quality assessment of the measurement area must be carried out again, taking the footprint into account (Foken et al., 2012;Mauder et al., 2021).
Alternatively, the measurement height could be adjusted so that the footprint remains almost identical. A not very precise choice of roughness length did not have a marked effect on the footprint, as the 2019 calculations showed.

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Code and data availability. The program for the calculation of the eddy-covariance data is available (Mauder and Foken, 2015). The daily CO2 flux data are available on Oliveira et al. (2020), other data on request from the first author (bruna.oliveira@ua.pt).

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Authors contribution. BRFO was the responsible for ModelEco's project funding and management, and responsible scientist for this Post-doctoral study including fieldwork, data analysis (CO2-part), and preparing the structure of the paper and of several of its sections; JJK was responsible for FIRE-C-BUDs' project funding and management, and data analysis (wind-320 analysis, and supported the writing of the paper. The final version of the paper was prepared by all authors.
Competing interests. The authors declare that they have no conflict of interest.
Thanks are due to FCT/MCTES for the financial support to CESAM (UIDP/50017/2020+UIDB/50017/2020), through national funds. This publication was funded by the German Research Foundation (DFG) and the University of Bayreuth within the funding program Open Access Publishing.