A Physics‐Based Universal Indicator for Vertical Decoupling and Mixing Across Canopies Architectures and Dynamic Stabilities

Air flows may be decoupled from the underlying surface either due to strong stratification of air or due to canopy drag suppressing cross‐canopy mixing. During decoupling, turbulent fluxes vary with height and hence identification of decoupled periods is crucial for the estimation of surface fluxes with the eddy covariance (EC) technique and computation of ecosystem‐scale carbon, heat, and water budgets. A new indicator for identifying the decoupled periods is derived using forces (buoyancy and canopy drag) hindering movement of a downward propagating air parcel. This approach improves over the existing methods since (1) changes in forces hindering the coupling are accounted for, and (2) it is based on first principles and not on ad hoc empirical correlations. The applicability of the method is demonstrated at two contrasting EC sites (flat open terrain, boreal forest) and should be applicable also at other EC sites above diverse ecosystems (from grasslands to dense forests).

problem is lacking (Aubinet et al., 2010). FLUXNET is the main observational tool to study global terrestrial carbon and water cycles and the accuracy of the network largely hinges upon proper identification of decoupled and coupled flow regimes. Only in latter case EC observations integrate over all sinks and sources and thus can provide biophysically meaningful estimates of carbon, water and heat budgets. Accurate estimates of terrestrial carbon cycle are sorely needed for constraining the global carbon budget (Friedlingstein et al., 2019).
Commonly the friction velocity (u * ) is used to identify decoupled periods from continuous flux time series, albeit this approach is known to be flawed, in particular at sites with dense canopies (Acevedo et al., 2009;Freundorfer et al., 2019;Jocher et al., 2018;Thomas & Foken, 2007a; Thomas et al., 2013). Various other metrics have been used to identify the weakly stable from the very stable flow regime (Mahrt et al., 1998;Sun et al., 2012;Williams et al., 2013). However, they all rely on uncertain site-specific threshold values and were developed for open areas and hence their applicability to forested regions remains unclear (Freundorfer et al., 2019). Canopy flows differ markedly from the air flows above short vegetation, due to prevalence of coherent flow structures (Finnigan, 2000;Finnigan et al., 2009;Raupach et al., 1996;Thomas & Foken, 2007b) and the momentum sink for the air flow caused by canopy drag. The latter can cause the air flows above forests to be decoupled from the forest floor also during daytime (Jocher et al, 2017(Jocher et al, , 2018Kruijt et al., 2000;Santana et al., 2018;Thomas et al., 2013).
In this study, we aim to advance the mechanistic understanding of flow coupling to the surface, in particular in the presence of emergent vegetation and/or strong stratification. Here we define a "weakly stable regime" to be governed by eddies which communicate with the surface (z-scaling applies), whereas in the "strongly stable regime" the large wall-attached eddies are not prevalent. A simple air parcel technique is used to evaluate the flow coupling to the surface. A novel metric is proposed to identify the flow regime and variables controlling the decoupling are discussed. The metric may be applied across the entire gradients from short canopies (e.g., grass, crop, and snow) to dense tall forests and hence applicable at most flux sites monitoring ecosystem-atmosphere interactions.

Theory
Coupled air layers are defined in this study as follows: air parcels travel between the coupled air layers and facilitate the exchange of heat, mass and momentum between the layers. Therefore, there is a direct interaction between the layers. In contrast, air parcels do not travel between decoupled air layers and hence there is no direct thermodynamic interaction between the layers (albeit waves can still transport momentum). When considering coupling of air layer at height z above ground with the surface, based on this definition there need to be air parcels that can traverse the vertical distance of z. This concurs with the notion that in coupled situations large wall-attached eddies that scale with z dominate the flow (Lan et al., 2018;Sun et al., 2012Sun et al., , 2020. Note that the concept proposed below is based on first principles and does not assume for example, the surface layer similarity theories to be valid. Similar air parcel approaches have been used (e.g., Mahrt, 1979;Mahrt et al., 2012;Sorbjan, 2006;Sorbjan & Balsley, 2008;Zeeman et al., 2013) to derive e.g. relevant length scales in the stable boundary layer, here it is used in canopy flows to examine the coupled air layer.
Movement of downward moving air parcels at the canopy height (h) is hindered by any opposing forces which include canopy drag caused by the foliage (e.g., Cescatti & Marcolla, 2004;Poggi, Katul et al, 2004a;Watanabe, 2004) and buoyancy force inflicted by stably stratified air layers. In order to reach the ground, an air parcels kinetic energy must match or exceed the work performed against the hindering forces. Based on this a critical speed (w e,crit ) for the air parcel can be derived (see supporting information): where γ is a constant (=0.277) depending on the horizontal wind and downward penetrating air parcel speed profiles below-canopy height h (e.g., Inoue, 1963;Amiro, 1990a;Poggi, Porporato, et al., 2004;Yi, 2008), c d  is the mean drag coefficient below h (equal to 0.15 for this study), LAI is leaf area index, U h is horizontal PELTOLA ET AL.

10.1029/2020GL091615
wind speed at the canopy height (m s −1 ), g is the acceleration due to gravity (m s −2 ), ˆ is the mean potential temperature below h and θ e is the potential temperature of the downward moving air parcel. If the speed of the air parcel is equal to w e,crit , then its kinetic energy is sufficient to counterbalance the work performed against the hindering forces. However, if it is less than this critical speed, then its downward movement stops before it reaches the ground and as a result interaction with the surface does not occur (see Figure 1).
In order to couple above-canopy flow with the forest floor, a large enough fraction of negative vertical wind speed fluctuations (w′) needs to be below w e,crit . Considering Taylor's frozen turbulence hypothesis, this coincides with the definition that in coupled flow large enough cross-sectional area of the flow at height z needs to be governed by strong downward gusts which interact with the surface. Here we defined the flow to be coupled with the surface when more than 5% of the w′ data were below w e,crit , weakly coupled when between 1% and 5% of w′ data were below w e,crit and decoupled when less than 1% were below w e,crit . Future work is needed to validate the general applicability of these thresholds, yet their applicability at two contrasting sites are demonstrated below (see also Section 4.4). Assuming Gaussian distribution for w′, these criteria can be described using the standard deviation of w (σ w ): Atmospheric observations are typically made at some distance above the canopy during which the speed of downward propagating air parcel may be already slowed down due to stratification. The change in the speed of the air parcel when it traverses between heights z and h can be calculated as PELTOLA ET AL.
where w e (z) and w e (h) are the air parcel speed at heights z and h and   is the mean air potential temperature between z and h. Hence, in order to evaluate the coupling of air at height z with the ground, Equation 1 should be used to calculate w e,crit at the canopy height (h) and then use Equation 3 to translate this value from h to z prior to comparing to σ w values at height z.
In the case of neutral stratification, w e,crit reduces to indicating that the limiting vertical wind speed needed to couple with the forest floor increases linearly with LAI and U h . On the other hand, in the case of flat surfaces without emergent vegetation (i.e., LAI ≈ 0), w e,crit reduces to where N is the Brunt-Väisälä frequency estimated using the bulk θ gradient ( Hence, in the case of LAI ≈ 0, the criterium for the flow to couple with the surface (Equation 2) can be described with the ratio between L B and height z.

Data and Instrumentation
Measurements were collected at two contrasting locations: observations at Hyytiälä boreal pine forest (61.845°N, 24.289°E, 181 m a.s.l) and during "Fluxes over snow-covered surfaces II" (FLOSS-II) campaign above snow-covered rangeland (40.659°N, 106.324°W, 2,477 m a.s.l). Hyytiälä is part of the Integrated Carbon Observation System (ICOS) measurement network (Franz et al., 2018) and has contributed to the global measurement network FLUXNET since the initiation of the site in 1996. The forest is governed by Scots pines (Pinus sylvestris) with approximate tree height of 17 m. One-sided LAI of the forest is 4 m 2 m −2 and the canopy layer is between 10 and 17 m. Turbulence profiles within the forest have been studied in Launiainen et al. (2007). In this study observations made during summer 2019 (May 25 to September 30) were utilized. The measurement configuration consisted of vertical fiber-optic based distributed temperature sensing (DTS) observations (until July 10), EC flux measurements (27 m height; Rebmann et al., 2018) and temperature and CO 2 concentration profiles (Montagnani et al., 2018). For details, see Peltola, Lapo, Martinkauppi et al. (2020a), however, there were four notable differences: (1) 10-min averaging period was used, (2) single-ended data (May 25 to June 3) were also included, (3) both directions in the double-ended configuration were utilized, and (4) the DTS temperature observations were denoised using singular value decomposition prior to analysis (Epps & Krivitzky, 2019). Note that denoizing has an effect only on Figure 2, since otherwise mean profiles were used. When calculating w e,crit , DTS measurements were utilized when available. All the data analyses were restricted to night-time periods (global radiation <5 W m −2 ). 10.1029/2020GL091615 Vickers, 2006;Sun et al., 2020). A 30 m tall tower located in a flat terrain with grass and partial snow-coverage was instrumented with three-dimensional sonic anemometers at seven levels and slow-response thermometers at eight levels. Quality-controlled and 5 min averaged data were retrieved from https://doi. org/10.5065/D6QC01XR (UCAR/NCAR -Earth Observing Laboratory, 2017). Coherent eddies consisting of sweep-ejection cycle (Finnigan et al., 2009;Thomas & Foken, 2007b) were observed in all of the examples, but only in (c) they were clearly coupled with the ground. The downward moving sweep phases of the coherent motions can be identified as the warm tongues penetrating into the cold below-canopy air space, whereas the ejections bring relatively cold below-canopy air to upper levels above the forest canopy (due to downward directed heat flux). Note that the sweeping phases in (a) did not reach the forest floor and as a result the flow was decoupled from the ground. This was identified also with the decoupling metric Ω (see subplot title).

Examples of Contrasting Flow Regimes
CO 2 concentration profiles showed clear differences between the three examples, as a result from the different mixing regimes. The overall concentration difference between the highest (27 m) and lowest level (0.5 m) were 26, 7, and 9 ppm, respectively. Note that in case (a) this concentration difference resulted almost entirely from the CO 2 pooled below 8.8 m height, since the CO 2 above this height was effectively flushed out from the ecosystem by the coherent eddies.

Decoupling in Relation to TKE Production and Transport
Above open terrain, Sun et al. (2012) argued that in stably stratified coupled flow regime turbulent kinetic energy (TKE) should be bulk shear-driven (U/z) due to large eddies and shear production dominating the TKE budget. Hence, they analyzed V TKE ( ) dependency on U and found a threshold value for U above which V TKE dependency on U was linear. Observations falling in this strong wind regime have been considered to relate to coupled flow regime (Acevedo et al., 2016;Freundorfer et al., 2019;Lan et al., 2018;Mahrt et al., 2015;Sun et al., 2016). Figures 3a and 3b show V TKE dependency on U for two heights in FLOSS-II dataset, with data differentiated to separate flow regimes (based on Equation 2) prior to analysis. In contrast to Sun et al. (2012), in the coupled regime no U threshold was observed and V TKE followed the same linear dependence on U regardless of wind speed value. This suggests that in the stable coupled regime TKE was driven by bulk shear as proposed by Sun et al. (2012), however, this holds regardless of U not confirming the interpretation in Sun et al. (2012). Similar results were found for the forest site (Hyytiälä) using above-canopy U and V TKE (not shown). Hence, we argue that flow decoupling cannot be judged based on U alone.
In prior studies, cross-canopy coupling have been analyzed by comparing concurrent measurements of σ w below-and above-canopies (Freundorfer et al., 2019;Jocher et al., 2017Jocher et al., , 2018Thomas et al., 2013). Linear dependence between the two observations of σ w were thought to signal coupling, since downward penetrating canopy-scale sweeps dominate the below-canopy TKE in coupled flow (Freundorfer et al., 2019;Russell et al., 2017;Vickers & Thomas, 2013). In accordance with these studies, the coupled flow regime was typically related to periods with high above-canopy V TKE with a linear dependence between above-and below-canopy V TKE (Figures 3c and 3d). In contrast, low above-canopy V TKE was related to decoupled regime. In this regime, below-canopy TKE was dominated by Kármán vortex streets created behind trees and hence independent of above-canopy TKE (Cava et al., 2008;Russell et al., 2017) since downward propagating sweeps did not reach the below-canopy air space (see also Figure 2b). In our study, the wake-production generated a clear secondary peak in turbulence spectra (especially in 1 m height data) at the vortex shedding frequency based on constant Strouhal number, U and tree trunk diameter (not shown). At intermediate above-canopy V TKE levels (0.5…0.8 m/s) the observations related to coupled flow regime departed from the linear dependence observed at higher V TKE values. This might be due to importance of both, wake-production and sweeps, on below-canopy TKE at these above-canopy TKE levels and further analyses are warranted.

Turbulent Fluxes in the Coupled and Decoupled Layer
The sensible heat flux (H) profiles in the FLOSS-II dataset were analyzed in the view of flow decoupling dependency on height (Equation 6, Section 4.4.1). Nocturnal flux profiles were calculated so that each of the seven measurement heights was used as the highest observational level identified to be coupled with the surface (denoted with z co ). Hence, observations below and above z co correspond to coupled and decoupled layers, respectively. The fluxes were normalized with the H values at height z co (H co ). Below z co nearly constant H was observed, whereas above z co the flux H decreased with height, since the flow above z co was not connected to the surface (Figure 4a). In the coupled air layer (i.e., below z co ), bin-averaged H was between 0.95H co and 1.18H co in agreement with the typical notion for constant-flux layer flows where the vertical turbulent fluxes are expected to vary by ±10%. Note that discrepancies between flux footprints at different heights and biases stemming from instrument calibrations may have also influenced the observed H profiles.
CO 2 fluxes measured above the Hyytiälä forest during night depended on the degree of coupling (i.e., Ω) when Ω < 0.61, whereas in the coupled regime the fluxes were independent of Ω due to direct coupling of PELTOLA ET AL.   Sun et al. (2012). Additionally, data were divided into different coupling regimes (see Equation 2) prior to analysis. Note that threshold wind speed (Sun et al., 2012) was not observed in the coupled regime. (c) and (d) Comparison of above-and below-canopy V TKE at Hyytiälä following Thomas et al. (2013). Gray dots = all the night-time data, circles and black lines = bin-averages for bins with more than 20 data points. Bottom: fraction of data in the three flow regimes (Equation 2). FLOSS-II, Fluxes over snow-covered surfaces II. flux measurement height with the ground with turbulent mixing being no longer limiting. Figures 4a and  4b show physically the same phenomenon, but for different sites. Fluxes above z co (Figure 4a) and during periods with Ω < 0.61 (Figure 4b) correspond to decoupled flow, whereas on the contrary above z co and during periods with Ω ≥ 0.61 correspond to coupled flow.
These results suggest that the method proposed in Section 2 can be used to estimate the depth of the layer that was coupled with the surface and hence, for example, to assess whether the observed turbulent fluxes related to the exchange of heat (FLOSS-II) or CO 2 (Hyytiälä) on the surface. Note that these results were obtained at two contrasting measurement sites without site-specific thresholds. This is due to using a ratio of variables related to kinetic energy (σ w ) and the energy required to couple with the ground (w e,crit ) in the analysis, instead of using σ w (Acevedo et al., 2009;Jocher et al., 2018;Thomas et al., 2013) or related variables (u * , U; e.g., Gu et al., 2005;Sun et al., 2012) alone. Furthermore, this ratio does not depend on the source for the turbulent mixing in any way, it merely compares the existing kinetic energy to the energy needed to couple with the ground. Hence the decoupling metric should be applicable also in situations when the source does not conform with the traditional boundary layer (e.g., upside down boundary layer; Mahrt, 2014;Mahrt et al., 2013).

Flows Above Short Vegetation
Above short vegetation (i.e., LAI ≈ 0), w e,crit depends linearly on z and N (Equation 5) and the definition for coupling (Equation 2) can be written as Hence, at a given value for N, the σ w needed to couple the flow with the surface increases linearly with height. This is in line with prior experimental findings (Acevedo et al., 2016;Mahrt et al., 2013). The increase reflects the fact that the kinetic energy of downward moving air parcel needs to be higher when the height increases since there is a thicker air column below the air parcel within which the buoyancy force opposes its movement, that is, the potential energy of the air parcel increases with height. In the FLOSS-II dataset, rarely the upper level was identified to be coupled with the surface when the observation level below was not (less than 1% of observations). In general, the lower levels were observed to be coupled with PELTOLA ET AL.
10.1029/2020GL091615 8 of 11 ), but heights above z co were not. Fluxes were normalized with H observed at z co (H co ) (b): Normalized nocturnal CO 2 fluxes measured at Hyytiälä plotted against Ω (lines = bin means, areas = ±σ). Data were filtered based on stationarity criteria (Foken & Wichura, 1996). The storage change term (Finnigan, 2006) was also included. Fluxes were normalized with 2-week running means of nocturnal CO 2 fluxes during coupled regime. Vertical dashed lines = fraction of w′ data below w e,crit . FLOSS-II, Fluxes over snow-covered surfaces II.
(b) (a) the surface more frequently than the upper levels, for instance 5 m height was coupled with the surface 64% of time, whereas 20 m height only 39% of time.

Flows Above Tall Vegetation
In the case of neutral stratification below-canopy height, using Equation 4 the definition for coupling (Equation 2) can be written as where I w is the vertical turbulence intensity at the canopy height  (Amiro, 1990a(Amiro, , 1990b and the influence of these parameters should be investigated. Clearly this method should be tested across range of sites with contrasting canopies, albeit similarities to the studies of Cava et al. (2008), Ghisalberti (2009), andNepf et al. (2007) do suggest of a more general applicability.

Conclusions
Poor understanding of the vSBL is an obstacle for all scientific studies investigating surface-atmosphere interactions, in particular in the case of canopy flows. Here, we propose a novel simple first-principle based scheme to identify periods when the air flow is not in interaction with the underlying surface (i.e., it is decoupled). It was shown to correctly identify periods when the measured turbulent fluxes were not representative of the fluxes at the surface. The metric for flow decoupling based on this concept enabled analytical derivation of flow decoupling dependency on height, stratification and leaf area index. The approach is an improvement to the commonly used methods based on the example, friction velocity filtering, since (1) the proposed approach takes into account also changes in forces hindering the coupling (canopy drag, stable stratification) unlike traditional methods which utilize metrics for turbulent mixing or production alone and (2) it is based on first principles and not on ad hoc empirical correlations. From a practical point-of-view, the approach requires only basic micrometeorological measurements (turbulence measurements at one height and temperature profile below it) in addition to knowledge of canopy density and hence should be applicable at most flux sites through the complete gradient from locations with short canopies to dense tall forests.