• Open Access

The role of coherent flow structures in the sensible heat fluxes of an Alaskan boreal forest


Corresponding author: G. J. Fochesatto, Department of Atmospheric Sciences, Geophysical Institute, and College of Natural Sciences and Mathematics, University of Alaska Fairbanks, 903 Koyukuk Dr., PO Box 757320, Fairbanks, AK 99775-7320, USA. (foch@gi.alaska.edu)


[1] Accelerations in the flow over forests generate coherent structures which locally enhance updrafts and downdrafts, forcing rapid exchanges of energy and matter. Here, observations of the turbulent flow are made in a highly heterogeneous black spruce boreal forest in Fairbanks, Alaska at ~2.6 h (12 m) and ~0.6 h (3 m), where h is the mean canopy height of 4.7 m. Wavelet analysis is used to detect coherent structures. The sonic temperature and wind data cover 864 half-hour periods spanning winter, spring, and summer. When mean global statistics of structures are analyzed at the two levels independently, results are similar to other studies. Specifically, an average of eight structures occurs per period, their mean duration is 85 s, and their mean heat flux contribution is 48%. However, this analysis suggests that 31% of the structures detected at 2.6 h, and 13% at 0.6 h, may be influenced by wave-like flow organization. Remarkably, less than 25% of the structures detected occur synchronously in the subcanopy and above canopy levels, which speaks robustly to the lack of flow interaction within only nine vertical meters of the forest.

1 Introduction

1.1 The Boreal Forest

[2] The analysis of the surface energy balance in the subarctic Alaskan interior is critical for understanding current conditions, and for predicting future trends in surface biogeochemical and hydrological processes, water availability, and energy transfer. The boreal forest comprises 11% of Earth's land surface [Bonan and Shugart, 1989], and specifically, the boreal spruce forest accounts for 33% of Alaskan vegetation [Fleming, 1997]. Cold temperatures, discontinuous permafrost, and aridity make the boreal forest unique, but at the same time vulnerable to climate change [Chapin et al., 2006]. In turn, this vulnerability can alter the forest directly or indirectly by promoting feedbacks to an extent not yet fully understood [Chapin et al., 2000]. The boreal forest is coupled directly to its local environment through sensible and latent heat fluxes, and surface albedo; it is also coupled to global climate through the fluxes of carbon dioxide (CO2) and methane (CH4) [Chapin et al., 2000]. Some studies have shown that boreal forests may be potential sources of CO2 during climate warming [Chapin et al., 2006], while others suggest that they may become sinks due to increasing plant productivity [Kimball et al., 2006]. Ultimately, many studies elucidate the complexity of the boreal forest, suggesting a nonuniform response to large-scale forcing [Chapin et al., 2000, 2005; Wilmking et al., 2004; Ueyama et al., 2010].

[3] Quantification of exchanges of energy and matter in the boreal forest is difficult because of the extent and variability of this ecosystem, as well as the remoteness of the high latitudes. Remote sensing can provide estimates of large-area fluxes in remote locations, but those estimates are based on the spatial and temporal scales of the measuring systems and thus vary one from another. One solution is to upscale local micrometeorological measurements to larger spatial scales in order to acquire an optimum representation of land-atmosphere interactions [Samain et al., 2012]. However, any such upscaling process in the boreal forest needs to consider the heterogeneity of canopy density and height, as well as nonstationary flows. Spatial and temporal lags in the storage and release of heat from within the forest [Arya, 1988] are also critical. For example, Turner et al. [1994] compared a heat flux contour diagram produced via wavelet analysis for three levels above a boreal black spruce forest in Quebec, Canada during the month of August. They found that under stable conditions in early evening, fluxes were generally negative at most levels except for a few areas with a positive flux near the canopy top. They attributed this to the final release of daytime heat that had been held locally within the canopy.

[4] Yet another factor impacting the storage term is the robust thermal stratification accompanied by persistent quiescent flows, both of which are signatures of interior Alaska. Thermal stratification of atmospheric boundary layer flows is common because long winters are characterized by a positive feedback between frequent high-pressure systems reinforced by radiative ground cooling [Shulski and Wendler, 2007; Mayfield and Fochesatto, 2013]. Terrain features also protect local valleys from the stronger winds of adjacent regions, resulting for instance, in mean winds of less than 1 m s−1 during December–January in Fairbanks [Shulski and Wendler, 2007]. Cold air drainage is also a prominent characteristic in the Alaskan interior which can impact local fluxes [Fochesatto et al., 2013]. For instance, Lee [1998] shows that exchange processes in tall canopies are affected by a commonly ignored mass flow component term which results from local rising (sinking) causing convergence (divergence) of a scalar. In this framework, he used observational data from a Canadian boreal forest to substantiate the argument of Grace et al. [1996], which states that cold air drainage reduces the local flux of CO2 above the forest. Neglecting this mass flow of CO2 will result in underestimates of locally fluxed CO2 and therefore overestimates of the amount of CO2 actually available for annual uptake by the forest [Lee, 1998]. Thus, extended periods of stratified flow may have unexpected effects on the vertical aggregation of energy and matter to larger spatial scales, effects which may not be visible to models or remote sensing instruments. This motivates further analysis of the trends of fluxes in the boreal forest of Alaska during both winter and the warm season and reminds one that closure for energy balance models cannot be achieved if microscale processes are evaluated with complete disregard for larger-scale forcing [Foken, 2008b; Foken et al., 2010].

1.2 Coherent Structures

[5] Exchanges of heat and moisture are driven by the amount of energy available at the canopy-atmosphere interface [Arya, 1988]. Under stationary conditions, thermal and mechanical turbulence draws energy from that interface to build fluxes. This turbulence is considered to be dissipative and therefore is composed of high-frequency inertial eddies of stochastic nature [Stull, 1988]. In the specific case of forest-atmosphere interaction, however, much of the energy exchange between vegetation canopies and the overlying atmosphere may derive from distinct, intermittent upward (ejection) and downward (sweep) motions [Raupach and Thom, 1981; Raupach, 1981; Raupach et al., 1996; Finnigan, 2000; Foken, 2008a]. Evidence of a sweep of warm air from aloft into the cooler forest on a stable night can be found as early as 1936 in the work of Siegel [Foken, 2008a]. Later, the ramp shapes in a scalar series resulting from sweeps and ejections were studied in detail by Taylor [1958], who originally hypothesized these ramps to result from “organized thermal structures of considerable vertical extent.” Later, Antonia et al. [1979] showed that these ramp features were transported mainly by the local velocity and could therefore be independent of buoyancy forces. Confirming that shear can be their driving force, Gao et al. [1989] showed that in the absence of convection (i.e., during near-neutral conditions), ramps over a Canadian deciduous forest still appeared within the time series of water vapor. Furthermore, the ensemble averaged temperature and fluctuating velocity fields analyzed by Gao et al. [1989] revealed that these ramps are comprised of distinct (~50 s duration) ejection/sweep cycles that can act on a scalar gradient, such as temperature, to produce a miniature frontal boundary (i.e., a microfront). The literature commonly refers to these events as “coherent structures.” Quoting Serafimovich et al. [2011], a coherent structure is: “… an aperiodic, three-dimensional well-organized low-frequency flow pattern with characteristic forms and lifetimes… which largely differs from the high-frequency turbulence…”

[6] It has been shown that the shear necessary to generate coherent structures derives from the inflection point in the vertical profile of the streamwise velocity that exists due to canopy drag [Raupach et al., 1996]. In the 1800 s, Rayleigh showed that such a velocity inflection point makes an inviscid flow unstable, resulting in horizontal vortices whose axes are oriented in the spanwise direction (i.e., perpendicular to the streamwise direction of the flow) [Bayly et al., 1988; Morland et al., 1991]. Gusts in the boundary layer above the canopy can instigate the formation of spanwise vortices [Finnigan, 2000; Finnigan et al., 2009]. The fact that spanwise vortices can become three-dimensional has been mentioned and/or investigated by many authors [Raupach and Thom, 1981; Rogers and Moser, 1992; Raupach et al., 1996; Finnigan, 2000; Finnigan et al., 2009]. Large eddy simulations over a canopy by Finnigan et al. [2009] suggest how Kelvin-Helmholtz waves at the vegetation-atmosphere interface may develop into horizontal spanwise vortices that undergo a helical pairing which results in a hairpin-shape configuration; sweeps and ejections are concentrated within the bends of the hairpins, where vertical motion is favored. This enhanced vertical motion magnifies a scalar gradient (in the case of temperature, this forms a microfront). An artistic representation of the evolution of an idealized coherent structure via this process is shown in Figure 1. Recent research suggests that an asymmetrical stretching mechanism is what causes the spanwise roller to split and form a lower sweep-generating hairpin, and an upper ejection-generating hairpin that is transported into the above inertial sublayer [Bailey and Stoll, 2012]. As our understanding evolves, we find that coherent structures form a total story of canopy-atmosphere interactions; they are tenuous, rapidly evolving three-dimensional vortex entities that form over roughness elements, the dynamics of which can assist in destroying the scalar gradients contained by the roughness elements themselves.

Figure 1.

Author's artistic rendering of the development of a coherent structure by shear due to the vertical velocity gradient at a black spruce forest canopy; adapted from Finnigan et al. [2009, Figure 14].

[7] The significance of coherent structures lies in their ability to contribute to fluxes of energy and matter. Barthlott et al. [2007] provide a comprehensive summary of authors who have evaluated the sensible heat flux contribution specifically from coherent structures compared to the total heat flux. They show that heat flux contributions from coherent structures range from as low as 40% [Lu and Fitzjarrald, 1994] to almost 90% [Bergström and Högström, 1989]. Other forest studies such as Serafimovich et al. [2011] and Thomas and Foken [2007a] suggest even less than 40%. It is clear that as automated detection techniques are applied to larger data sets, the flux contribution from coherent structures becomes more representative of actual conditions, and declines from earlier studies where only a small data set during ideal circumstances was assessed [Barthlott et al., 2007]. Despite that coherent structures are not always the dominant process for turbulent transport [Barthlott et al., 2007], their contributions can be important, and the degree to which such structures contribute to fluxes in the high latitudes is worth continued investigation.

[8] Earlier, it was explained how shear may produce coherent structures. However, it has also been demonstrated that when convective conditions exist, the organization of turbulent motion can be enhanced by larger convective eddies, or “attached eddies” [Poggi et al., 2004; Thomas et al., 2006; Thomas and Foken, 2007b]. Therefore, under highly unstable conditions, any detection of coherent structures may result in a population with contributions from both convective and/or shear processes [Thomas and Foken, 2007b]. Furthermore, many authors have stressed that under stable conditions, ramp-like features in a temperature series may be gravity waves, or be strongly influenced by gravity waves [Paw U. et al., 1992; Lee et al., 1997; Cava et al., 2004; Thomas and Foken, 2007b; Serafimovich et al., 2010]. Gravity waves and turbulence can have similar frequency spectra, spatial scales, and/or geometric shapes in a scalar time series [Finnigan et al., 1984; Lee et al., 1997; Cava et al., 2004]. The detection of coherent structures should therefore also be expected to be complicated by the presence of waves whenever the flow is stable. While linear waves cannot transport heat energy because vertical velocity is 90° out of phase with temperature, nonlinear waves can transport scalars [Stull, 1988], just as do coherent structures. Furthermore, gravity waves have been shown to feed kinetic energy into local turbulence; as such, waves and turbulence can be both synchronous and well correlated [Finnigan et al., 1984; Nappo, 2002; Lu et al., 2005]. Gravity waves may also alter the pattern of momentum flux contributions from the sweep and ejection phases of a coherent structure that is occurring at the same time as the wave [Serafimovich et al., 2010]. Whether waves and/or turbulence contributes to sensible heat fluxes, separating these two phenomena is important for establishing a more complete understanding of canopy layer physics, especially in the subarctic boreal forest where stratified flows are common.

[9] Finally, another consideration regarding the significance of coherent structures is their ability to affect large vertical extents within and above a vegetation canopy synchronously. For cases over a forest canopy, coherent structures may force exchanges between the vegetation and the overlying atmosphere, and may therefore play a role in coupling above and below canopy flows [Shaw et al., 1989; Thomas and Foken, 2007a]. Therefore, it is often added to the definition of a coherent structure that it must produce roughly synchronous temperature ramps at multiple levels within and above the forest canopy [Bergström and Högström, 1989; Gao et al., 1989; Shaw et al., 1989]. To this end, Feigenwinter and Vogt [2005] detect ramp features in three levels above an urban canopy independently, but statistically evaluate only the features that occur within ±25 s of one another at all heights (i.e., those that “dominate the exchange”). The work of Lu and Fitzjarrald [1994] locates ramps from anemometer data at one height above the Harvard forest and then extrapolates that detection to the subcanopy anemometer. Their composited time series revealed that vertical velocity fluctuations were in phase at both levels, suggesting that coherent structures detected above the canopy generally extend into the subcanopy data in their forest.

[10] The objective of this work is to use an automated detection algorithm to extract coherent structures from the turbulent temperature time series in an Alaskan black spruce boreal forest across three seasons at the above canopy and subcanopy levels. From this, we evaluate what physical properties of coherent structures detected in this study are unique to our higher latitude, and then we discern the importance these structures might have in the vertical aggregation of heat fluxes within the forest. The organization of this paper is as follows. Section 2 describes the study site in detail. Section 3 describes the quality control procedure applied to the turbulent measurements, the signal processing method to extract turbulent components of the flow, the methodology used to determine turbulent data which may be under the influence of organized wave-like motion, and the multiresolution technique (i.e., wavelet transform) applied to extract the coherent structures themselves. Section 4 first treats both measurement levels independently and evaluates all detected structures, including their contributions to the total flux, and their transport efficiencies. Structures influenced by waves are then described. Next, the coherent structures which affect both the above-canopy and subcanopy simultaneously are located and evaluated. Section 5 discusses these results in the context of previous studies, and with regard to the environmental and climatic conditions of the subarctic Alaskan boreal forest. Section 6 summarizes the salient conclusions.

2 Study Area

[11] Fairbanks is located in interior Alaska at 64°49'N latitude and 147°52'W longitude. This region is characterized by an arid continental climate that is isolated from both the wetter and more moderate regime south of the Alaska Range, and from the colder Arctic tundra north of the Brooks Range. The seasonality of the region is extreme (records range from −62°C to +38°C), but long severe winters statistically dominate the short warm summers, resulting in a subfreezing annual average temperature [Shulski and Wendler, 2007]. The micrometeorological site for this analysis is the University of Alaska Fairbanks (UAF) north campus site. This site is located in the boreal forest north of the Geophysical Institute on the west ridge of the UAF at an altitude of 165 m above sea level (Figure 2). The overstory is predominantly black spruce (Picea mariana), with a 60% cover density. The understory is composed of small trees, shrubs (Vaccinium sp., Betula nana, Alnus incana), and mosses (Sphagnum sp.) [Kitamoto et al., 2007]. Soil profiles reveal an organic layer which ranges from 13 to 26 cm deep, underneath which is a mineral layer. The site is underlain by discontinuous permafrost [Iwata et al., 2010].

Figure 2.

Topographical map showing terrain in the Fairbanks area. Approximate location of the UAF north campus site is indicated by the solid black dot. Approximate elevations of local terrain features are labeled in meters above sea level. Map generated from National Geographic USGS Mapping Software (powered by TOPO!).

[12] A forest inventory (Figure 3) was undertaken using an aerial image to establish a 200 m grid surrounding the micrometeorological tower, within which 25 equal area transects were identified to perform a tree sampling. The total mean canopy height (h) is 4.7 m, with a standard deviation of ±3.14 m. The lowest mean canopy height is 2.6 m, and the tallest is 10.9 m. Additionally, the number of trees within each sample varies greatly, from five to ninety-one. This variability in canopy height and tree density emphasizes the heterogeneity of the boreal forest, resulting from strong biological gradients determined by local factors such as permafrost, slope, and drainage. Within the forest, a micrometeorological tower is equipped with two R.M. Young Model 81000 3D ultrasonic anemometers mounted at 0.6 h (3 m) and 2.6 h (12 m). The anemometers sample at 20 Hz with a threshold of 0.01 ms−1 and provide the three velocity components of the air flow (u, v, and w), as well as sonic temperature (T).

Figure 3.

Aerial map of the UAF north campus site, showing the approximate range of mean canopy heights (white circles). Dark (light) gray indicates taller (lower) spruce. The numbers on the edges of the top image are Universal Transverse Mercator (UTM) coordinates in meters (Zone 6 N, using the NAD83 datum).

3 Data Processing and Methods

3.1 Data Selection and Quality Control

[13] Due to the extreme contrast between winter and summer in subarctic continental locations, we choose a seasonal clustering of data in lieu of classification by flow-specific conditions such as, for example, stability. From the most complete data sets with the least glaring quality issues, we select a sample of winter, spring, and summer days from 2012 (Table 1) (at the onset of this work, fall data were not yet available). Note that in Fairbanks, March is considered a winter month since the average monthly temperature is still well below freezing [Shulski and Wendler, 2007]. After selection, we break the set of measurements into half-hour periods for analysis. Despite the concern that varying period lengths are required for the analysis of turbulent fluxes based on differences in the flow regime [Acevedo et al., 2006], 30 min is a generally accepted period of time to allow all turbulent processes to collectively contribute to the total flux, as shown from ogive tests [Lee et al., 2004].

Table 1. Selected Diurnal Cycles for This Study Covering Winter, Spring, and Summer of 2012 in UTCa
 Julian DayDate Julian DayDate Julian DayDate
  1. aNote that March is considered winter because in Fairbanks, the mean daily high for that month is still below freezing.
Winter365 FebruarySpring932 AprilSummer17624 June
 4312 February 943 April 1875 July
 5322 February 954 April 1897 July
 611 March 1009 April 1908 July
 633 March 10110 April 19311 July
 644 March 10615 April 19412 July
 655 March      

[14] The sonic temperature and velocity time series are despiked using an algorithm based on Vickers and Mahrt [1997]. Also, periods with confirmed dropouts (sections of data abruptly removed from the local mean by instrument error) are rejected. Prior to extracting the turbulent properties, we perform the streamline coordinate rotation according to Kaimal and Finnigan [1994].

3.2 Identification of Wave-Like Periods

[15] Regarding the concern that gravity waves can complicate the detection of coherent structures, we seek a method to evaluate how wave-like is the flow regime for the periods we consider. Vincent and Fritts [1987] demonstrated that the partial correlation of the turbulent components of the horizontal flow (u′ and v′) is a mathematical proxy for the oscillations of gravity waves embedded within the wind field. As such, the traditional Stokes parameters can be adapted to evaluate the degree of polarization (δ) of u′ and v′, which provides a quantitative measure of the degree to which wave-like organization is contributing to the total fluctuation [Eckermann, 1996]. We evaluate whether waves act upon specific periods where coherent structures have been detected, and as such focus our attention in the frequency range in which canopy waves and coherent structures are most likely to coexist (from 0.1 to 0.003 Hz, or event durations of 10 to 300 s) [Barthlott et al., 2007, their Figure 6]. The form of the Stokes parameters used here is adapted from Vincent and Fritts [1987] and Eckermann [1996], and the set of equations (1) to (5) describe them:

display math(1)
display math(2)
display math(3)
display math(4)
display math(5)

[16] Here, the subscripts R and I indicate the real and imaginary parts of the windowed Fourier transform of the turbulent velocity fields (u′ and v′) within the frequency interval from 0.1 to 0.003 Hz. The coefficient A scales the squared Fourier coefficients to power spectral densities [Eckermann, 1996], but its value is ignored here because it self-cancels when δ is calculated. Using this methodology, we evaluate the 30 min mean δ corresponding to each half-hour period in the analysis. Then, applying the criterion of Lu et al. [2005], we flag periods where δ > 40% as being under possible wave influence, while those with δ ≤ 40% are flagged as primarily turbulent driven.

[17] To evaluate whether this criterion produces reasonable results, we first note that δ clearly decreases at both the 2.6 h (12 m) and 0.6 h (3 m) levels from winter to summer (Table 2), and even has a diurnal cycle during warmer periods wherein larger values of δ occur at night (not shown). This is logical because higher values of δ are expected during colder periods, where gravity waves are facilitated by the presence of stratified flow conditions [Nappo, 2002].

Table 2. Summary of the Mean Half-Hour Wave-Like Polarization Indicator Coefficient (δ, in %), for Three Seasons and for the Ensemble Across Seasons
Season2.6 h (12 m)0.6 h (3 m)

[18] Evaluations of δ as a function of wind direction also corroborate that this criterion is reasonable for evaluating the wave-like behavior of the flow. Specifically, the data for all three seasons combined reveals that the mean wind direction for periods where δ > 40% is typically northerly or westerly. The foothills of the White Mountains rise from ~300 to 700 m to the north and west of the study site (Figure 2). As shown in Fochesatto et al. [2013], shallow cold air masses flow down the Goldstream Valley in winter, undercutting the stagnant air in the valley west of Fairbanks. Any such drainage type flows originating from the hills in any season may “bounce” as they enter the study site under stable conditions, potentially resulting in gravity waves.

3.3 Detection of Coherent Structures

[19] Several methods for detecting coherent structures and evaluating the effects of their induced vertical velocity on scalars have been reported [Shaw et al., 1989; Collineau and Brunet, 1993a, 1993b; Thomas and Foken, 2005; Barthlott et al., 2007; Thomas and Foken, 2007a]. Visual identification of ramps in temperature works well for small data sets [Gao et al., 1989; Barthlott et al., 2007]. Alternatively, coherent structures can be analyzed by quadrant analysis whereby plots of a turbulent scalar (x axis) and vertical velocity (y axis) determine the sign and magnitude of fluxes with coherent ejection and sweep motions [Raupach and Thom, 1981; Bergström and Högström, 1989; Gao et al., 1989]. While useful for evaluating flux contributions from organized structures, quadrant analysis alone is inadequate for describing the coherent structures in space and time domains [Thomas and Foken, 2005].

[20] Wavelet analysis was first used to detect coherent structures in turbulent flows above forest canopies by Collineau and Brunet [1993a] and has since become common practice over forests and other roughness elements [Lu and Fitzjarrald, 1994; Feigenwinter and Vogt, 2005; Thomas and Foken, 2005; Barthlott et al., 2007]. Wavelet analysis has the ability to quantitatively determine the time when coherent structures occur and also the approximate duration of the structures. For example, Collineau and Brunet [1993a] demonstrated that the Mexican-Hat wavelet (MHAT) exhibits a zero-crossing at the microfront location. Barthlott et al. [2007] also showed that the zero-crossing point of the MHAT wavelet coefficient, combined with the adjacent minima in the wavelet, can be used to determine the beginning and the end (i.e., the duration, D) of each ramp event. This method for detecting D differs from previous studies. For instance, Gao et al. [1989] use the vertical velocity to define D as the zone comprised by a continuous updraft, plus the subsequent continuous downdraft, located at the microfront; this has the weakness that the vertical velocity signal can be noisy and nonmonotonic. Other studies use a single value of D that characterizes each period of analysis, centered on the microfront locations [Lu and Fitzjarrald, 1994; Feigenwinter and Vogt, 2005; Thomas and Foken, 2005; Thomas and Foken, 2007a, 2007b]. Typically, this value is calculated by time integration of the wavelet transform to yield the global wavelet power spectrum, the first peak of which (FMAX) characterizes the time scale of the structures that provide the most energy to the turbulent processes, i.e., coherent structures [Collineau and Brunet, 1993a]. Then, the peak frequency of the wavelet associated with FMAX is used in conjunction with the time resolution of the data to generate a single value of D for each period [Thomas and Foken, 2005, 2007a, 2007b]. Similarly, Lu and Fitzjarrald [1994] use twice the dominant wavelet scale associated with FMAX. Using a single value of D for each period, however, will not capture the variations in duration that each ramp feature can possess within an evaluation period. To this end, we find the procedure of Barthlott et al. [2007] most appealing and employ this method on our data.

[21] After data quality control (section 3.1), we proceed as described in steps 1 through 4 in section 2.3 of Barthlott et al. [2007]. The wavelet transform is given by:

display math(6)

Here, Wn (s) is the continuous wavelet transform of the temperature time series T(t), by the MHAT wavelet, Ψ(t, s), and s is the scale dilation of the wavelet transform. Similarly, n is a position translation [Collineau and Brunet, 1993a; Barthlott et al., 2007]. The global wavelet power spectrum, W(s), used to find FMAX as described above, is then given by:

display math(7)

[22] Since small, insignificant changes in temperature can be detected by this procedure, it is necessary to screen the resulting wavelet function so as to eliminate the MHAT wavelets whose amplitudes are less than a prescribed amount [Barthlott et al., 2007]. Based on a series of tests, Barthlott et al. [2007] chose to eliminate all wavelets whose amplitudes were not 40% or more of the largest amplitude in that particular series. In this study, threshold values of 20%, 40%, and 60% were tested to confirm that the 40% threshold is also reasonable for our study site.

[23] Dynamic stability plays a role in evaluating the duration of each temperature ramp because it determines whether the microfront proceeds or precedes the ejection [Barthlott et al., 2007]. To evaluate dynamic stability, Barthlott et al. [2007] use the Obukhov Length (L*), a value which determines the relative importance of buoyancy versus mechanical mixing [Stull, 1988]. The sign of L* will be positive for stable flows and negative for unstable conditions. The concern here is that our data are from a forest canopy, wherein the Monin-Obukhov Similarity Hypothesis on which L* is predicated may be violated due to heterogeneous conditions and nonstationary flows. Furthermore, since we are calculating L* as a mean value for each half-hour, it is possible for stability to transition during that time. Therefore, a visual inspection was performed on the results of the boreal forest data to discern if the use of the sign of L* is valid for determining the duration of the ramp features. After testing 48 half-hour periods, we conclude that using the sign of L* is a reasonable approach in the present study site (Figure 4).

Figure 4.

Wavelet detection of coherent structures for (a) unstable conditions where L* < 0, and (b) stable conditions where L* > 0. Oscillatory trace line is the wavelet function selected according to the local maximum in the wavelet power spectrum. Superimposed in black trace is the 1 s normalized temperature signal (zero mean, ±1 σ). Shading in gray indicates the duration of each detected structure. Solid squares at the wavelet peaks indicate structures whose contribution to the temperature power spectrum is at least 40% of the most energetic within the half-hour series. Horizontal line is the 40% threshold.

4 Contribution to the Total Turbulent Flux by Coherent Structures

[24] The study area is heterogeneous regarding canopy height and density (Figure 3), and often experiences quiescent winds and stratified flows. Due to these conditions, we evaluate turbulent data from within and above the canopy with no presupposition that coherent structures at the two heights should necessarily be part of the same event. A qualitative review of the data suggests that while ramp features sometimes occur synchronously in both levels, often they do not. Therefore, we assume that it is possible for coherent structures to be initiated at different canopy heights. Since stratified flow may limit the three-dimensional development of turbulence [Finnigan et al., 1984], coherent structures may not always mature enough to penetrate the entire forest. To this end, we first detect and analyze the properties of all detected structures at each level in the forest independently, including their heat flux contributions and transport efficiencies.

[25] Using the results from the multiresolution wavelet analysis (section 3.3), the sensible heat flux contribution from coherent structures (FCOH) compared to the total eddy-covariance derived sensible heat flux (FTOT) is determined from Lu and Fitzjarrald [1994]. Here, FCOH is defined as the sum total of sensible heat fluxes from all coherent structures during the entire 1800 s period analyzed according to equation (8):

display math(8)

where NCOH is the number of coherent structures, t is 1800 s, and the subscript (COH) refers to values corresponding only to coherent structures. Note that due to the method for evaluating D, tCOH will vary for each coherent structure. Similarly, the value inline image for any single coherent structure k is indicated in equation (9), in which the temporal means of w and T are calculated based on the mean values over the entire analyzed period:

display math(9)

The total sensible heat flux including coherent structures and stochastic components (FTOT) is:

display math(10)

4.1 Characteristics of Coherent Structures in the Study Area

[26] Before analyzing the effects of coherent structures on turbulent flow exchanges, it is instructive to review the mean global properties of all of the detected events. Results show that the average number of coherent structures at both levels and across three seasons is about eight per half-hour period, with seasonal means at the two levels ranging from ~7 to 9 (Figure 5). This result aligns with Steiner et al. [2011] who find a median of five to nine events per half-hour period within a midlatitude deciduous forest. Our results are also similar to Barthlott et al. [2007], who find an average of 7 to 11 structures per half-hour period over an open field, and to those of Feigenwinter and Vogt [2005], whose analysis above an urban canopy during unstable conditions reveals around 7 to 10 per half-hour period. For this study, the mean number of coherent structures and the standard deviations are both slightly larger during spring (Figure 5). Overall, the difference in the mean number of structures between seasons and between the two forest levels is relatively consistent for this study area.

Figure 5.

Number of coherent structures per half-hour period. (a) Winter (306 samples), (b) spring (281 samples), (c) summer (277 samples), and (d) across seasons (864 samples). Solid vertical (dashed horizontal) lines below the histograms are means (standard deviations). The bin size per histogram is 20.

[27] On average, the duration of a coherent structure (D) for both levels and across three seasons is about 85 s, with a slightly higher mean value for summer than for winter or spring (Figure 6). Overall, D is consistent between the two levels and across seasons. Other literature had typically shown D to be shorter for forested locations, for instance about 50 s [Gao et al., 1989], 53 to 54 s [Lu and Fitzjarrald, 1994], and 10 to 30 s [Serafimovich et al., 2011; Eder et al., 2013]. However, Steiner et al. [2011], who also used the Barthlott et al. [2007] method over a forest, found large median values of D as well (i.e., 91 to 116 s). Possibly, the dynamic method of determining a unique D for each coherent structure [Barthlott et al., 2007] might be one reason for the statistically larger durations in this and the work of Steiner et al. [2011]. Recall that Gao et al. [1989] also used a dynamic method, but their analysis was based on vertical velocity. Eder et al. [2013] and Serafimovich et al. [2011] used a single value of D for each period, as described previously.

Figure 6.

Same as Figure 4 except for the duration of coherent structures. (a) Winter (2137 cases at 0.6 h; 2253 at 2.6 h), (b) spring (2525 cases at 0.6 h; 2366 at 2.6 h), (c) summer (2028 cases at 0.6 h; 1900 at 2.6 h), and (d) across seasons (6690 cases at 0.6 h; 6519 at 2.6 h).

[28] When extending this comparison to nonforested sites, one notes that Barthlott et al. [2007] found a range of durations over the open field, specifically means of 61 to 65 s for stable conditions and 83 to 98 s for unstable periods. Similarly, Feigenwinter and Vogt [2005] found larger event durations of 90 s over an urban canopy during unstable conditions (again, they used a fixed value of D). Based on this comparison, the mean duration of coherent structures in this study area is larger than for some other forest studies, despite our low mean canopy height. Whether the methodology, the flow conditions, and/or the canopy architecture play a role would require further investigation.

[29] Frequency distributions reveal that the range of coherent structure durations becomes slightly smaller in summer (Figure 6). This, coupled with the slightly higher means for summer, suggests a subtle shift to consistently longer events during warmer periods where conditions are more likely to be unstable. Barthlott et al. [2007] showed that as conditions become unstable, the probability of having longer coherent structures increases. However, for our data, this shift is not robust, which implies that the duration of coherent structure in our forest may be less sensitive to stability that in other locations. Frequency distributions also show some bimodality, particularly in the winter data (Figure 6a). One reason could be that our data clustering was by season rather than by flow-specific classifications. During winter, we note significant changes in D within the same day, with some periods dominated by lower-frequency temperature fluctuations and others with higher frequencies. This variation appears to be related to the presence of breaking gravity waves (low frequencies) and inertial oscillations (higher frequencies), coupled with their ability to penetrate (or not) multiple forest levels.

4.2 Flux Contribution and Fluxing Efficiency of Coherent Structures

[30] As previously mentioned, automated detection techniques and larger data sets reveal smaller heat flux contributions than earlier studies [Barthlott et al., 2007], so now it becomes crucial to compare the modern studies across varying landscapes to ascertain if there is a universal importance in coherent structures to the local energy balance. One problem in comparing the heat flux contribution of coherent structures to the total heat flux (FCOH/FTOT) is that when turbulence is very low, this quantity can exceed 100% [Barthlott et al., 2007]. Feigenwinter and Vogt [2005] also encountered this issue, and attributed it in part to the outward and inward interactions (i.e., noncoherent motions) that can occur in concert with coherent structures. In addition, we also find a high number of small values of FCOH/FTOT (i.e., less than 5% at 0.6 h). We isolated the periods where the flux contribution from coherent structures was very small or very large (i.e., 5% and less, or 100% and above). These data, hereafter denoted as FCOHextreme, clearly populate the tails of the distribution with very low mean fluxes (Table 5). Eliminating FCOHextreme leaves 748 periods at 2.6 h (12 m), and 657 periods at 0.6 h (3 m) for all subsequent analyses regarding flux contributions and fluxing efficiency.

[31] Results show that the mean flux contribution from coherent structures ranges from about 44% to 53% between the two levels over the seasons (Figure 7), which is consistent with the statistical formulation of some larger data sets. For example, Lu and Fitzjarrald [1994] found the mean contribution to be about 40%, and Steiner et al. [2011] found 44% to 48%, both over midlatitude deciduous forests. While the mean flux contribution from coherent structures in this study is similar at both the 2.6 h (12 m) and 0.6 h (3 m) levels for summer, there is actually a slightly larger mean heat flux contribution at the 0.6 h (3 m) level during winter and spring (and overall). Most interesting, however, is the frequency distributions which indicate that the dominant value of coherent flux contributions shifts seasonally from being largest at 0.6 h (3 m) in winter to being largest at 2.6 h (12 m) in summer (Figure 7).

Figure 7.

Same as Figure 4 except for the flux contribution from coherent structures (i.e., FCOH/FTOT, for contributions between 5% and 100%). (a) Winter (191 cases at 0.6 h; 245 at 2.6 h), (b) spring (238 at 0.6 h; 249 at 2.6 h), (c) summer (228 at 0.6 h; 254 at 2.6 h), and (d) across seasons (657 cases at 0.6 h; 748 at 2.6 h).

[32] Dividing the time that coherent structures were present during a half-hour period (in s), by the total length of a half-hour period (1800 s), provides the time coverage of coherent structures. Across three seasons, we find that coherent structures occupy an average of 36% of each period at both levels. This is similar to the 34 to 38% time coverage found across stability classes by Barthlott et al. [2007]. Related to the time coverage is the fluxing efficiency of coherent structures, which is a ratio of their heat flux contribution during a given half-hour period, divided by the percentage of time that they exist within that period; values above (below) 1.0 are considered efficient (inefficient) [Barthlott et al., 2007]. From Figure 8, it can be seen that at 2.6 h (12 m), the dominant value of efficiency for coherent structures exceeds 1.0 during all three seasons, while at 0.6 h (3 m), the dominant value of efficiency only exceeds 1.0 during spring (Figure 8).

Figure 8.

Fluxing efficiency of coherent structures whose flux contributions lie between 5% and 100% at (a) 0.6 h (657 cases), and (b) 2.6 h (748 cases). The vertical line denotes an efficiency of 1 (< 1 is inefficient; > 1 is efficient). The number of bins per histogram is 20.

[33] To summarize, we include Table 3, which compares our results with those of other studies where wavelet analysis was also used to detect coherent structures. Rows one through six are studies done within forests, the first two of which use the method of Barthlott et al. [2007]. The last two rows, shaded in gray, were done in nonforest environments. One finding is that the number of coherent structures is similar for both forest and nonforest regions. This may result from the fact that, despite the types of roughness elements over which the flow travels, coherent structures are self-limiting in that their negative momentum fluxes ultimately destroy the vertical velocity gradients that initiate them.

Table 3. Summary of Literature Review in Which Wavelet Analysis Is Used to Detect and Evaluate Coherent StructuresaThumbnail image of
  • aColumns 3–7 are number of structure per half-hour period; duration (D) of structures in seconds; time coverage (%) of structures; flux contribution from structures (%); fluxing efficiency. Last two rows indicate nonforested study sites. Dash indicates that data are unavailable.
  • b= Data means.
  • c= Data medians.
  • [34] A primary difference amongst these studies is the duration of structures (D), as was previously discussed. The heat flux contribution by coherent structures also varies, but all are well below the larger values of 75 to 90% given from earlier studies on smaller data sets [Gao et al., 1989; Bergström and Högström, 1989]. It is worth mentioning that differences in heat flux contribution may also result from methodology. Specifically, Eder et al. [2013] note that studies who use the method of Lu and Fitzjarrald [1994] to determine FCOH/FTOT (rows 1, 2, 6, and 7) will count all the fluxing within the duration of a structure as a coherent flux, whereas studies who use the method of Collineau and Brunet [1993b] (rows 3–5) will average out the turbulent fluxes at scales significantly below the event duration, D. Furthermore, differences in determining D can also impact the amount of flux provided by coherent structures (i.e., longer events yield greater flux contributions). In general, the length of the data sets, season(s) during which the data were collected, data screening criteria, detection/analysis techniques, canopy characteristics, and precise measurement heights will scatter results across studies. Considering these differences, results across authors are reasonably consistent. However, the data for this study site contain a strong influence from the wave-like flows associated with stratified regimes, and also a large number of coherent structures that are isolated at only one level.

    4.3 Analysis of Periods Under the Influence of Wave-Like Flow

    [35] Frequency distributions for δ at both levels confirm that most of the periods are more turbulent than wave-like, especially during the warmer seasons (Figure 9). However, the fraction of actual half-hour periods influenced by waves is significant: 29% at 2.6 h (12 m), and 15% at 0.6 h (3 m) across seasons (Table 4). Also, we assume that if a given half-hour period is wave-like, then all coherent structures detected therein are potentially waves or turbulent features influenced by waves. Based on this assumption, the fraction of actual coherent structures determined to be under a wave influence is about 31% for the 2.6 h (12 m) level and 13% in the 0.6 h (3 m) level across seasons (Table 4). Clearly, the 2.6 h (12 m) level consistently shows a higher polarization, implying more wave-like organization of the flow at that level. These results suggest that a significant portion of the coherent structures detected in the boreal forest could be complicated by waves and/or wave-turbulence interactions. As a comparison, Cava et al. [2004] evaluated nighttime data over a pine forest in North Carolina and found that while almost 50% of a given night's data may contain canopy waves, a mean of only 6% for the 21 summer evening periods they analyzed was determined to be dominated by canopy waves.

    Figure 9.

    Thirty minute mean polarization (δ). (a) Winter (306 cases); (b) spring (281 cases); (c) summer (277 cases); and (d) across seasons (864 cases). The bin size per histogram is 20.

    Table 4. Summary of the Seasonal Occurrence of Wave-Like Periodsa
    Season 2.6 h (12 m) 0.6 h (3 m) 
    1. aColumns 3 and 5 show the number of half-hour periods (or, in the last row, the number of coherent structures) determined to be under a wave-like influence. Columns 4 and 6 show the corresponding percentages.
    Winterperiods with waves134 72 
    total periods analyzed30644%30624%
    Springperiods with waves76 40 
    total periods analyzed28127%28114%
    Summerperiods with waves42 21 
    total periods analyzed27715%2778%
    TOTALperiods with waves252 133 
    total periods analyzed86429%86415%
    wave influenced structures2052 901 
    total structures detected671531%689913%

    [36] We use this polarization criterion to cluster the flux contributions from coherent structures that are more likely to be purely turbulent (FCOH), and contributions from structures more likely to be under the influence of waves (FWAVE) (Figure 10). Results across three seasons indicate that the mean flux contributions for FWAVE are about 43% at 2.6 h (12 m) and 55% at 0.6 h (3 m). For FCOH, the means are 46% at 2.6 h (12 m) and 49% at 0.6 h (3 m). These mean values are not largely different from one another, nor are they much different from the previous evaluation of mean flux contributions of all structures combined (recall Figure 7). The standard deviation for FWAVE, however, is more than a 20% increase over the standard deviation of FCOH at both levels. This is particularly evident at the 0.6 h (3 m) level (Figure 10a) and suggests a slightly broader range of values for FWAVE. This would be consistent with the conclusions of Cava et al. [2004], who found that canopy waves broaden the spectrum of the scalar time series in their data.

    Figure 10.

    Flux contribution from coherent structures under a wave-like regime (FWAVE, 196 cases at 2.6 h; 69 cases at 0.6 h), and a more turbulent regime (FCOH, 552 cases at 2.6 h; 588 cases at 0.6 h). The bin size per histogram is 20.

    [37] Clustering all data by δ shows that periods under the influence of waves typically have low mean sensible heat flux values. Table 5 compares the statistical parameters regarding the total heat flux for all periods classified as FWAVE (δ > 40%), and also the same statistical summary for all periods classified as FCOHextreme (FCOH/FTOT is ≤ 5% or ≥ 100%). We note that these two populations are not the same, but they do overlap (i.e., at the 12 m level, 22% of FWAVE also meet the criteria of FCOHextreme; at the 3 m level, 48% of FWAVE meet the criteria of FCOHextreme). What is remarkable is that the mean flux contributions by coherent structures is not much different during wave-influenced periods, when the mean total flux is small, than it is for more turbulent periods when the mean total flux is greater. Thus, we find that the flux contribution by coherent structures is insensitive to the magnitude of the total flux and therefore does not necessarily assess the importance of the individual structures.

    Table 5. Statistical Summary of Sensible Heat Flux Values (W m−2) Under Conditions of Extreme Fluxing Contribution (FCOHextreme) and Also Under the Influence of Wave-Like Motion (FWAVE)
     FCOHextreme FWAVE 
     2.6 h (12) m0.6 h (3 m)2.6 h (12 m)0.6 h (3 m)
    Standard deviation4.52.93010.4

    4.4 Analysis of Synchronous Coherent Structures

    [38] In response to the concern that coherent structures may be of greater importance when they can impact multiple levels within a forest at once [Gao et al., 1989; Bergström and Högström, 1989; Shaw et al., 1989], we evaluate our data to see how many of the ramps we detected in the two levels are synchronous. If ramp shapes occur synchronously at both levels, then we assume this implies the presence of a coherent structure that was capable of penetrating from one level of the forest to the other. To do this, one must first define what synchronous means in terms of flows within a canopy. Since the microfront tends to appear first in upper levels and lags slightly in time at lower levels [Taylor, 1958; Gao et al., 1989], some amount of offset between events at different levels is required. For the Canadian forest analyzed by Gao et al. [1989], the mean canopy height is 18 m. They determined that within the canopy, temperature changes took about 10 s to descend 12 m, which translates to 7.5 s for the 9 m difference in this study. Feigenwinter and Vogt [2005] considered structures synchronous when they occurred within ±25 s at three levels above their 24 m urban canopy. We compromise between these two studies and use a lag time window of ±0 to 10 s (closer to Gao et al., [1989]). The reason for the plus or minus is to account for slight inaccuracies in the zero-crossing of the MHAT wavelet which sometimes do not occur precisely at the end of a microfront. To explore whether or not this time lag is appropriate, we also flag cases where the microfronts are within ±10 to 20 s (closer to Feigenwinter and Vogt [2005]), and then compare the results.

    [39] Scanning the data with the ±0 to 10 s criteria confirms the hypothesis that ramps are rarely synchronous in both levels. Specifically, the percent of the total ramps detected whose microfronts occur within ±0 to 10 s of one another are about 16.5% in winter, 21.5% in spring, and 22% in summer (Table 6). Despite a small increase through spring and summer, the data suggest that on average less than one quarter of the events we detect in the two levels occur within 0 to 10 s of one another. When we analyze cases where microfronts are within ±10 to 20 s, the percentage of cases is even lower. Since the anemometers are only 9 m apart in the vertical, this speaks robustly to the difference in flow regimes that can occur within a shallow layer of our forest, even during warmer seasons.

    Table 6. Percentages of Coherent Events That are Synchronous Between Both Levels, for Each Day and for the Season (“Total”)a
    1. aTime lags are ±0 to 10 s (“10 s”) and ±10 to 20 s (“20 s”). Note that the number of synchronous temperature ramps is identical in both levels, but the total number of ramps detected varies between levels (therefore the percentages are slightly different between levels).
    Winter Julian Day
     36 43 53 61 63 64 65 Total 
     10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s
    2.6 h (12 m)15822812818101491812108169
    0.6 h (3 m)15823912817914922141191710
    Spring Julian Day
     93 94 95 100 101 106   Total 
     10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s  10 s20 s
    2.6 h (12 m)281520161817191321162016  2115
    0.6 h (3 m)251421161717181219141814  2015
    Summer Julian Day
     176 187 189 190 193 194   Total 
     10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s10 s20 s  10 s20 s
    2.6 h (12 m)271824162515181619132415  2315
    0.6 h (3 m)251721142113171620132315  2114

    [40] If we evaluate the mean flux contribution from synchronous ramps only, and compare this to the mean flux contributions for all ramps as shown in Figure 7, there is a noticeable decline in this value. Across three seasons, the mean flux contribution from synchronous ramps which are ±0 to 10 s apart is 9–14%, and for cases that are ±10 to 20 s apart, the flux contribution drops to around 5–10% (Table 7). Thus, the heat flux contribution from only the coherent structures that were determined to be synchronous in this analysis is small, despite that the flux contributions from all detected structures at any one level are similar to what has been shown in other locations.

    Table 7. Fraction of Coherent Flux Contribution (FCOH/FTOT) for Synchronous Events Compared to All Detected Eventsa
     2.6 h (12 m)0.6 h (3 m)
    1. aSynchronous structures are defined by the time lag intervals of ± 0 to 10 s and ±10 to 20 s, and are compared with the (FCOH/FTOT) contribution of all events (“All”).
    SeasonAll±0 to 10 s±10 to 20 sAll±0 to10 s±10 to 20 s

    5 Discussion

    [41] Similarities in mean global statistics for all detected structures between ours and other studies suggest that structures have somewhat universal properties. Where our results differ from others who used wavelet analysis on large data sets in forests is first in the slightly longer durations (D) of our coherent structures. Recall also that D was larger in the work of Steiner et al. [2011]. One reason could be that both studies used the method of Barthlott et al. [2007] to derive D, which scales more dynamically with individual structures. However, the canopy height for Steiner et al. [2011] was 22.5 m, and our canopy was only 4.7 m. Since the size and spacing of eddies generated from shear at the canopy should scale in proportion to the canopy height [Raupach et al., 1996], one might expect shorter durations for our study area. However, based on Taylor's hypothesis [Stull, 1988], this evaluation has to be tempered with the fact that a lower wind speed would move structures more slowly, resulting in longer durations as measured from a stationary tower. Barthlott et al. [2007] showed that for stable conditions, coherent structures were more likely to be shorter; for this study, event duration only grows slightly from winter to summer, suggesting that other parameters besides stability control their duration. All of these hypotheses should be considered in light of the fact that the strong heterogeneity of our canopy height may be adding complexity to the formation of structures, such that structures of varying scales may interact at once. Further analysis is required to investigate what other physical parameters might be involved. Also, using the sign of the Obukhov Length (L*) occasionally results in inaccuracies when measuring the duration of a ramp. The detection algorithm will also sometimes group a few less well-defined ramps together as one feature. Thus, some imperfections in the detection process may also contribute to the slightly longer duration times in this study.

    [42] Another difference between this and other studies is in regard to the flux contribution of the coherent structures to the total 30 min heat flux (FCOH/FTOT). Our results for FCOH/FTOT were similar to other forested and nonforested regions, especially the ones which used the Barthlott et al. [2007] method for determining event duration and/or the Lu and Fitzjarrald [1994] method for calculating FCOH/FTOT (Table 3). However, the fact that the dominant values of FCOH/FTOT transition from being higher at 0.6 h (3 m) in winter to being higher at 2.6 h (12 m) in summer was a notable finding in our results (Figure 7). This, combined with the high standard deviation in tree heights for the boreal forest, suggests that coherent structures detected by the two sonic anemometers may sometimes come from separate events initiated at different canopy heights. Since coherent structures are often initiated near the top of a canopy where shear instability is highest [Raupach et al., 1996], it follows then that FCOH/FTOT should be largest within the upper half of the canopy at which the structures are initiated, and weaker above and below this height as shown by Gao et al. [1989, their Figure 11]. For the black spruce forest, the upper portion of the canopy near the micrometeorological tower is about 2 to 4 m in height. Thus, we should consistently see higher values of FCOH/FTOT at 0.6 h (3 m) if coherent structures are initiated locally there. If we consider only mean values of FCOH/FTOT, this is generally true because the mean value of FCOH/FTOT tends to be higher at 0.6 h (3 m), except for summer (Figure 7). However, the density distribution of FCOH/FTOT is not always normal, and so the dominant value does not reflect that FCOH/FTOT is consistently higher at 0.6 h (3 m). We hypothesize that during winter, coherent structure might be more frequently initiated within the lower canopy, local to the site. During summer, coherent structures might be more often initiated from the higher canopy at the periphery of our study site. Further, we could be seeing a combination of coherent structures whose physical sizes vary, but which become superimposed as they enter the forest. More detailed investigations of the scale of the detected structures and their synchronicity would be required to determine this.

    [43] Another critical element is the stratification within the boreal forest, which clearly makes the flow susceptible to gravity waves. In this study, we used an adaptation of the Stokes parameters to suggest that almost one third of the structures we detect at 2.6 h (12 m, i.e., above the canopy) could be complicated by wave-like behavior (Table 4); at the subcanopy level 0.6 h (3 m), this value was lower. Since we expect waves to be ducted within layers of comparable stratification, the fact that there are considerably more waves in the 2.6 h (12 m) flow suggests that even a 9 m vertical difference is significant when considering the flow regime in our forest. It is important to note that in this study, we include daytime periods and periods during warmer, potentially more convective regimes when evaluating the wave-like nature of the flow, in contrast to other studies on gravity waves which focus only on nighttime data. Despite this, we still find a high number of wave-influenced cases, emphasizing the importance of stratification on the analysis of any kind of organized structures in the black spruce boreal forest.

    [44] Finally, we showed that less than a quarter of the features we detect at the subcanopy and above-canopy levels are synchronous, i.e., produced by the same coherent structure. As a result, FCOH/FTOT from only the synchronous events is significantly less than when all structures are included in each level independently (Table 7). This was a most remarkable finding, because it suggests that most of the time, coherent structures may not be the dominant mechanism in the vertical aggregation of sensible heat within our boreal forest. Furthermore, the vertical distance over which we are evaluating the flow is only 9 m; the lack of synchronous ramps between these two levels speaks robustly to the lack of interaction between the subcanopy and above-canopy levels in our black spruce forest. Ultimately, implications of this finding are that when upscaling heat fluxes within the boreal forest, one must also be concerned with other modes besides organized motion. Clearly, low-flow conditions could be influencing this result. We also note that the first maximum in the global wavelet power spectrum (FMAX), which is used to define the range of frequencies for organized turbulence, can often be broad and hard to define [Barthlott et al., 2007]. Imposing a criterion on the kurtosis of the global wavelet spectrum might help with this analysis, as it would provide a quantitative manner of rejecting periods where this value is not robust enough to be reliable.

    6 Conclusions

    [45] In conclusion, we detect coherent structures in the turbulent temperature time series for 864 half-hour periods spanning winter, spring, and summer of 2012, using an automated wavelet analysis technique at both the above-canopy (2.6 h or 12 m) and subcanopy (0.6 h or 3 m) levels within an Alaskan black spruce boreal forest whose mean canopy height (h) is 4.7 m. When analyzed at each of these two levels independently, global mean statistics for all detected structures show that the number of structures per half-hour period, their durations, their heat flux contributions, and their fluxing efficiencies are not largely different from other studies in diverse locations. Specifically, considering all the structures we detected at both levels and across all three seasons, we find an average of eight coherent structures every 30 min and a mean duration of 85 s. Eliminating events with extreme flux contribution values during times of low total fluxing (FCOHextreme), we find a mean heat flux contribution of 48%, and a mean fluxing efficiency of around 1.5.

    [46] However, our analysis shows that as much as 31% of the structures detected at 2.6 h (12 m), and 13% of those detected at 0.6 h (3 m), may be complicated by a wave-influenced flow regime and therefore may not be purely coherent turbulent structures. These wave-influenced periods are often characterized by low total heat fluxes, but when analyzed separately, the flux contributions from structures during these periods are similar to our pervious values. This suggests that flux contributions from wave-influenced events may be similar to that from more turbulent events, despite differences in the total heat flux. Most importantly, we find that less than 25% of structures affect both levels simultaneously, a finding that speaks robustly to the lack of flow interaction in only nine vertical meters of our forest. This result suggests that the vertical aggregation of sensible heat fluxes within a black spruce boreal forest is complicated and that other modes of fluxing besides organized motion (e.g., stochastic or dispersive fluxes) are important.


    [47] This research was supported by the Alaska NASA EPSCoR program award NNX10NO2A and by the Alaska Space Grant Program. Authors would also like to thank Glenn Juday from the School of Natural Resources and Agricultural Sciences of the University of Alaska Fairbanks for his support in the forestry inventory section of this paper. We thank the very positive comments and feedbacks from reviewers.