Canopy architecture and turbulence structure in a coniferous forest

CANOPY ARCHITECTURE AND TURBULENCE STRUCTURE IN ACONIFEROUS FOREST

B. MARCOLLA1,2, A. PITACCO3 and A. CESCATTI1,�

1Centro di Ecologia Alpina, 38040 Viote del Monte Bondone (Trento), Italy; 2Department of Civiland Environmental Engineering, University of Trento, Italy; 3Department of Environmental

Agronomy and Crop Production, University of Padua, Italy

(Received in final form 14 August 2002)

Abstract. Synchronous sonic anemometric measurements at five heights within a mixed coniferousforest were used to test two different parameterisations of canopy architecture in the application ofa second-order turbulence closure model. In the computation of the leaf drag area, the aerodynamicsheltering was replaced with an architectural sheltering, assumed to be analogous to the clumpingindex defined in radiative transfer theory. Consequently, the ratio of leaf area density and shelteringfactor was approximated by the effective leaf area or the mean contact number, both obtained fromthe inversion of non-destructive optical measurements. The first parameter represents the equivalentrandomly dispersed leaf area in terms of shading, the second is the average number of leaves thata straight line intercepts penetrating the canopy with a certain zenith angle. The selection of thisdirection was determined by the analysis of the mean angle of the wind vector during sweep events.The drag coefficient values obtained from the inversion of the momentum flux equation, using thetwo proposed parameterisations, are in good agreement with values found in the literature. Thepredicted profiles of turbulence statistics reasonably match actual measurements, especially in thecase of the mean contact number parameterisation. The vertical profile of leaf drag area, obtained byforcing the turbulence model to match the observed standard deviation of vertical velocity (σw), isintermediate between the two empirical ones. Finally, the proposed canopy parameterisations wereapplied to a Lagrangian transport model to predict vertical profiles of air temperature, H2O and CO2concentration.

Keywords: Canopy architecture, Drag coefficient, Scalar transport, Turbulence statistics.

List of Symbols

a leaf area density

Cd drag coefficient

Cd new definition of the drag coefficient

C scalar concentration

D dispersion matrix

ea effective leaf area

G angular distribution

� Corresponding author, E-mail: cescatti@cealp.it

Boundary-Layer Meteorology 108: 39–59, 2003.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

40 B. MARCOLLA ET AL.

LAI leaf area index

mcn mean contact number

n number of observations

Pm sheltering factor

Pm architectural sheltering factor

S source/sink intensity

T canopy gap fraction

(x, y, z) cartesian coordinates

(u, v,w) wind velocity components

(u, v,w) mean components of wind velocity

(u′, v′, w′) fluctuating components of wind velocity

uh mean wind velocity at the top of the canopy

u∗ friction velocity

λ0 clumping index

(σu, σv, σw) standard deviations of wind velocity components

u′w′ uw covariance

θ zenith angle

ζ cumulative leaf drag area

1. Introduction

Recent studies on the role of terrestrial ecosystems in carbon and water cyclesare based on long-term measurements of mass and energy exchanges betweenvegetation and the atmosphere (Goulden et al., 1996). Approximately 180 exper-imental sites organised into an international network (Baldocchi et al., 2001) arecontinuously monitoring CO2, H2O and turbulent heat fluxes with a standardisedmethodology (Aubinet et al., 2000). This effort is supported by theoretical andexperimental investigations on turbulent diffusion, which is largely responsible forthe scalar transport within and above plant canopies. In particular, a detailed know-ledge of the turbulence structure is required for theoretical studies on turbulentflows over complex terrain (Kaimal and Finnigan, 1994; Lee, 1998), the applicationof Lagrangian transport model for footprint analysis (Baldocchi, 1997; Rannik etal., 2000; Markannen et al., 2003), and the prediction of canopy micrometeorology(Baldocchi and Meyers, 1998; Lai et al., 2000; Albertson et al., 2001).

Considering that turbulence structure depends on the interaction betweencanopy architecture and atmospheric boundary-layer dynamics, several modelsprovide a one-dimensional description of the wind field given the canopy structure,under the assumptions of horizontal homogeneity, neutrality and steady state con-ditions (Wilson and Shaw, 1977; Meyers and Paw U, 1986; Wilson, 1988; Ayotte et

ARCHITECTURE AND TURBULENCE IN CONIFERS 41

al., 1999; Massman and Weil, 1999). The role of plants is quantified by the leaf dragarea (ζ ), which accounts for the effects of leaf area density (a), drag coefficient(Cd) and sheltering (Pm) on the wind field (Thom, 1971). The independent estimateof these three canopy parameters is one of the major problems in the applicationsof turbulence closure models. In particular, the effects of sheltering and drag on thewind field cannot be easily separated nor estimated by independent measurementsof canopy architecture. In the literature, two approaches are generally applied tothe leaf drag area parameterisation from measured wind data: The estimation of thedrag coefficient with the momentum flux equation using independently measuredvalues of leaf area density (Meyers and Paw U, 1986; Amiro, 1990b; Katul andAlbertson, 1998), or the estimation of leaf drag area as a whole by minimising theerrors between observed and predicted data (Wilson, 1988; Ayotte et al., 1999).Both approaches lead to good estimations of mean wind profiles and shear stress,while normal stresses are generally overestimated.

In the present work, alternative parameterisations of the canopy are proposed,in which an architectural sheltering factor (Pm) is introduced and the leaf areadensity corrected by this sheltering effect is estimated by two canopy propertiesused in radiative transfer: the effective leaf area and the mean contact number. Bothparameterisations are based on the inversion of optical measurements of canopygap fraction and, besides establishing an important link between aerodynamicaland radiative properties of plant canopies, they have the great advantage of avoidingdestructive and time-consuming biomass analysis.

Following these innovative approaches for the determination of the leaf dragarea, the drag coefficient (Cd), which explains the wind speed dependence of thephenomena, remains the only unknown in the momentum flux equation and can becalculated from measured profiles of the mean wind velocity (u) and covarianceu′w′. The effects of the alternative parameterisations on the output of a second-order closure model (Massman and Weil, 1999) have been tested comparing thepredicted and observed wind field. In addition to the experimental canopy para-meterisation, an ‘optimal’ profile of leaf drag area has been calculated by forcingthe model prediction of σw profile to match the measured values.

Finally, the implications of the different approaches on the scalar concentrationprofiles, predicted by a Lagrangian transport model, have been evaluated for typicalvertical patterns of CO2 and heat source/sinks.

2. Materials and Methods

2.1. STUDY SITE

Measurements were performed at an intensive study site (Lavarone, Italian Alps;45.96◦ N, 11.28◦ E; 1300 m asl, mean annual temperature 7 ◦C, total annualprecipitation 1150 mm), where ecosystem energy, water, and carbon fluxes are con-tinuously monitored within the framework of the European network CarboEuroflux

42 B. MARCOLLA ET AL.

(Valentini et al., 2000). The area is characterised by an uneven-aged mixed forestdominated by Abies alba (70%), Fagus sylvatica (15%) and Picea abies (15%),with an average of 1300 stems ha−1 (dbh > 75 mm) and a leaf area index (LAI) of9.6, expressed as half of the total surface area according to Chen and Black (1992).The canopy has a dominant layer reaching 33–36 m and crown lower limits atabout 12 m. In the understorey suppressed beeches form a discontinuous secondlayer from 0 to 4 m.

A 36-m tall tower is equipped with instruments for the measurement of micro-meteorological variables (radiation components, wind, humidity, and temperature)and of momentum, energy and mass fluxes (water and carbon dioxide) by meansof the eddy covariance technique according to the Euroflux methodology (Aubinetet al., 2000). The meteorological tower is located on a gently rolling karst plateauand has a homogeneous vegetated fetch larger than 1 km in all directions, exceptfor a 45 degree sector (300 m fetch in the south-south-west direction).

2.2. WIND MEASUREMENTS AND DATA PROCESSING

During summer 1998 (Julian days 230–271) five sonic anemometers were installedat 9.5, 16.5, 24, 28.5, 36 m heights on the tower. The instruments at the two lowerlevels were Campbell CSAT3 (Campbell Scientific Inc., Logan, Utah), while theothers were Gill R2 (Gill Instruments, Lymington, U.K.). The analogue output sig-nals of the anemometers were synchronously sampled at a frequency of 60 Hz by aNational Instrument DAQCard AI-16XE-50 using programs written in LabVIEW.Block averages at 20 Hz were stored in half-hourly binary files for subsequentprocessing. Data were processed with the software EdiRE (1.3.2.11 version byRobert Clement, personal communication, 2001) with self-defined procedures.

Half-hourly values of mean wind direction, temperature and sensible heat flux,u, standard deviations of velocity components (σu, σw, σw), and mean shear stress(u′w′), were computed for each level after applying three coordinate rotations tothe top anemometer data and one rotation to the measurements within the canopyspace, according to Baldocchi and Meyers (1988).

To avoid stable conditions, the analysis of the wind field was limited to daytimedata (from 0800 to 1900 local time), characterised by frictional velocities higherthan 0.1 m s−1, and by a standard deviation of sonic temperature lower than 2 ◦C(to exclude periods with water droplets on the anemometer heads). Periods withthe stability parameter (measurement height normalised with the Obukhov length)in the range (−0.05, 0.05) were classified as neutral. Half-hourly statistics weregrouped according to wind direction (four classes) and intensity (four classes) atthe top level. Wind direction was classified in four quadrants centred on the cardinaldirections, while the limits of wind speed classes were set in order to have aneven distribution of records. In addition, the half-hourly mean penetration anglesof eddies into the canopy (θ) were computed for 10 days to infer the frontal area asseen by the wind during the sweep phases. For this purpose, the sweep and ejection

ARCHITECTURE AND TURBULENCE IN CONIFERS 43

events were determined by means of the quadrant-hole technique (Finnigan, 1979)and the mean zenith angles of the wind vector were computed as:

θ = 1

n

∑i

arctg

(u + u′

i

w + w′i

) {u′ > 0 and w′ < 0 (sweep)u′ < 0 and w′ > 0 (ejection)

, (1)

where n is the number of observations in each half-hour. The flux angle distri-butions for sweep and ejection were eventually calculated for the two uppermostlevels (36 and 28.5 m).

2.3. CANOPY ARCHITECTURE

A major limitation in the application of turbulence closure models to plant canopiesis the quantitative description of plant architectural features determining the aero-dynamics and the momentum absorption. In current literature, the leaf drag area isdescribed by vertical profiles of three architectural parameters of the canopy: Leafarea density, drag coefficient and sheltering factor (Thom, 1971; Massman, 1997),

ζ(u, z) =∫ z

0

Cd(u, z′)a(z′)Pm(u, z′)

dz′. (2)

As pointed out by Massman, the drag coefficient and sheltering factor are notcompletely separable one from the other, depending both on canopy geometricproperties and on the wind field. An indirect estimate of these parameters cannotbe obtained from the inversion of wind data, since the drag area calculation involvesthe product of them.

For this reason, the combination of the sheltering and drag coefficient is usuallyestimated as a unique parameter by inverting wind profile data, while leaf areadensity is derived from independent measurements (Wilson, 1988; Katul and Al-bertson, 1998). Following this approach, the effect of the leaf spatial arrangementis mixed with the drag coefficient of plant elements, which should merely dependon their shape and flexibility.

Considering that the sheltering factor is much more strongly influenced by can-opy structure than by the wind field, while the drag coefficient is mainly affectedby the wind speed (Landsberg and Powell, 1973; Grant, 1984), we propose theuse of a drag coefficient Cd(u, z) describing the wind speed dependence of thedrag force, and of an architectural sheltering factor Pm(z), merely dependent onthe spatial pattern of the leaf area. Accounting for the self-shading between canopyelements, the architectural sheltering reduces the leaf frontal area ‘seen’ by thewind. An analogous role is played by the clumping index (λ0) in light interception.The clumping index has been defined by Nilson (1971), within a Markov schemeof radiation interception, viz.

T (θ, z) = exp(−G(θ, z)λ0(θ, z)a(z)/ cos(θ)), (3)

44 B. MARCOLLA ET AL.

where T is the canopy gap fraction, G the leaf angular distribution, a the leafarea density and θ the zenith angle; λ0 expresses the probability of a leaf to benon-shaded by another leaf in the nearby canopy layer.

Assuming that the shaded leaves do not contribute to the momentum absorption,the architectural sheltering coefficient Pm(z) is equal to 1/λ0. Using this analogy,the sheltering factor is embedded in the estimates of canopy architecture obtainedfrom the inversion of gap fraction measurements.

The product of λ0 and leaf area has been defined as effective leaf area (ea) andrepresents the equivalent randomly dispersed leaf area in terms of shading (Chenet al., 1991). In continuous plant canopies, the effective leaf area can be easilyretrieved from measurement of gap fraction (Equation (4) below) by the inversionof Equation (3) or, in case of multi-angular gap-fraction measurements, with othermore robust inversion methods (Miller, 1967),

a(z)/Pm(z) = a(z)λ0(θ, z) = ea(z) = − ln(T (θ, z)) cos(θ)/G(θ, z). (4)

In the inversion procedure, the canopy has been described according to the geo-metrical model presented in Cescatti (1997) (Figure 1), which takes into accountthe spatial heterogeneity of the canopy and thus enables a realistic computation ofradiative and architectural properties of anisotropic systems such as forest canopies(Cescatti, 1998). The vertical profile of effective leaf area has been estimated ac-cording to the methodology reported in Cescatti (1999) and Law et al. (2001). Forthis purpose, gap fraction measurements in five angular bands have been performedwith the Plant Canopy Analyzer (PCA) LAI-2000 (LiCOR Lincoln, Nebraska) in800 recorded locations at the forest floor, within a distance of 60 m from the tower.

Considering that the wind zenith angle during the sweep events was ratherconstant, in the computation of the drag area, the leaf area has been alternativelysubstituted with a physical estimate of the number of interceptions (leaves) alongthe average sweep direction of the wind. This parameter is known in radiativetransfer as ‘mean contact number’ (mcn), and represents the average number ofleaves that a straight line will pass through when penetrating the canopy with acertain zenith angle (Campbell and Norman, 1989). The technical limitations inthe estimation of gap fraction at high zenith angles (landscape shading, scattering,etc.) suggested the use of the lower PCA ring (60–75 degrees) to compute the meancontact number,

mcn(θ, z) = − ln(T (θ, z)) = G(θ, z)a(z)λ0(θ, z)/ cos(θ). (5)

In order to describe the vertical profile of mean contact number, gap fraction meas-urements were collected on the tower, with 5 PCA readings every 1 m for a total of150 records.

ARCHITECTURE AND TURBULENCE IN CONIFERS 45

Figure 1. Three-dimensional representation of crown shapes and positions obtained with the modelFOREST (Cescatti, 1997) for a 60 m × 15 m transect surrounding the tower. The canopy model wasused to estimate the vertical profile of effective leaf area.

2.4. DRAG COEFFICIENT

The interaction of plant canopies with the wind field is described in current liter-ature by the concept of cumulative leaf drag area (Thom, 1971; Massmann, 1997),according to Equation (2). To simplify the parameterisation of canopy architecture,the number of parameters was reduced from three to two using the two followingalternative strategies:1. Combining leaf area and sheltering effect in the effective leaf area sensu –

Chen et al. (1991). This strategy implies that the drag coefficient takes into ac-count the effects of wind speed and leaf angular distribution on the momentumabsorption by canopy elements,

ζ(uh, z) =∫ z

0Cea

d (uh, z′)ea(z′) dz′. (6)

46 B. MARCOLLA ET AL.

2. Combining leaf area, sheltering effect and leaf angular distribution in the meancontact number (mcn) along the mean wind direction during sweep events.Using this approach, the drag coefficient only accounts for the wind speedeffect on the momentum absorption,

ζ(uh, z) =∫ z

0Cmcn

d (uh, z′)mcn(z′) dz′. (7)

The drag coefficient has been calculated from the momentum flux Equation (8),valid for steady state, homogeneous turbulence with no mean horizontal pressuregradient and negligible dispersive and molecular momentum fluxes in the verticaldirection,

du′w′

dz= −C

ea, mcnd (z)(ea(z), mcn(z))u2(z). (8)

Assuming the drag coefficient to be constant in the canopy space, Equation (8)can be integrated from the lowest measuring level to the canopy top for eachhalf-hourly period to compute the drag coefficient for the two proposed canopyparameterisations, namely ea and mcn,

Cea, mcnd = − u′w′(ztop) − u′w(zbottom)∫ ztop

zbottom(ea(z′), mcn(z′))u2(z′) dz′ . (9)

Averages and standard deviations of the drag coefficients were calculated for eachwind speed and direction class from half-hourly daytime values. The mean dragcoefficient for each wind speed class was finally computed as the average of thedrag coefficients obtained for the different direction classes.

2.5. DIRECT AND INVERSE APPLICATION OF A SECOND-ORDER CLOSURE

MODEL

The two different approaches to canopy parameterisation were used in the applica-tion of the second-order closure model proposed by Massman and Weil (1999), topredict the vertical profiles of turbulence statistics. The model gives an analyticalexpression for the second-order moments as functions of the cumulative leaf dragarea, coupling the exponential wind profile after Albini (1981) with the equationsfor the variances of the wind components reported in Wilson and Shaw (1977),under the assumptions of horizontal homogeneity of the canopy, a steady statecondition for the wind field, and neutrality. The Massman and Weil model hasbeen parameterised with the average drag coefficients as computed from the exper-imental data for the two different approaches to canopy parameterisation. Finally,model predictions were compared with the observed turbulence statistics above andwithin the canopy using the mean absolute error as statistical index to quantify themodel accuracy (Power, 1993).

ARCHITECTURE AND TURBULENCE IN CONIFERS 47

In addition, measured turbulence statistics have been used to estimate an ‘op-timal’ vertical profile of the leaf drag area according to the Massman and Weilmodel. For this purpose, a Beta function was assumed to describe the vertical pro-file of the leaf drag area (Meyers and Paw U, 1986), and its two shape parameters,together with the total drag area, were estimated by minimising the mean squareerror between model predictions and experimental observation of σw. The assignedtop boundary condition for σw/u∗ was 1.25, typical of a constant stress surfacelayer (Garratt, 1994). The numerical optimisation of the model has been performedwith a C++ code using the Hooke and Jeeves numerical algorithm (Hooke andJeeves, 1961).

2.6. SIMULATION OF THE TURBULENT DIFFUSION

The sensitivity of the scalar field predicted by a Lagrangian transport model to thevariation of the σw vertical profile was tested. The aim was to investigate the effectsinduced by the two proposed canopy parameterisations on scalar concentrationprofiles.

The concentration field was estimated using the dispersion matrix approach(Raupach, 1989), while a random walk model (Baldocchi, 1992) was applied forthe determination of the matrix coefficients (Dij ). The vertical profile of σw, re-quired by the random walk for the simulation of particle trajectories (Thomson,1987), was computed through the Massman and Weil model for the two scenarios(ea and mcn).

The concentration value (C) at each canopy level was calculated as,

Ci − Cref =∑

j

DijSj �zj , (10)

while four different patterns of the source profiles Sj were compared. The patternswere defined in order to simulate typical sensible, latent heat and carbon dioxidedaytime sink/sources (Figure 8) (Albertson et al., 2001). Finally, the concentra-tions calculated from the two canopy parameterisations were compared with theconcentration ranges obtained using the measured profile of σw, varied with twiceits standard error and its standard deviation. In total six concentration profiles werecalculated for each source pattern. Two of them are related to profiles of σw pre-dicted with the ea and the mcn parameterisations in the Massman model, while theothers, related to the measured mean and standard deviation of σw profile, wereused to define a confidence interval.

48 B. MARCOLLA ET AL.

3. Results and Discussion

3.1. VERTICAL PROFILE OF CANOPY ARCHITECTURE

The zenith angle distributions of the wind during sweep and ejection events isreported in Figure 2. The mean sweep angles are in the order of 8–9 degrees witha standard deviation of about 3 degrees at both 36 and 28.5 m levels. The ejectionangle is steeper (67 and 63 degrees at 36 and 28.5 m levels, respectively) and witha larger coefficient of variation. All the distributions have a negative skewness,being the sweep angle distribution at 28.5 m the most skewed. Sweep angle dis-tributions at both levels, and ejection distribution at the top level, are leptokurticwhile the ejection angle distribution at the 28.5-m level is weakly platykurtic, thisdistribution is also the less skewed.

Considering that the major contribution to momentum absorption arises fromthe sweep events (Raupach and Thom, 1981; Finnigan, 2000), the mean con-tact number along the mean sweep angle was considered as the most appropriaterepresentation of the canopy frontal area.

The profiles of effective leaf area and of mean contact number reported in Fig-ure 3 are rather different. In particular, the effective leaf area shows an absolutemaximum at about 20 m and a relative maximum at 4 m due to the understoreyvegetation. On the contrary, the mean contact number profile shows a clear peak atabout 25 m, while it is quite similar to the effective leaf area profile in the lowercanopy layers. Such differences are due both to the different features representedand to the different footprint areas of the two methodologies. Concerning the firstaspect, the indirect estimate of the effective leaf area depends on the canopy gapfraction over the entire hemisphere, while the mean contact number was estimatedon the lowest PCA band at 60–75 degrees. The profile of effective leaf area wasobtained by the combination of optical measurements and 3-D canopy modelling(Law et al., 2001), and should be considered the average profile over a circular areaof about 1 ha. On the contrary, the profile of mean contact number was estimatedfrom the inversion of light measurements along the tower in the angular band 60–75 degrees, and therefore involves decreasing sampling areas at increasing heights.At the base of the tower the footprint area of the mcn estimate is about 1 ha, as forthe ea estimate.

3.2. WIND SPEED DEPENDENCE OF THE DRAG COEFFICIENT

Figure 4 shows the drag coefficients estimated by inverting Equation (8) for the fourwind speed classes (Table I). The average coefficients are in the range 0.15–0.25,close to the value 0.2 adopted by Massman (1997). The drag coefficients calculatedfor the two approaches are very similar. This result supports the hypothesis thatboth the effective leaf area and the mean contact number can be consistently usedin the parameterisation of the canopy, as an alternative to the ratio of the leaf areato the sheltering factor.

ARCHITECTURE AND TURBULENCE IN CONIFERS 49

Figure 2. Frequency distributions and statistical moments of the wind zenith angles during sweepand ejection events for the two uppermost levels 36 and 28.5 m. Data refers to half-hourly daytimeintervals for a 10-day period. Sweep and ejection events have been defined on the basis of a standardquadrant analysis.

The mean drag coefficient drops by 36% from the first to the second wind speedclass and then slightly decreases in the third and fourth classes. The standard devi-ation is larger in the first class (the variation coefficient is greater than 1), smallerand more stable in the other classes. Decreasing drag coefficients at increasingwind speeds have been observed by Thom (1971) for long circular cylinders, and byLandsberg and Powell (1973) in a wind-tunnel experiment on apple trees, althoughthe decrease occurred in this latter case at higher values of wind speed.

Considering that this analysis has been performed on a coniferous canopy,which is characterised by rigid shoot and branch structures, the strong decrease ofthe drag coefficient at low wind speeds cannot be explained with the leaf alignment

50 B. MARCOLLA ET AL.

Figure 3. Vertical profiles of effective leaf area (ea) in a 1-ha plot surrounding the tower and of themean contact number (mcn) for the lower LiCOR PCA band (60–75 degrees) along the tower.

TABLE I

Ranking of half-hourly periods in four classes according to mean horizontal wind speed and stability.

Wind Class limits Half-hourly Turbulence Stable Neutral Unstable

speed periods intensity periods periods periods

class m s−1 σu/u ζ > 0.05 −0.05 < ζ < 0.05 ζ < −0.05

1 u ≤ 1.54 149 0.78 0.04 0.06 0.90

2 1.54 < u ≤ 2.19 115 0.52 0.05 0.07 0.88

3 2.19 < u ≤ 2.71 110 0.46 0.02 0.23 0.75

4 2.71 < u ≤ 6.19 116 0.41 0.01 0.35 0.64

ARCHITECTURE AND TURBULENCE IN CONIFERS 51

Figure 4. Mean and standard deviation of the drag coefficient for the different wind speed classes. Es-timates have been obtained from Equation (9) for the two different strategies in the parameterisationof canopy architecture.

along the streamlines. Alternatively, this behaviour could be related to the unsteadyconditions common at low wind speeds. In the case of a highly intermittent turbu-lence, the mean wind speed could underestimate the real velocity scale, leading toan overestimation of the canopy drag coefficient. This hypothesis is supported bythe turbulence intensity in the four wind speed classes reported in Table I, whichclosely matches the drag coefficient trend.

3.3. TURBULENCE STATISTICS

Mean values and standard deviations of the observed turbulence statistics havebeen compared with the predictions of the Massman and Weil model, using thetwo different canopy parameterisations (Figures 5 and 6).

Concerning the horizontal wind speed, measurements show a steep decrease atthe canopy top and a secondary maximum in the trunk space, similar to that ob-served by Baldocchi and Meyers (1988) and by Amiro (1990a) for a spruce canopywith an open trunk space. The Massman and Weil model cannot reproduce thispattern, being based on a monotonic, exponential decay of the wind speed. Bothcanopy parameterisations predict a steep decrease to occur at lower canopy heightscompared to the measured trend. In particular, predictions based on the effective

52 B. MARCOLLA ET AL.

Figure 5. Observed means and standard deviations of u at the different measuring height and profilespredicted by the Massman and Weil (1999) model. The mean absolute error (MAE) is reported forthe two different canopy parameterisations.

leaf area do not match the observed pattern both in the upper and lower parts ofthe canopy. On the contrary, estimates based on the mean contact number seem tobetter reproduce the observations with a slight underestimation in the trunk space.This is confirmed by the estimate of the mean absolute error, which decreases byabout 33% using mcn instead of ea for the canopy parameterisation.

In Figure 6, the profiles of the second-order statistics are reported. It shouldbe underlined that in the model the reference height statistics are assigned as topboundary conditions and refer to a constant stress surface layer (Garratt, 1994).In the interpretation of the differences between predicted and observed turbulencestatistics, one should consider that the model assumption of horizontal homogen-eity, neutrality and steady state wind conditions cannot be fully satisfied in a fieldexperiment. In Figure 6 profile predictions based on the ea scenario are too smoothto match observation. On the contrary, profiles based on the mcn parameterisationare in good agreement with the observed profiles of σu, σv, σw, except for theunderestimation of values at the reference height for σv and σw. The mean absoluteerrors of data predicted with the mcn approach are smaller than those obtainedwith the ea strategy for all the three velocity components. The reduction is of

ARCHITECTURE AND TURBULENCE IN CONIFERS 53

about 35% for σu and σv and of 30% for σw. The accuracy of the two approachesin determining the vertical profile of u′w′ is rather similar, suggesting that thisstatistic is less sensitive than the previous ones to the parameterisation of canopyarchitecture. In the analysis of these results, it should be considered that the averagedrag coefficient of the canopy was estimated by inverting the model against meas-urements of u and u′w′ and therefore, the model is forced to predict the observedcumulative decrease in the u′w′ profiles. The mcn approach overestimates the u′w′decrease in the higher canopy layers, and only in this case the ea parameterisationperforms better (MAE ea = 0.09, MAE mcn = 0.12).

The vertical profile of leaf drag area that minimises the squared errors betweenobserved and predicted values of σw is shown in Figure 7a, together with the twoempirical profiles based on the estimates of ea and mcn. The maximum of thepredicted profile is at a similar height to the one in the mcn scenario, while themaximum of the ea scenario occurs at a lower height. The shape of the optimalprofile, described by a beta function, is intermediate between the two empiricalones, being smoother than mcn and more peaked than ea.

The profiles of σw predicted using the three different profiles of drag area, andthe observed values reported in Figure 7b, show that the largest differences occurbetween 0.45h and 0.8h. The profile predicted in the mcn scenario is similar to theoptimised one, showing a slightly steeper gradient between the second and fourthmeasurement levels.

The comparative analysis indicates that the inferred drag area profile is some-how intermediate between the two empirical profiles, suggesting that both theconcepts of effective leaf area and mean contact number at low angles could playa significant role in the parameterisation and understanding of the wind-canopyinteractions. In order to clarify the real aerodynamic meaning of these two para-meters, further investigation on contrasting canopy architectures are needed bothin wind-tunnel and field experiments.

3.4. CONCENTRATION PROFILES

Canopy architecture strongly affects the efficiency of turbulent transport and there-fore canopy microclimatology. Because of this linkage, the parameterisation ofthe canopy drag area plays a crucial role in the application of soil-vegetation-atmosphere transport models (SVAT). The sensitivity analysis reported in Figure 8shows that profiles of scalar concentrations, related both to ea and mcn, are gener-ally close to the ones predicted with the observed turbulence statistics; ea profilesseem to perform better in the case of heat fluxes (Figure 8a,b) where the sourcesare concentrated in the upper part of the canopy. This is probably due to the strongpeak in drag area observed in the mcn scenario in the layers where the sourcesare concentrated. The trapping effect related to the strong gradient in σw could beresponsible for the overestimation of air temperature and water concentrations. InFigure 8c,d the prediction of the mcn scenario for CO2 concentration falls within

54 B. MARCOLLA ET AL.

Figure 6. Observed means and standard deviations of turbulence statistics σu, σv , σw and u′w′ atdifferent measuring heights and profiles predicted by the Massman and Weil (1999) model. Themean absolute error (MAE) is reported for the two different canopy parameterisations.

ARCHITECTURE AND TURBULENCE IN CONIFERS 55

Figure 7. Observed vertical profiles of effective leaf area, mean contact number and optimal dragarea (a); predicted profiles of σw for the three different canopy parameterisations and observed data(b).

the range σw ± twice its standard error. On the contrary the ea scenario under-estimates the CO2 concentration in the lower half of the canopy. The consistentbehaviour of the model for the mcn scenario could support the use of this method-ology in Lagrangian footprint models applied to eddy covariance measurements ofCO2 fluxes.

4. Conclusions

• In current literature, the description of canopy structure for the application ofturbulence closure models is based on vertical profiles of leaf area density,drag coefficient and sheltering factor. At present no experimental method isavailable to estimate the last two parameters separately. The effect of shel-tering, although conceptually well defined, is therefore generally embeddedin the drag coefficient (Wilson, 1988; Katul and Albertson, 1998). This ap-proach overestimates the variability of the drag coefficient among differentcanopies, because it includes the variability of the sheltering and thereforeof the leaf spatial distribution (Meyers and Paw U, 1986). In this work, analternative method is presented, in which the sheltering effect on momentum

56 B. MARCOLLA ET AL.

Figure 8. Profiles of scalar concentration predicted by a random walk Lagrangian model using theobserved profiles of σw ± twice its standard error, of σw ± its standard deviation, and the profilespredicted by the Massman and Weil (1999) model for the different canopy parameterisations. Thesimulation was performed using four profiles of source/sinks intended to represent: Daytime sensible(a) and latent (b) heat fluxes, daytime CO2 fluxes with different canopy assimilation versus soilrespiration (c, d).

ARCHITECTURE AND TURBULENCE IN CONIFERS 57

absorption is replaced with an architectural sheltering effect that is consideredto be analogous to the clumping effect on radiative transfer. Using this analogy,the sheltering is embedded in the estimates of the vertical profile of effectiveleaf area or mean contact number obtained from the inversion of gap fractionmeasurements.

• Using the proposed approaches to canopy parameterisation, the estimates ofthe drag coefficient are close to the average value reported in the literature(0.2; Massman, 1997), and decrease by 36% from the first to the second windspeed class.

• The mean contact number at the mean sweep angle seems to be a physicallygrounded representation of the canopy frontal area as ‘seen’ by the incomingwind, providing an improved estimate of turbulence statistics.

• When using the mean contact number in the prediction of turbulent statistics,the application of the transport model with typical CO2 source/sink profilesproduces accurate estimates of scalar concentration, supporting the applicationof this methodology to carbon related studies.

• Applying concepts borrowed from radiative transfer theory, a useful bridgehas been established between canopy aerodynamics and the radiative regime.Besides the novel theoretical relevance of this linkage, a major outcome is thepractical estimation of key canopy properties determining mass and energyexchanges by fast, non-destructive, yet reliable, optical methods.

Acknowledgements

We thank Robert Clement (University of Edinburgh) for supplying the EdiRE soft-ware, Umberto Giostra (University of Urbino) for providing part of the meteoro-logical instrumentation and for stimulating discussions, Marco Tubino (Universityof Trento) for fruitful suggestions, and Heidi Hauffe for the linguistic revision.The constructive comments of two anonymous reviewers greatly improved themanuscript. Special thanks are due to Roland Vogt and Mathias Bleyl (MCR-Lab,University of Basel) for instrumentation, software and assistance during the fieldexperiment. This study was supported by the CaRiTRo Foundation and by theProvince of Trento (DL 14616).

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