ATMOSPHERIC TURBULENCE WITHIN AND ABOVEA CONIFEROUS FORESTByXuhui LeeB. Sc. (Meteorology) Nanjing Institute of Meteorology, ChinaM. Sc. (Micrometeorology) Nanjing Institute of Meteorology, ChinaA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF SOIL SCIENCEWe accept this thesis as conformingto the required standard...LcTHE UNIVERSITY OF BRITISH COLUMBIAJanuary 1992© Xuhui Lee, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of b L t’1 ((:::The University of British ColumbiaVancouver, Canada/ I -Date 1-DE-6 (2/88)AbstractAn experiment to study the exchange processes within and above an extensive coniferousforest of Douglas-fir trees was conducted on Vancouver Island during a two-week rainlessperiod in July and August 1990. The stand, which was planted in 1962, thinned andpruned uniformly in 1988, had a (projected) leaf area index of 5.4 and a height of h = 16.7m. The experimental site was located on a 50 gentle slope. The primary instrumentationincluded two eddy correlation units which were operated in the daytime to measure thefluctuations in the three velocity components, air temperature and water vapour density.One unit was mounted permanently at a height of 23.0 m (z/h = 1.38) and the other atvarious heights of (z/h in brackets) 2.0 (0.12), 7.0 (0.42), 10.0 (0.60), and 16.7 m (1.00)with two to three 8-hour periods of measurement at each level. Profiles of wind speed andair temperature were measured continuously during the experimental period at heightsof 0.9, 2.0, 4.6, 7.0, 10.0, 12.7, 16.7 and 23.0 m using sensitive cup anemometers and finewire thermocouples, respectively. Radiation regimes and air humidity were measuredboth above and beneath the overstory of the stand.The vertical structure of the stand affected, to a great extent, the vertical distributionsof the velocity statistics (wind speed, variance, turbulence intensity, Reynolds stress,skewness and kurtosis), air temperature, sensible and latent heat fluxes. The effectwas also evident in the quadrant representation of the fluxes of momentum, sensibleheat and water vapour. Negative Reynolds stress persistently occurred at the lowerheights of the stand (z/h = 0.12 and 0.42). The negative values were related to the localwind speed gradients and it is believed that the longitudinal pressure gradient due toland-sea/upslope-downslope circulations was the main factor responsible for the upward11transport of the momentum at these heights. Energy budget was examined both aboveand beneath the overstory of the stand. The sum of sensible and latent heat fluxesabove the stand accounted for, on average, 83% of the available energy flux. Beneath theoverstory, the corresponding figure was 74%. On some days, energy budget closure was farbetter than on others. Counter-gradient flux of sensible heat constantly occurred at thecanopy base (z/h = 0.42), invalidating the conventional gradient-diffusion relationshipor K-theory at this height. Near the forest floor, however, K-theory with a far-field eddydiffusivity appeared to work satisfactorily. The daytime profiles of the dimensionlesspotential temperature, zO/O, where the characteristic temperature, O was defined asthe ratio of the kinematic sensible heat flux to the square root of the vertical velocityvariance both measured above the stand (z/h 1.38), were found to be well stratifiedby Hg/HT, the ratio of the sensible heat flux measured near the forest floor (z/h = 0.12)to that measured above the stand (z/h 1.38). The profile of /.9/O was simulatedby combining the random flight technique for the dispersion of sensible heat from theelevated canopy source and the gradient-diffusion model with a far-field diffusivity forthe dispersion from the ground-level source. The simulated profile agreed reasonably wellwith the measured one. The simulation results suggested that the profile of zO/O wasnot sensitive to the shape of the wind speed profile.iiiTable of ContentsAbstract iiList of SymbolsList of Tables )cviList of FiguresAcknowledgements X >O11 Introduction 12 Statistical Properties of the Velocity Field 52.1 Introduction 52.2 Experimental Methods 62.2.1 Site Description 62.2.2 Instrumentation and Data Collection 92.2.3 Inter-comparison of Instruments . . 102.3 Results and Discussion. 142.3.1 Monin-Obukhov Similarity above the Stand . . 142.3.2 Means and Variances of the Velocity Components 172.3.3 Higher Order Moments 232.3.4 Reynolds Stress 25iv2.3.5 Quadrant Representation of Reynolds Stress 312.4 Summary and Conclusions 372.5 References 383 Eddy Fluxes of Sensible Heat and Water Vapour 443.1 Introduction 443.2 Experimental Methods 453.2.1 Site Description 453.2.2 Instrumentation 453.2.3 Theoretical Considerations 473.3 Results and Discussion 513.3.1 Eddy Fluxes above the Stand 513.3.1.1 Energy Budget Closure 513.3.1.2 Canopy Resistance and the Omega Factor 563.3.2 Eddy Fluxes beneath the Overstory 613.3.2.1 Energy Budget Closure 613.3.2.2 Temporal and Horizontal Variations in the Energy Budget Components 643.3.3 Profiles of Eddy Fluxes 663.3.4 Quadrant Representation of Eddy Fluxes 703.4 Summary and Conclusions 753.5 References 774 Observation and Simulation of Air Temperature Profiles 834.1 Introduction 834.2 Experimental Methods 844.2.1 Site Description 84V4.2.2 Instrumentation.854.3 The Model 854.3.1 Construction of Trajectories 854.3.2 Simulation of Air Temperature and Vertical Sensible Heat Flux 874.4 Results and Discussion 924.4.1 Observation of Air Temperature Profiles 924.4.1.1 Diurnal Changes in the Air Temperature Profile 924.4.1.2 Normalization of Air Temperature Profiles 944.4.2 Simulation Results 964.4.2.1 Validation of the Numerical Scheme 964.4.2.2 Simulation of the Potential Temperature in the Stand 984.4.2.3 Test of the Effect of the Wind Speed Profile 1024.4.2.4 Flux-Gradient Relationships near the Forest Floor . 1044.5 Summary and Conclusions 1064.6 References 1065 Conclusions 110Appendices 113A Photographs of the Site and Instrumentation 113B Wake Production in the Reynolds Stress Budget 118C Comparison of Eddy Correlation Units over a Bare Field 121C.1 Comparison of Velocities 122C.2 Comparison of Momentum Flux 126C.3 Comparison of Scalar Fluxes 129viC.4 SummaryD An Analytical Expression for Legg and Raupach’s Model11.1 A Modified Langevin Equation for the Canopy EnvironmentD.2 Single Particle Transition ProbabilityProfiles of Concentration and Flux for a Plane SourceReferences131E. 1 IntroductionE.2 Experimental MethodsE.2.1 Site DescriptionE.2.2 InstrumentationE.2.3 Comparison of Anemometers.E.2.4 Data ProcessingE.2.4.1 Coordinate RotationE.2.4.2 Spectral AnalysisE.3 Results and DiscussionE.3.1 Wind RegimesE.3.1.1 Daily Pattern .E.3.1.2 Comparison of Wind146148149149149151153153153155155155the Stand 155159161161162164164D.3D.4135135138141144E Turbulence in an Old Growth Douglas-fir Stand on a SlopeSpeed inside and outsideE.3.1.3 Wind Speed Profiles near the Forest Floor .E.3.2 Turbulence StatisticsE.3.2.1 Variance and Momentum FluxE.3.2.2 Turbulence IntensityE.3.2.3 Higher Order MomentsE.3.3 Power SpectraviiE.3.4 Energy Budget near the Forest Floor 168E.4 Concluding Remarks 169E.5 Literature Cited 172F Maps of the Browns River Research Site 177viiiList of SymbolsA plant element area density (m2/3)AT amplitude of the diurnal course of air temperature (°C)Cd effective drag coefficient of plant elementsCe scalar concentration for an elementary point sourceC scalar concentration for a plane sourceD spacing among trees (Chapter 2, D = 4.2 m for the standat Browns River)D saturation deficit (Chapter 3, kPa)D arithmetic average of the daytime saturation deficit (kPa)Fe vertical scalar flux1 for an elementary point sourceFg scalar flux from the forest floorF,H flux fraction of sensible heat or water vapourin the quadrant-hole analysisF vertical scalar flux for a plane sourceG soil heat flux (W/m2)H hole size in tile quadrant-hole analysisH sensible heat flux (W/m2)H’ hole size above which haff of the eddy flux occurs (Chapters 2 and 3)‘The term ‘flux’ in this dissertation is an abbreviation for ‘flux density’ as commonlyused in micrometeorology literature.ixH’ sensible heat flux simulated for finite fetches (Chapter 4, W/m2)Hg sensible heat flux from the forest floor (W/m2)HT total sensible heat flux from the stand (W/m2)conditioning function in the quadrant-hole analysisK diffusivity in Batchelor’s diffusion equation (m2/s)Kr kurtosis of the u velocity componentKr kurtosis of the v velocity componentKr kurtosis of the w velocity componentK1 far field eddy diffusivity (m2/s)L Monin-Obukhov length, defined as— kgH7/) (m)M number of fluid particles released in the ensemble experimentMcross(z) net number of fluid particles that cross height zin the ensemble experimentF transition probability density of the vertical positionof a marked fluid particleshear production term in Reynolds stress budgetP wake production term in Reynolds stress budgetR net radiation flux (W/m2)S rate of heat storage in the layer between the 0 and 23.0 mheights per unit ground area (Chapter 3, W/m2)S global solar irradiance (horizontal surface) (Appendix E, W/m2)S(z) source density or flux divergence of sensible heator water vapour (Chapter 3)S(z) source density of sensible heat (Chapter 4, W/m3)xdaytime average global solar irradiance (horizontal surface, W/m2)Sk skewness of the u velocity componentSk skewness of the v velocity componentSk skewness of the w velocity componentS:,H fraction of Reynolds stress in the quadrant-hole analysisS1 rate of latent heat storage in the air between the 0 and 23.0 mheights per unit ground area (W/m2)Sb rate of heat storage in needles and branches per unit ground area (W/m2)S3 rate of sensible heat storage in the air between the 0 and 23.0 mheights per unit ground area (W/m2)St Strouhal number (= 0.21)S rate of heat storage in tree trunks per unit ground area (W/m2)T average time interval (= 30 mm)Ta air temperature (°C)daytime average air temperature (°C)variance of air temperature (°C2)Ti. Lagrarigian integral time scale (s)Tb temperature of needles and branches (°C)T turbulent transport term in Reynolds stress budgetT characteristic air temperature, defined as J/u (°C)U 30-minute averaged wind speed measuredwith cup anemometers (Chapter 2, m/s)U 30-minute averaged wind speed measuredwith hot wire anemometers (Appendix E, m/s)xiU daytime average wind speed measured with cup anemometers (m/s)Ur wind speed measured with a hot wire anemometers at height Zr (m/s)V 30-minute averaged equivalent cup wind speed forsonic anemometers, defined as ‘i/u? + v? (m/s)<Xm > total streamwise distance traversed by marked fluid particle min the ensemble experiment (m)Z vertical position of a marked fluid particlein the ensemble experiment (m)a7 constant in the Monin-Obukhov scaling of o’ (= 0.9)a constant in the Monin-Obukhov scaling of o (= 1.9)constant in the Monin-Obukhov scaling of ( 1.1)cnb specific heat of needles and branches (J/(°C kg))c specific heat of air at constant pressure (J/(°C kg))d displacement height (Chapter 2, d = 0.7h)d effective source height (Chapter 3, m)d diameter of the tree trunk (Appendix E)f vertical gradient of the variance of the Eulerian vertical velocity (m/s2)fF component of the form drag vector exerted on a unit mass of airfV component of the viscous drag vector exerted on a unit mass of airh height of the stand at Browns River (= 16.7 m)i turbulence intensityi turbulence intensity for the u velocity componenti turbulence intensity for the v velocity componentxiii turbulence intensity for the w velocity componentk von Karman constant (= 0.4)m mass of needles and branches per unit volume of air (kg/m3)n natural frequency (Hz)p atmospheric pressure (kPa)ra aerodynamic resistance to water vapour and sensible heat diffusion (s/rn)r bulk canopy resistance (s/rn)daytime mean canopy resistance (s/rn)rh daytime average relative humidityrm aerodynamic resistance to momentum transfer (s/rn)slope of the saturation vapour pressure at air temperature (kPa/°C)t time (s)tf a migration time, defined as xf/u (s)tj,H time fraction in the quadrant-hole analysisu longitudinal velocity component (m/s)u streamwise velocity component (Appendix E, m/s)u1 one of the two horizontal components of the instantaneous velocityvector in the instrument coordinate system (m/s)variance of the u velocity component (m2/s)u component of the velocity vector in tensor notation (m/s)u, a set of uniform random numbers in the range 0—i (Chapter 4)ttref wind speed at the reference location (m/s)u,, friction velocity, defined as (m/s)XIIIkinematic Reynolds stress (m2/s)v lateral velocity component (m/s)v1 one of the two horizontal components of the instantaneous velocityvector in the instrument coordinate system (m/s)variance of the v velocity component (m2/s)w vertical velocity component (m/s)w velocity component perpendicular tothe slope surface (Appendix E, m/s)Lagrangian vertical velocity of a marked fluid particleat release (m/s)variance of the w velocity component (m2/s)variance of the Eulerian vertical velocity(Chapter 4 and Appendix D, m2/s)Lagrangian vertical velocity of a marked fluid particleat step ri (m/s)w(z0,t) Lagrangian vertical velocity of a marked fluid particle (m/s)covariance between the vertical velocity component and air temperatureor kinematic sensible heat flux (°C m/s)wT covariance between the vertical velocity componentof unit 1 and air temperature of unit 2 (°C m/s)covariance between the vertical velocity component and watervapour density or water vapour flux (g/(m2s))wp,1 covariance between the vertical velocity componentof unit 2 and water vapour density of unit 1 (g/(m2s))xiv(w’T’)2 kinematic sensible heat flux measured with unit 2 (°C m/s)(w’pji water vapour flux measured with unit 1 (g/(m2s))x longitudinal component of position vector (m)horizontal position of a marked fluid particle at release (m)Xf horizontal position of the leading edge of a plane source (m)position vector in tensor notation (m)horizontal position of a marked fluid particle at step n (m)fetch (in)y lateral component of position vector (in)z height or vertical component of position vector (m)z1 vertical position of a marked fluid particle at release (m)vertical position of a marked fluid particle at step n (m)z0 height of the source for a marked fluid particle (Appendix D, m)effective roughness length of the ground surface (Appendix E, m)Zr reference height (= 23.0 m for the stand at Browns River)Zr reference height (= 2.0 m for the stand near Woss)z. height of roughness sublayer (m)coefficient in the Langevin equation (Appendix D)/3 Bowen ratiotime step at step n (s)/Ta change over a 30-minute interval in air temperature averagedover the layer between the 0 and 23.0 m heights (°C)xv/-Tnb change over a 30-minute interval in the average temperatureof needles and branches (°C)change over a 30-minute interval in water vapour density averagedover the layer between the 0 and 23.0 m heights (g/m3)zO potential temperature difference, defined as 0— O(Zr) (°C)7 psychrometric constant (kPa/°C)A latent heat of vaporization of water (J/kg)A coefficient in the Langevin equation (Appendix D)AE latent heat flux (W/m2)v kinematic viscosity (m2/s)McNaughton and Jarvis’s Omega factorw diurnal angular frequency (= ir/12 rad/h)term of the interaction between velocity and pressure fieldsin Reynolds stress budgetphase angle of the diurnal course of air temperature (rad)q power spectrum of quantity op air density (g/m3)Pv water vapour density (g/m3)Pv* characteristic water vapour density, defined as 7j/u (g/m3)square root of the variance of air temperature (°C)square root of the variance of the u velocity component (m/s)square root of the variance of the w velocity component (m/s)variance of Lagrangian vertical velocity (Chapter 4 and Appendix D, m2/s)mean depth of plume or square root of the variance ofthe vertical position of a marked fluid particle (m)xvi0•Pv square root of the variance of water vapour density (g/m3)r time scale for parameterizing 1’ (s)O potential air temperature (°C)O contribution of the canopy source to potential air temperature (°C)Og contribution of the ground-level source topotential air temperature (°C)0 characteristic potential temperature, defined as HT (°c)pCpJw(Zr)Gaussian white noisea set of Gaussian random numbers with zero mean and unit variancedeparture from temporal or ensemble averagedeparture from spatial averagetemporal or ensemble averaging operator<> spatial averaging operatorxviiList of Tables2.1 Average values of weather variables at z/h = 1.38 for the period 06:00—18:00 PST, the period of operation of the eddy correlation units, and therelative height of the lower eddy correlation unit (z/h) for the Douglas-firstand at Browns River. 3, U, J’ and h represent global solar irradiance(horizontal surface), wind speed measured with a cup anemometer, airtemperature and relative humidity (average water vapour pressure dividedby saturated water vapour pressure at Ta), respectively. The height of thestand (h) was 16.7 m 82.2 Values of Reynolds stress —u’w’, standard deviations of the longitudinaland vertical velocity components (o. and and the mean longitudinalvelocity component (ii) at the indicated levels for the five runs selectedfor quadrant-hole analysis of Reynolds stress for the Douglas-fir stand atBrowns River. The stability parameter (z—d)/L was calculated from themeasurements at z/h = 1.38 334i,0 + ‘-3,02.3 Intermittence parameters (H and tj,jp), exuberance (, ) and‘-‘2,0 + ‘-‘4,0the ratio of the contribution to Reynolds stress by sweeps to that by ejections for the Douglas-fir stand at Browns River 353.1 Average values of the energy budget components, R, G, S, H and .AE(W/m2)during the indicated periods for the Douglas-fir stand at BrownsRiver. Also shown are the values of the ratio, (H + )E)/(R — S — G),and the daytime Bowen ratio, /3 54xviii3.2 Daytime average values of the energy budget components, R, G, H andAE (W/m2) beneath the overstory of the Douglas-fir stand at BrownsRiver in July 1990. Also listed are the ratio, (H + )E)/(R — G), thedaytime Bowen ratio, 3, and the relative height (z/h) of the measurementof H and \E 633.3 Values of the covariances of the vertical velocity component and air temperature (T) and the vertical velocity component and water vapourdensity standard deviations of air temperature (UT), water vapourdensity (a) and the vertical velocity component (o) at the indicatedheights for the five runs selected for quadrant-hole analysis of eddy fluxesof sensible heat and water vapour for the Douglas-fir stand at BrownsRiver. The stability parameter (z— d)/L was calculated from the measurernents at z/h = 1.38 713.4 Summary of the results of quadrant-hole analysis for sensible heat flux ofthe five runs in Table 3.3 733.5 Summary of the results of quadrant-hole analysis for water vapour flux ofthe five runs in Table 3.3 74E.1 Comparison of the wind speed (m/s) at a height of 2 m measured bya hot wire anemometer (U) with the ‘cup’ speed measured by a sonicanemometer (V) on 9 August 1989 in the old growth Douglas-fir standnear Woss 154E.2 Turbulence statistics at a height of 2 m on 9 August 1989 in the old growthDouglas-fir stand near Woss, where U is the mean streamwise componentof the velocity inside the stand and Uref is the wind speed at the referencelocation outside the stand. The time of the runs is given in Table E.1. . 165xixE.3 Components (W/m2) of the energy budget of the forest floor of the oldgrowth Douglas-fir stand near Woss in August 1989. R is net radiationflux, G is the heat flux into the soil, H and AE are the eddy fluxes ofsensible and latent heat, respectively. Also listed are the measure of energy budget closure (R,1—G—H—\E) and the average value of the global(horizontal surface) solar irradiance (S, W/m2) outside the stand 170xxList of Figures2.1 Profile of leaf area density of the Douglas-fir stand at Browns River. Thetotal (projected) leaf area index was 5.4 72.2 Covariances of w and T (a), w and Pv (b), and w and u (c) measured atz/h = 1.00 versus those measured at z/h = 1.38 for the Douglas-fir standat Browns River on 31 July and 1 August 1990 112.3 Comparison of equivalent ‘cup speed’ V measured by sonic anemometerswith wind speed U measured by cup anemometers in the Douglas-fir standat Browns River during the entire experimental period in 1990: (a) lowerunit at z/h = 0.12 (D), 0.42 (.), 0.60 () and 1.00 (A) and (b) upperunit at z/h = 1.38 132.4 Enhancement factor (measured eddy diffusivity divided by that predictedwith the flux-gradient relationships of Dyer (1974)) calculated from theprofile measurements at z/h = 1.00 and 1.38 and flux measurements atz/h = 1.38 for the Douglas-fir stand at Browns River: (•), sensible heat;(+), momentum. The stability parameter (z — d)/L was calculated fromthe flux measurements at z/h = 1.38 162.5 Dimensionless standard deviations of the vertical velocity component (/u),air temperature (UT/T*) and water vapour density (op,/pv*) as functionsof the stability parameter (z — d)/L at z/h = 1.38 for the Douglas-firstand at Browns River. Squares: measured; lines: calculated from Equations (2.1—2.3) 18xxi2.6 Profiles of normalized daytime wind speed in the Douglas-fir stand atBrowns River: (.), wind speed measured using cup anemometers (U) andaveraged over nine days, where the numbers are correlation coefficients(R) between the wind speed at the illdicated heights and that at z/h =1.38; (o), longitudinal velocity component (u) measured using one sonicanemometer located for 2—3 days at various heights and normalized againstthat measured by the other sonic anemometer located permanently at z/h= 1.38 192.7 Profiles of daytime average velocity variance in the Douglas-fir stand atBrowns River: (o), longitudinal component (v,12); (.), lateral component(J); (v), vertical component (). The average values of the standarderror of the mean (SEM) for u’2 and v’2 were 0.08 m2/s on the top andabove the stand and 0.01 m2/s within the stand, and the correspondingvalues for w’2 were 0.02 and 0.01 m2/s 212.8 Profiles of daytime average turbulence intensity in the Douglas-fir standat Browns River: (o), longitudinal component (ia); (.), lateral component(in); (v) vertical component (i). The average values of SEM were 0.04for i and i and 0.02 for i, 222.9 Profiles of daytime average velocity skewness in the Douglas-fir stand atBrowns River: (o), longitudinal component (Sky); (.), lateral component(Sky); (v) vertical component (Sk). The average values of SEM were0.06 for Sk and Sky and 0.04 for Sk 242.10 Profiles of daytime average velocity kurtosis in the Douglas-fir stand atBrowns River: (o), longitudinal component (Kr); (.), lateral component(Kry); (v), vertical component (Kr). The average values of SEM were0.13 for Kr and Kr and 0.10 for Kr 26xxii2.11 Profile of daytime average kinematic Reynolds stress in the Douglas-firstand at Browns River. The average value of SEM were 0.014 m2/s onthe top and above the stand and 0.002 m2/s within the stand 272.12 Stress fraction (S,H) plotted against hole size (H) for the Douglas-fir standat Browns River for five values of z/h: 1.38 (x), 1.00 (A), 0.60 (o), 0.42(+), and 0i2 (D) 343.1 Comparison of the sum of the eddy flux densities (H + )E) measured atz/h = 1.38 and the available energy flux density (R — S— G) for theDouglas-fir stand at Browns River during the entire experimental periodin 1990. The dash line represents the linear regression forced through zerowith a slope of 0.83 523.2 Energy budget closure as shown by the comparison of values of R (0)and H + \E + S + G () for the Douglas-fir stand at Browns River on (a)a partly cloudy day (1 August) and (b) a clear day (28 July 1990). Alsoshown are the variations of H (a), \E (.), G (A) and S (x) 553.3 Comparison of eddy fluxes measured at z/h = 1.38 as indicated by H (.)and \E (A) and at z/h 1.00 as indicated by H (o) and )E (A) for theDouglas-fir stand at Browns River on 31 July, 1990. Also shown are(0) above the stand and H + \E + G + S (.) for z/h = 1.38 573.4 Daytime variation of (a) canopy resistance r, and (b) saturation deficitD for the Douglas-fir stand at Browns River on 19 July (0) and 20 July,1990 (u) 593.5 Courses of daytime mean canopy resistance (o) and mean saturationpressure deficit D (.) for the Douglas-fir stand at Browns River in 1990. 60xxiii3.6 Daytime variation of Omega factor (cl) for the Douglas-fir stand at BrownsRiver on 19 July (C) and 20 July, 1990 (.) 623.7 Variation of the energy budget components, R (C), H (o), AE (.) andG (A) beneath the overstory of the Douglas-fir stand at Browns River on(a) a partly cloudy day (26 July) and (b) a clear day (20 July, 1990). Alsoshown is the variation of the net radiation flux density above the stand (u) 653.8 Comparison of the kinematic sensible heat flux at 2 m (z/h = 0.12)above the forest floor of the Douglas-fir stand at Browns River measuredat four positions in July 1990 with three 1-dimensional sonic anemometer/thermocouple units (#1138, #1139, #1143) and one 3-dimensionalsonic anemometer/thermometer unit (3-d): (0), #1138; (v) #1143; (+),3-d 673.9 Normalized profiles of daytime averaged sensible heat flux (o) and watervapour flux (.) in the Douglas-fir stand at Browns River in 1990. Theaverage values of the standard error of the mean was 0.085 at z/h = 0.60and 0.025 at all other heights 683.10 Flux fraction F,H plotted against hole size H for sensible heat flux at z/h= 1.38 (x), 1.00 (A), 0.60 (o), 0.42 (+), and 0.12 (0) 764.1 Profiles of S(z), u(z), a(z) and TL(z) used as model inputs. See Equations (4.9—4.12) for analytical forms 914.2 Diurnal change in the profile of the 30-minute averaged potential temperature observed in the Douglas-fir stand at Browns River on 26 July 1990.The time shown above the profiles marks the end of each 30-minute run 93xxiv4.3 Dimensionless daytime potential temperature, z.O/O versus relative sourcedensity, Hg/HT in the Douglas-fir stand at Browns River measured on 19,20 and 26 July 1990: (a), z/h 0.60; (b), z/h = 0.28; (c), z/h = 0.05.. 954.4 Profiles of the dimensionless daytime potential temperature, iO/O averaged over the four ranges of relative source density, Hg/HT in the Douglas-fir stand at Browns River. The measurements were made on 19, 20 and26 July 1990 974.5 Comparison of air temperature, 0 and vertical kinematic heat flux, H’/pcsimulated using the random flight technique (lines) with those obtainedfrom the analytical solutions of Taylor (1921) (squares) at the downwindedge of a 100 m long plane source placed at height z0 in homogeneousturbulence 994.6 Comparison of the profile of the potential temperature simulated for H/HT =0.2 with the observed profile averaged over the the runs with Hg/HT 11the range 0.15—0.25 in the Douglas-fir stand at Browns River 1004.7 Comparison of normalized vertical heat flux simulated using the randomflight technique with a fetch x = 960 m (H’/HT, dash line) with thatcalculated from Equations (4.5) and (4.9) for advection-free conditions(H/HT, solid line) 1014.8 The effect of the wind speed profile on the simulation of potential temperature resulting from the canopy sensible heat source for three fetches (xv):(—) wind speed within the stand defined by Equation (4.10); (- - - -) windspeed within the stand defined by Equation (4.13). Other parameters arethe same as in Figure 4.6 103xxv4.9 Comparison of modelled (C) kinematic sensible heat flux, H9/(pc,) withthat measured (.) at z/h = 0.12 in the Douglas-fir stand at Browns Riveron (a) 19, (b) 20, and (c) 26 July 1990 105A.1 Eddy correlation unit operated permanently at the height of 23.0 m (z/h= 1.38) in the Douglas-fir stand at Browns River. It consisted of one 3-dimensional sonic anemometer, one krypton hygrometer and one fine wirethermocouple and was pointed in the NNE direction. The daytime winddirection was NE to NNE 114A.2 Eddy correlation unit operated at various heights in the Douglas-fir standat Browns River. It consisted of one 3-dimensional sonic anemometer/thermometer and one krypton hygrometer. The photograph was taken whenit was mounted at a height of 10.0 m (z/h = 0.60) 115A.3 Main instrument tower used in the Browns River experiment 116A.4 Forest floor and trunk space of the Douglas-fir stand at Browns River. . 117C.1 Streamwise velocity (C) and equivalent cup wind speed (.) measured withunit 2 versus those measured with unit 1 over the bare field in Delta on 3and 5 October 1991 123C.2 Vertical velocity variance, w’2 measured with unit 2 versus that measuredwith unit 1 over the bare field in Delta on 3 October 1991 124C.3 Equivalent cup wind speed measured with the 3-dimensional sonic anemometers versus wind speed measured with the cup anemometer over the barefield in Delta on 3 and 5 October 1991: unit 1 (C); unit 2 () 125C.4 Kinematic momentum flux, measured with unit 2 versus that measured with unit 1 over the bare field in Delta on 3 October 1991 127xxviC.5 Kinematic momentum flux, as a function of the square of the averagestreamwise velocity component, 112 for unit 1 (D) and unit 2 (.) over thebare field in Delta on 3 and 5 October 1991 128C.6 Kinematic sensible heat flux, measured with unit 2 versus that measured with unit 1 over the bare field on 3 October 1991 130C.7 Air temperature variance, measured with unit 2 (sonic signal) versusthat measured with unit 1 (thermocouple signal) over the bare field inDelta on 5 October 1991 132C.8 The sum of the turbulent heat fluxes, H + )E versus the available energyflux, R — G over the bare field in Delta on 3 (0) and 5 (•) October 1991 133D.1 Comparison of concentration profiles resulting from the release of 1 gramof mass at height z0 and time zero: (—) calculated using the analyticalsolution (D.21) and (0) simulated using the random flight technique. . . 142E.1 Comparison of the 30-minute average wind speed measured with a hotwire anemometer with that measured with a cup anemometer at a heightof 2 m in the old growth Douglas-fir stand near Woss during the entireexperimental period of 1989 152E.2 Daily pattern of 5-minute average wind speed and direction observed on aclear day (9 August 1989) at a height of 4.2 m on the logging road outsidethe old growth Douglas-fir stand near Woss 156E.3 Same as in Figure E.2 except at a height of 2 m inside the stand. Thewind vane was stalled during the period between 0:00 and 7:00 PST. . 157xxviiE.4 Comparison of 30-minute average wind speed at a height of 2 rn insidethe old growth Douglas-fir stand near Woss with that at a height of 4.2rn outside the stand during the period from July 29 to August 19, 1989.Also shown is the equation for the best fit line 158E.5 Profiles of 30-minute average wind speed during the period from 09:30PST 9 August to 06:00 PST 10 August 1989 near the forest floor of theold growth Douglas-fir stand near Woss. The time shown above eachprofile marks the end of the 30-minute run. The dashed line represents alogarithmic profile calculated from Equation(E.1) with a value of 0.005 mfor z0 and a value of 1 rn/s for Ur 160E.6 Turbulence intensity (i) as a function of mean streamwise velocity (iz) ata height of 2 m inside the old growth Douglas-fir stand near Woss 163E.7 Power spectra of the streamwise (u) and vertical (w) velocity componentsfor the period 13:15—14:15 PST on 9 August 1989 at a height of 2 m in theold-growth Douglas-fir stand near Woss. Also shown is the slope predictedfor the inertial subrange 166E.8 Daytime courses of the energy budget components of the forest floor of theold growth Douglas-fir stand near Woss on 17 August 1989: (0) R,— G,(o) H, and (.) AE. The sky was overcast 171F.1 Topographic map of the area around the Browns River Research Site.Contour elevations are in 1000’s feet above mean sea level. The forestsurrounding the site is second growth Douglas-fir of similar age whichextends at least 5 km in all directions 178xxviiiF.2 Positions of the instruments used in the Browns River experiment: maininstrument tower (0), tower for measuring diffuse solar irradiarice abovethe stand (A), tram for radiation measurements (—), model deer (.),and one-dimensional sonic anemome ter/thermometer units (.). Contourelevations are in metres above mean sea level 179xxixTo my wife, YuhongxxxAcknowledgementsI wish to acknowledge the University Graduate Fellowships of B.C. and research andteaching assistantships in the Soil Science Department of University of B.C. The fundingfor the research work was provided through grants from the Natural Science and Engineering Research Council of Canada, Canadian Forest Products Inc. and MacMillanBloedel Limited.During my Ph.D. program I have been helped by many people. In particular, Iwish to extend my sincere thanks to Dr. T.A. Black, my supervisor, for his steering roleand participation in the field experiments, his constructive comments on drafting thedissertation and his great friendship, and to his family for their kindness in many ways. Ialso wish to thank Dr. M.D. Novak for his encouragement and his interest in my researchover the years. Thanks also go to Drs. T.M. Ballard and I.S. Gartshore for being in mysupervisory committee and for their assistance; Bob Sagar, Jing-Ming Chen and RickKetler for their friendship and help with the experiments; Ralph Adams for designingthe hot wire anemometer system for the old growth experiment; Al Mcleod and JohnHarwijne for their help in selecting the research sites; and last, but not least, David Lohand John Janmaat for their help in the field experiments.xxxiChapter 1IntroductionThe understanding of forest canopy-atmosphere exchange is of great importance to avariety of scientific issues, such as global and regional CO2 and water balances, and thetransport, dispersion and deposition of air borne pollutants. The conventional gradient-diffusion relationship, or K-theory, has been used for many years to study the exchangeprocesses near the surface of the earth. However, experimental studies in the past twodecades have shown that turbulent exchange in the upper part of and immediately aboveforests and plant canopies of other types is dominated by large intermittent eddies. Because the sizes of these eddies are comparable to canopy height, which is the scale ofscalar concentration and velocity gradients, the validity of K-theory is questionable. Inrecent years, much attention has been directed to alternative approaches, such as randomflight simulations in a Lagrangian framework (e.g. Leclerc ct al. 1988, Legg et al. 1986,Legg and Raupach 1982) and higher order closure models (Meyers and Paw U 1986,Wilson 1988, Wilson and Shaw 1977). These theories are, however, still at an early stageof development. More experimental studies are required to provide data for testing andfurther development of the theories.Recently experiments have been conducted on atmospheric turbulence in forest standsof various tree species, e.g. in mixed deciduous forests of oak and hickory trees (Baldocchiand Meyers 1988) and of mainly aspen and red maple trees (Shaw et al. 1988), in a forestof pine trees (Deiimead and Bradley 1985), and in forests of aspen, pine and spruce trees(Amiro 1990a and 1990b). In this work, a coastal coniferous forest of Douglas-fir trees1Chapter 1. Introduction 2on Vancouver Island was selected as the site for a turbulent exchange experiment.Douglas-fir is an important tree species in the northwest coastal region of NorthAmerica. In western Oregon, Washington and British Columbia, Douglas-fir occupiesabout 15.8 million hectares (Oliver et al. 1986). The evapotranspiration process fromDouglas-fir stands has been studied extensively using the energy balance approach withthe guidance of Monteith’s big leaf model (Monteith 1965) or its improved versions (e.g.Kelliher et al. 1986, Tan and Black 1976, McNaughton and Black 1973, Fritschen et al.1985). Yet relatively little is known about the turbulent characteristics of the air flowand the exchange processes within and above forests of this type. The overall goal ofthe study reported here is to examine in detail the turbulence regimes and the exchangeprocesses within and immediately above this selected stand. The study was part ofa collaborative research project which aimed to develop silvicultural prescriptions thatwould satisfy timber production objectives while creating black-tailed deer winter rangeon the Island. It is also intended to contribute to an improved understanding of theexchange processes in forest environments in general.This dissertation consists of three papers. The first paper (Chapter 2) is limited to thestatistical properties of the velocity field within and above the stand. The second paper(Chapter 3) concentrates on the eddy fluxes of sensible heat and water vapour within andabove the stand. The third paper (Chapter 4) analyses the profiles of air temperatureusing Lagrangian theories for scalar dispersion. The conclusions of the dissertation arepresented in Chapter 5. Supplementary results and discussions can be found in theAppendices.ReferencesAmiro, B.D.: 1990a, ‘Comparison of turbulence statistics within three Boreal forestChapter 1. Introduction 3canopies’, Boundary-Layer Meteorol. 51, 99-121.Amiro, B.D.: 1990b, ‘Drag coefficients and turbulence spectra within three Boreal forestcanopies’, Boundary-Layer Met eorol. 52, 227-246.Baldocchi, D.D. and Meyers, T.P.: 1988, ‘Turbulence structure in a deciduous forest’,Boundary-Layer Met eorol. 43, 345-364.Denmead, O.T. and Bradley, E.F.: 1985, ‘Flux-gradient relationships in a forest canopy’,in Hutchison, B.A. and Hicks, B.B. (eds.), The Forest-Atmospheric Interaction, D.Reidel Publishing Co., Dordrecht, 421-442.Fritschen, L.J., Gay L. and Sympson J.: 1985, ‘Eddy diffusivity and instrument resolution in relation to plant height’, in Hutchison, B.A. and Hicks, B.B. (eds.), TheForest-Atmospheric Interaction, D. Reidel Publishing Co., Dordrecht, 583-590.Kelliher, F.M., Black, T.A. and Price, D.T.: 1986, ‘Estimating the effects of under-story removal from a Douglas-fir forest using a two-layer canopy evapotranspirationmodel’, Water Resource Research, 22, 1891-1899.Leclerc, M.Y., Thurtell, G.W. and Kidd, G.E.: 1988, ‘Measurements and Langevinsimulations of mean tracer concentration fields downwind from a circular line sourceinside an alfalfa canopy’, Boundary-Layer Meteorol. 43, 287-308.Legg, B.J. and Raupach, M.R.: 1982, ‘Markov-chain simulation of particle dispersionin inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerianvelocity variance’, Boundary-Layer Metcorol. 24, 3-13.Legg, B.J., Raupach, M.R. and Coppin, P.A.: 1986, ‘Experiments on scalar dispersionwithin a plant canopy. Part III: An elevated line source’, Boundary-Layer Meteorol.35, 277-302.Chapter 1. Introduction 4McNaughton, K.G. and Black, T.A.: 1973, ‘A study of evapotranspiration from aDouglas-fir forest using the energy balance approach’, Water Res. Res. 9, 1579-1590.Meyers, T. and Paw U, K.T.: 1986, ‘Testing of a higher-order closure model for modelingairflow within and above plant canopies’, Boundary-Layer Met eorol. 37, 297-311.Oliver, C.D., Hanley, D.D. and Johnson, J.A.: 1986, Douglas-fir: Stand Managementfor the Future, College of Forest Resources of University of Washington, Seattle,Washington.Price, D.T. and Black, T.A.: 1990, ‘Effects of short-term variation in weather on diurnalcanopy CO2 flux and evapotranspiration of juvenile Douglas-fir stand’, Agric. For.Meteorol. 50, 139-158.Shaw, R.H., Den Hartog, G. and Neumann, H.H.: 1988, ‘Influence of foliar densityand thermal stability on profiles of Reynolds stress and turbulence intensity in adeciduous forest’, Boundary-Layer Meteorol. 45, 391-409.Tan, C.S. and Black, T.A.: 1976, ‘Factors affecting the canopy resistance of a Douglas-firforest’, Boundary-Layer Meteorol. 10, 475-488.Wilson, J.D.: 1988, ‘A second-order closure model for flow through vegetation’, BoundaryLayer Meteorol. 42, 371-392.Wilson, R.N. and Shaw, R.H.: 1977, ‘A higher order closure model for canopy flow’, J.Appi. Met eorol. 14, 1197-1205.Chapter 2Statistical Properties of the Velocity Field2.1 IntroductionThe description of turbulence statistics is a prerequisite to understanding turbulent transport of water vapour, carbon dioxide, trace gases, heat and particles within and beneathforest canopies and in the surface layer above the forest stands. Velocity statistics arerequired either as inputs to canopy flow models (e.g. Shaw and Wilson 1977) and Lagrangian dispersion models (e.g. Chapter 4) or for testing these models. The asymmetricand intermittent nature of the flow within the stand affects the release and deposition ofspores (Aylor 1991), while high turbulence intensity of the flow may play an importantrole in enhancing heat loss from wild animals (Sagar et al. 1991). Thermal stability wasreported to influence some of the statistics within forests (Shaw et al. 1988, Leclerc etal. 1991), and its influence on the flux-gradient relationships immediately above forestshas been frequently observed to be different from that for smooth surfaces (e.g. Raupach1979).This Chapter is limited to the statistical properties of the velocity field within andabove the selected Douglas-fir stand. The objectives of this Chapter are: (1) to document the stability regimes using the Monin-Obukhov length scale and to examine theapplicability of Monin-Obukhov scaling above the stand; (2) to describe the statistics ofthe velocity field, including mean wind speed, Reynolds stress, variance, turbulence intensity, skewness, and kurtosis, with discussion of the mechanism of momentum transferin the lower part of the stand; and (3) to quantify the intermittency and identify the5Chapter 2. Statistical Properties of the Velocity Field 6kinds of turbulent motion which dominate momentum transfer using the quadrant-holeconditional sampling technique.2.2 Experimental Methods2.2.1 Site DescriptionThe experiment was performed in late July and early August, 1990 in a coniferous standnear Browns River located approximately 10 km west of Courtenay on Vancouver Island,125°10’W, 49°42’N, at an elevation of 450 m (Appendix F). The overstory species isDouglas-fir (Pseudotsuga menziesii Franco), planted in 1962. In 1988, it was thinned to575 stems/ha and pruned to a height of approximately 6 m uniformly over a 600 m x600 m plot. The forest floor was littered with dead branches and tree trunks, with alittle understory vegetation (salal, Oregon grape and huckleberry) less than 0.5 m tall.The average trunk diameter at a height of 1.3 m was 0.20 m. A visual inspection fromthe instrument tower provided an estimate of 16.7 m for the height of the stand (h).Surrounding the plot are unthinned and unpruned stands of Douglas-fir trees of similarage and height which extend several kilometres.The profile of the leaf area density of the stand was obtained from intensive destructive sampling on four trees of selected sizes. A branch was sampled every two whorls.The base diameter of all branch on the four trees and the diameter at a height of 1.3m of 250 trees were measured. The area of needle samples pressed between two glassplates was measured with a video-camera image analysis system (Skye Instruments Ltd.,Liandrindod Wells, UK). Leaf area density of the stand was obtained from the relationships between dry needle weight (dried for 8 hours at 80°C) and the projected needlearea, between branch diameter and dry needle weight, and between tree diameter andfoliage area per tree. The profile of leaf area density is presented in Figure 2.1. The total(projected) leaf area was 5.4.Chapter 2. Statistical Properties of the Velocity Field 71.5Leaf area density (m2/3)Figure 2.1: Profile of leaf area density of the Douglas-fir stand at Browns River. Thetotal (projected) leaf area index was 5.4.Chapter 2. Statistical Properties of the Velocity Field 8Table 2.1: Average values of weather variables at z/h = 1.38 for the period 06:00—18:00PST, the period of operation of the eddy correlation units, and the relative height of thelower eddy correlation unit (z/h) for the Douglas-fir stand at Browns River. 3, U,and rh represent global solar irradiance (horizontal surface), wind speed measured with acup anemometer, air temperature and relative humidity (average water vapour pressuredivided by saturated water vapour pressure at Ta), respectively. The height of the stand(h) was 16.7 m.Date PeriodHour (PST)11:30—18:0009:30—16:3009:00—16:3011:00—1 7:3008:30—16:0012:00—19:0009:00—16:3012:30—17:3009:00—1 7:00z/h U Ta h SkyW/m2 m/s °C %19 Jul 0.12 655 2.1 22.8 37 clear20 Jul 646 2.1 24.7 28 clear26 Jul 501 1.8 16.4 73 partly cloudy27 Jul 0.42 637 2.4 17.6 61 clear28 Jul 622 1.7 21.2 51 clear29 Jul 0.60 619 1.7 24.7 39 clear30 Jul 578 2.0 24.5 44 clear31 Jul 1.00 524 1.8 19.3 64 mainly clear1 Aug 548 1.9 16.5 64 partly cloudyThe experimental site is located on an east-facing slope with an inclination angle ofapproximately 5. The coastline is located at 12 km to the east of the site and is orientedin a SE—NW direction. About 350 m to the east of the instrument tower, the prunedplot ends and the slope becomes steeper (12°). About 60 m to the west of the tower,there is a very narrow silvicultural access road; beyond this the canopy is rather sparse.Further to the west, at a distance of approximately 500 m, is a small hill. During thedaytime, the wind blows constantly from the NE to NEE sector as a result of sea-to-landand upsiope winds. In the night-time, the wind direction shifts 180°.The most recent rainfall event prior to the experiment occurred on 6 July, 1990.The weather remained mostly clear during the experimental period. Table 2.1 lists thedaytime average values of weather variables for the nine days of the experiment.Chapter 2. Statistical Properties of the Velocity Field 92.2.2 Instrumentation and Data CollectionMicrometeorological measurements were made mainly from a 25 cm wide, 24 m tallguyed triangular open-lattice steel tower (Appendix A). Two eddy correlation units,which measured the fluctuations in the three velocity components, air temperature andwater vapour density, were mounted 1.5 m from the tower. The first unit (hereafterreferred to as the upper unit) consisted of one 3-dimensional sonic anemometer (AppliedTechnologies Inc., Boulder, CO, Model BH-478B/3, 25 cm path length), one fine wirethermocouple (chromel-constantan, 13 1um in diameter) and one krypton hygrometer(Campbell Scientific Inc., Logan, UT, Model K20, 0.795 cm path length). This unit wasoperated permanently at a height of 23.0 m (z/h = 1.38) during the experimental period.The second unit (hereafter referred to as the lower unit) consisted of one 3-dimensionalsonic anemometer/thermometer (Applied Technologies Inc., Model SWS-211/3V, 10 cmpath length) and one krypton hygrometer (Campbell Scientific Inc., Model K20, 1.021cm path length). It was operated at the following heights (z/h in brackets): 2.0 (0.12),7.0 (0.42), 10.0 (0.60), and 16.7 m (1.00) (see Table 2.1).The analogue voltage signal from the thermocouple of the upper unit was amplifiedby an amplifier (Neff Instrument Corp., Duarte, CA, Model SCO19) with a gain of 2000and a bandwidth of 10 Hz. The six analogue signals (five from the upper unit andone from the hygrometer of the lower unit) were sent to an A/D board built in theelectronics of the sonic anemometer/thermometer of the lower unit, resulting in a totalof ten channels of digital data with a sampling rate of 9.9 Hz. The data were sent via aserial port to a lap-top XT micro-computer (Zenith Data Systems Corp., St. Joseph, MI,Model ZWL-184-02 Supersport with 20 Mb hard drive), and transferred to 80 Mb datacartridge magnetic tapes using a tape backup system (Colorado Memory Systems Inc.,Loveland, CO, Model DJ-10), usually after a period of about 8 hours of continuous dataChapter 2. Statistical Properties of the Velocity Field 10collection, for subsequent analysis. In addition, the analogue signals from the upper unitwere sampled in parallel at 10 Hz by a data logger (Campbell Scientific Inc., Model 21Xwith extended software II), which gave on-line calculations of the most important meanstatistics for the purpose of monitoring the performance of the unit.Turbulence statistics were calculated over 30-minute intervals after the experiment. Atwo-way coordinate rotation was applied to the statistics above and on top of the stand,following the procedure of Tanner and Thurtell (1969), and a one-way coordinate rotationwas applied to the statistics inside the stand, following the procedure of Baldocchi andHutchison (1987).Air temperature and wind speed were measured continuously over the whole experimental period with fine wire thermocouples (chromel-constantan, 26 ttm in diameter)and sensitive cup anemometers (C.W. Thornthwaite Associates, Centerton, NJ, Model901-LED), respectively, at heights of 0.9, 2.0, 4.6, 7.0, 10.0, 12.7, 16.7, and 23.0 m. Supporting measurements included humidity, wind direction, and radiation (net, global anddiffuse irradiances) above the stand and near the forest floor (see Chapter 3 for details).The data logging for these instruments was accomplished by five additional data loggers (Campbell Scientific Inc., Models 21X and CR5). All data logging systems weresynchronized to within a few seconds.Eddy correlation sensors were pointed into the prevailing wind directions in the daytime. Only the turbulence data collected in the daytime were considered for analysis.2.2.3 Inter-comparison of InstrumentsOn 31 July and 1 August 1990, the lower unit was operated at the height of the tree tops(z/h = 1.00). Figure 2.2 shows the 30-minute covariances measured at z/h = 1.00 plottedagainst those measured at z/h = 1.38. There was good agreement between the two unitsin the measurement of T, the covariance between the vertical velocity component (w)Chapter 2. Statistical Properties of the Velocity Field 110.4am°C/s 11aN0 1a0 0.2 0.4w’T’, z/h=1.380.04C221:1gf(m2s)-0.4•a jb aa./ aa_r0.02 ///Y -0.2 aa aa •00 0.02 0.04 -02 -0.4w’p , z/h=1.38 u’w’, z/h=1.38Figure 2.2: Covariances of w and T (a), w and Pv (b), and w and u (c) measured at z/h= 1.00 versus those measured at z/h = 1.38 for the Douglas-fir stand at Browns Riveron 31 July and 1 August 1990.Chapter 2. Statistical Properties of the Velocity Field 12and air temperature (T). For w’p’, the covariance between w and water vapour density(pv), the scatter was somewhat larger, but overall was about the 1:1 line. A reduction of20% was observed in —?, the covariance between the longitudinal velocity component(u) and to or the kinematic Reynolds stress, from z/h 1.00 to z/h 1.38. The decreasein Reynolds stress with increasing height was also observed by Baldocchi and Meyers(1988) over a deciduous forest, with a higher reduction rate of 48% from z/h = 1.00to z/h = 1.45. They suggested that one of the reasons for the decrease was the verticaldivergence of Reynolds stress associated with the pressure perturbations and convergenceof streamlines due to topographic effects, which was also likely to be a contributing factorin the present study. As pointed out later, the longitudinal pressure gradient due toland-sea/upslope-downslope circulations might also contribute to the vertical divergenceof Reynolds stress.In order to compare the measurements made by the sonic anemometers with themeasurements made by the cup anemometers, the equivalent average ‘cup’ wind speed,V was calculated for the sonic anemometers for every 30-minute period usingV=/u?+v?where u1 and v1 are the two horizontal components of the instantaneous velocity vector,and the overbar denotes temporal averaging. The results are summarized in Figure 2.3.The correlations between V and U, the 30-minute average wind speed measured withcup anemometers, were very good, indicating a stable performance of the instruments.But overall the value of U was higher than that of V, which was likely the result ofoverspeeding of the cup anemometers in turbulent flow (Coppin 1982).The two eddy correlation units were compared over a smooth bare field on level groundon 3 and 5 October, 1991. The details are given in Appendix C.Chapter 2. Statistical Properties of the Velocity Field 133 II /aA1:1 VA2--/ AAU_I-_- AAA1-4-Oo 1 2 3b /DD_1IaD2--Dz_1--I I • I I1 2 3U (mIs), cup anemometerFigure 2.3: Comparison of equiva’ent ‘cup speed’ V measured by sonic anemometers withwind speed U measured by cup anemometers in the Douglas-fir stand at Browns Riverduring the entire experimental period in 1990: (a) lower unit at z/h = 0.12 (0), 0.42 (•),0.60 () and 1.00 (A) and (b) upper unit at z/h = 1.38.Chapter 2. Statistical Properties of the Velocity Field 142.3 Results and Discussion2.3.1 Monin-Obukhov Similarity above the StandThe surface boundary layer over an extensive plant canopy can be considered as twoparts: the upper part, the inertial sublayer (Tennekes 1973) in which the flux-gradientrelationships established on the basis of Monin-Obukhov similarity are obeyed, and thelower part, the roughness sublayer (Raupach et al. 1980) or transition sublayer (Garratt1980), which is close to and within the canopy itself (Raupach and Thom 1981). Threekinds of the surface influence in the roughness sublayer have been identified: First, thereexists horizontal inhomogeneity, dramatically demonstrated by the horizontal variationsin the wind profile over artificial canopies in wind tunnels (Mulhearn and Finnigan 1978,Raupach et al. 1986), although there does not appear to be any measurements of either wind speed or scalar concentrations over outdoor canopies reported to confirm thisfeature. Second, the transfer processes in the roughness sublayer are greatly enhanced,with the enhancement effect greater for scalars than for momentum. This feature wasattributed to a ‘wake production effect’ (Thom et al. 1975). It has been observed over avariety of forests (Garratt 1978 and 1980, Shuttleworth 1989, Thom et al. 1975, Raupach1979, Denmead and Bradley 1985, Hogstrom et al. 1989), over a model canopy in a windtunnel (Raupach et al. 1980), and over bushland (Chen and Schwerdtfeger 1989). Third,counter-gradient fluxes can occur in the roughness sublayer under certain circumstances(Chen and Schwerdtfeger 1989).Garratt (1980) proposed a scaling law, z,, — d 3D, for momentum flux, where z, isthe height (above the ground surface) of the roughness sublayer, d is the height of thedisplacement plane (assumed to be 0.7 h in the present study, see Jarvis et al. 1976) andD is the spacing of roughness elements. The mean tree spacing in the stand of the presentstudy is about 4.2 m. Based on Garratt’s proposal, the top two measurement levels (z/hChapter 2. Statistical Properties of the Velocity Field 15=1.00 and 1.38) were located within the roughness sublayer. With sensible heat fluxbeing the dominant output component of the energy budget of the stand (Chapter 3)and relatively low wind speed, the stability parameter, (z — d)/L, where L is the MoninObukhov length, was typically of large magnitude, the value varying mainly between—0.20 and —5.0 at z/h = 1.38. Eddy diffusivities under these moderately to stronglyunstable conditions, calculated from the profile measurements at z/h = 1.00 and 1.38 andthe flux measurements at z/h = 1.38, were found to be enhanced by factors of, on average,1.3 for momentum flux and 1.9 for sensible heat flux, as compared to the diffusivitiescalculated using the flux-gradient relationships pertaining to smoother surfaces (Dyer1974). But the dependence of the enhancement on the stability was not monotonic(Figure 2.4).Monin-Obukhov similarity requires that the dimensionless standard deviations of thevertical velocity component and scalar concentrations be functions of (z — d)/L. In thesurface layer under free convection conditions (large —(z — d)/L), these functions havethe forms= a[—(z — d)/L}’13 (2.1)= aT[—(z — d)/L}’13 (2.2)p/Pv* = a[—(z — d)/LJ’/3 (2.3)where o-,, 0T and are the standard deviations of the vertical velocity component, airtemperature and water vapour density, respectively, and u,, T and Pv* are the corresponding characteristic scales defined as= T = Pv* =The values of the constants a, a and u werefound to be about 1.9, 0.9 and 1.1, respectively, over rather smooth surfaces (Hogstrom and Smedman-Hogstrom 1974, TakeuchiChapter 2. Statistical Properties of the Velocity Field 16I IS0)’0 “•••I + +I++ 4++++0 I I Io 10 20Figure 2.4: Enhancement factor (measured eddy diffusivity divided by that predictedwith the flux-gradient relationships of Dyer (1974)) calculated from the profile measurements at z/h = 1.00 and 1.38 and flux measurements at z/h = 1.38 for the Douglas-firstand at Browns River: (s), sensible heat; (+), momentum. The stability parameter(z — d)/L was calculated from the flux measurements at z/h = 1.38.Chapter 2. Statistical Properties of the Velocity Field 17et al. 1980, Wyngaard et al. 1971, Monji 1973, Panofsky and Tennekes 1977, Maitaniand Ohtaki 1987). Ohtaki (1985) found that (2.1)—(2.3) performed well in wheat fields.Figure 2.5 shows the dimensionless standard deviations as functions of the stabilityat z/h = 1.38. The value of o/u at small —(z — d)/L was about 1.16, close to 1.25, atypical value for the neutral surface layer (Panofsky and Dutton 1984). There were largeuncertainties in uT/T and Jp/v* for small values of —(z — d)/L. At large —(z— d)/L,the trend is clear: o/u was well approximated by the 1/3 power law, and 0T/T* andu/p by the —1/3 power law. Overall the measurements and the predictions agreewell for large —(z — d)/L, with slight differences probably caused by the rather arbitrarychoice of the value of d.Stability was found to have little effect on the statistics within the stand. In contrast,Shaw et al. (1988) observed that the normalized Reynolds stress and turbulence intensity at the middle of a deciduous forest showed clear decreases with the onset of stableconditions from moderately unstable conditions.2.3.2 Means and Variances of the Velocity ComponentsFigure 2.6 shows the profiles of daytime cup wind speed (U) normalized against that atz/h = 1.38 and averaged over the nine days listed in Table 2.1, and longitudinal velocitycomponent (u) normalized against that at z/h = 1.38. During the experimental period,the 30-minute average cup wind speed and the longitudinal velocity component at z/h= 1.38 varied between 0.94 and 3.28 m/s and between 0.22 and 2.60 m/s, respectively.The normalized cup wind speed decreased sharply from z/h = 1.38 to z/h = 0.60, witha minimum of 0.25 occurring at z/h = 0.60. There was a marked secondary maximumat around z/h = 0.12, the normalized value being 0.40. The existence of secondarymaximum is a common feature of the wind speed profiles in forest stands having a trunkspace relatively free of branches where air movement is less restricted (e.g. Allen 1968,Chapter 2. Statistical Properties of the Velocity Field 18*642*00Figure 2.5: Dimensionless standard deviations of the vertical velocity component (o/u),air temperature (aT/T) and water vapour density (o/p) as functions of the stabilityparameter (z — d)/L at z/h = 1.38 for the Douglas-fir stand at Browns River. Squares:measured; lines: calculated from Equations (2.1—2.3).04010 20Chapter 2. Statistical Properties of the Velocity Field 191.5 I 11.0 0.98079N0.770.5—0.710.660.460.680 I I0 0.5 1.0Nonnalized wind speedFigure 2.6: Profiles of normalized daytime wind speed in the Douglas-fir stand at BrownsRiver: (.), wind speed measured using cup anemometers (U) and averaged over ninedays, where the numbers are correlation coefficients (R) between the wind speed at theindicated heights and that at z/h = 1.38; (o), longitudinal velocity component (u) measured using one sonic anemometer located for 2—3 days at various heights and normalizedagainst that measured by the other sonic anemometer located permanently at z/h = 1.38.Chapter 2. Statistical Properties of the Velocity Field 20Shaw 1977, Baldocchi and Hutchison 1987, Baldocchi and Meyers 1988). The correlationcoefficient between the cup wind speed at the height of the secondary maximum and thatat z/h = 1.38 was lower than those between the wind speed at all other heights and thatat z/h = 1.38 (Figure 2.6). This indicates that the wind at the height of the secondarymaximum was least coupled to that above the stand compared to the wind at the otherheights. The profile of the normalized longitudinal velocity component was similar to theprofile of the normalized cup wind speed.In the following plots of the vertical profiles of statistics in this Chapter, valuesat z/h = 1.38 were averaged over 31 July and 1 August, while those at lower heightswere averaged over the corresponding operating periods (Table 2.1). The plots of theseensemble averages should retain the basic features of these statistics as functions of heightbecause the atmospheric conditions were similar throughout the experimental period.Figure 2.7 illustrates the dependence of the velocity variance on height. The varianceof the vertical velocity component was smaller than the variances of the longitudinal andlateral components, a feature in agreement with the observations made in agriculturalcrops by Shaw et al. (1974), Finnigan (1979a) and Wilson et al. (1982), and in forests byBaldocchi and Hutchison (1987), Baldocchi and Meyers (1988), Shaw et al. (1988) andAmiro (1990), and decreased approximately linearly with decreasing height. But unlikemost of the experimental results of those workers who showed that u’2 was larger thanv’2, the profiles of u’2 and v’2 in the present study were quite similar both in magnitudeand in shape. Both variances were relatively constant with height in the layer extendinga few metres above the stand and decreased rapidly with depth into the stand. Bothreached minima at z/h = 0.60, where their values were about equal to the value of w’2.Below this height, both increased slightly with depth.Figure 2.8 shows the vertical profiles of turbulence intensity (velocity standard deviation divided by the average longitudinal velocity component) for the three velocityChapter 2. Statistical Properties of the Velocity Field 211.51.0—N0.500 0.5 1.0Variance (m2/s)Figure 2.7: Profiles of daytime average velocity variance in the Douglas-fir stand atBrowns River: (o), longitudinal component (u’2); (.), lateral component (v’2); (v),vertical component (w’2). The average values of the standard error of the mean (SEM)for u’2 and v’2 were 0.08 m2/s on the top and above the stand and 0.01 m2/s withinthe stand, and the corresponding values for w’2 were 0.02 and 0.01 m2/s.I IChapter 2. Statistical Properties of the Velocity Field 221.51.0N0.50-0 1.0Turbulence intensityFigure 2.8: Profiles of daytime average turbulence intensity in the Douglas-fir stand atBrowns River: (o), longitudinal component (ia); (.), lateral component (in); (v), verticalcomponent (i). The average values of SEM were 0.04 for i and i, and 0.02 for i.0.5Chapter 2. Statistical Properties of the Velocity Field 23components: longitudinal (ia), lateral (ia) and vertical (i). These profiles reflect thecombined effect of the variance (Figure 2.7) and the longitudinal velocity component(Figure 2.6) profiles. On average, at z/h 1.38, i and i had a value of 0.52. Theyincreased gradually in magnitude with decreasing height. At z/h = 0.12, the values ofi and i were 0.75 and 0.81, respectively. The profiles of and i reported here weresimilar in shape and magnitude to that for the u component observed in a Japanese larchplantation (Allen 1968), but differed from those observed in a spruce forest by Amiro(1990) and in a deciduous forest by Baldocchi and Meyers (1988) in that their profiles ofi and iv showed marked maxima in the middle of the canopy.The turbulence intensity of the vertical velocity component, i was approximatelyconstant at 0.34 in the layer 1.00<z/h<1.38. It increased sharply with depth into thecanopy. A maximum value of 0.68 occurred at z/h = 0.60, where the wind speed waslowest (Figure 2.6). Below this height, the intensity decreased with decreasing height.The value of i near the forest floor (z/h = 0.12) was about 0.30. A well-defined maximumin the i profile seems to be a common phenomenon occurring in the layer between themiddle and upper third of forest stands (Amiro and Davies 1988, Baldocchi and Meyer1988, Shaw et al. 1988, Bradley et al. reported in Wilson et al. (1982), Amiro 1990). Inmost cases, the maximum value falls in the range between 0.6 and 0.8.2.3.3 Higher Order MomentsSkewness describes the asymmetry of a probability density distribution. The profiles ofvelocity skewness are presented in Figure 2.9. The average values of the skewness forthe three velocity components at z/h = 1.38 were close to zero, the value for a Gaussiandistribution. The values of Sk and Sk increased linearly with decreasing height untilthey reached maximum values of 0.73 and 0.57, respectively, at the middle of the canopy(z/h = 0.60), where the wind speed was lowest (Figure 2.6). Below this height both SkChapter 2. Statistical Properties of the Velocity Field 241.0N0.50-0.4 0.0 0.8SkewnessFigure 2.9: Profiles of daytime average velocity skewness in the Douglas-fir stand atBrowns River: (o), longitudinal component (Sky); (.), lateral component (Sky); (v),vertical component (Sk). The average values of SEM were 0.06 for Sk and Sk and0.04 for Sk.1.5 I I0.4Chapter 2. Statistical Properties of the Velocity Field 25and Sk decreased with decreasing height. Positive values of Sk were consistent withthe theoretical arguments of Shaw and Seginer (1987) that the penetration of occasionalsweeps of fast moving air into the canopy from above should result in positive Sk.However, they did not expect the nonzero Sk as reported here.Intense turbulent activity above a vegetation canopy is carried downward whereasin the interior of the canopy there is no source for the creation of large updrafts (Shawand Seginer 1987). Consequently, the vertical velocity component immediately abovethe stand and in the canopy layer was negatively skewed. The most negative value of—0.52 for Sk occurred at the middle of the canopy (z/h = 0.60). The profile of Sk waspractically a mirror image of the profiles of Sk and Sky, a pattern observed previouslyin several other experimental studies (Seginer et al. 1976, Raupach et al. 1986, Shawand Seginer 1987, Amiro 1990).Kurtosis is a measure of peakness or flatness of a probability density distribution. Fora Gaussian distribution, it has a value of 3. As shown in Figure 2.10, the kurtosis valuesfor the three velocity components above the stand in this study were not significantlydifferent from 3. Higher values of kurtosis were observed in the canopy layer, indicatingthe existence of active extreme events in this layer. Like that of skewness, the magnitudeof kurtosis peaked at z/h = 0.60. The peak values for Kr, Kr, Kr were 5.1, 5.1 and4.1, respectively. Kurtosis was smaller in the trunk space, the values at z/h = 0.12 being3.2, 2.9 and 3.9, respectively. This might indicate that the canopy layer above suppressedthe activity of extreme events by blocking the penetration of large gusts from above thestand and imposing a thermal inversion (Chapter 3) on the trunk flow.2.3.4 Reynolds StressThe variation of Reynolds stress with height is presented in Figure 2.11. The ratio, u/ii,at z/h = 1.38 was 0.20 + 0.08. A reduction of 20% in the stress occurred from the treeChapter 2. Statistical Properties of the Velocity Field 261.5 —______1.0 —N0.50—KurtosisFigure 2.10: Profiles of daytime average velocity kurtosis in the Douglas-fir stand atBrowns River: (o), longitudinal component (Kr); (.), lateral component (Kr); (v)vertical component (Kr). The average values of SEM were 0.13 for Kr and Kr and0.10 for Kr.3 4 5Chapter 2. Statistical Properties of the Velocity Field 271.51.0-N0.5-0 I I0 0.1 0.2- U’ W’ (m2/s)Figure 2.11: Profile of daytime average kinematic Reynolds stress in the Douglas-fir standat Browns River. The average value of SEM were 0.014 m2/s on the top and above thestand and 0.002 m2/s within the stand.Chapter 2. Statistical Properties of the Velocity Field 28tops to z/h = 1.38. The stress decreased sharply with depth into the canopy due tomomentum absorption by the foliage. It was negative at the base of the canopy (z/h =0.42) and in the middle of the trunk space (z/h = 0.12), with magnitudes of about 25%of that at z/h = 1.38.Negative Reynolds stress persistently occurred at z/h = 0.12 and 0.42, with only twoexceptions in a total of seventy one 30-minute runs. The most negative values were —0.052m2/s at z/h = 0.12 and —0.058 m2/s at z/h = 0.42. An explanation for the negativevalues can be obtained by examining the Reynolds stress budget (Raupach et al. 1986)o— —i,o” —,,____<uw> = 0 = — <W’2> ---— <uçu’ + uu >at oz ax3 ax,P3 Pw0 1 Ou’ Ow’—— <u’w2>+ — <p’(— + )>Oz p Oz OxT (2.4)where u, and x (i=1, 2, 3) are the components of velocity and position vectors, respectively, in tensor notation, (u, v, w) and (x, y, z) are velocity and position vectorsin meteorological notation, t is time, p is pressure, p is air density; triangular bracketsand double primes denote, respectively, spatial averages (horizontally) and departurestherefrom; and overbar and single prime denote, respectively, temporal averages and departures therefrom. On the RHS of (2.4), P3 and P,, are shear production and wakeproduction, respectively, representing local interactions, T is turbulent transport, representing interactions between layers, and 1’ is the interaction between velocity and pressurefields. In (2.4) we omit small terms such as dispersive flux divergence, molecular flux divergence, molecular dissipation and pressure transport, according to the studies of Shaw(1977) and Raupach et al. (1986).It is iiot feasible to estimate the magnitudes of the individual terms of (2.4) in theChapter 2. Statistical Properties of the Velocity Field 29stand of the present study, but qualitative conclusions can be drawn from (2.4). Byparameterizing 1 as (Wilson and Shaw 1977, Wyngaard 1981)where r is a time scale, (2.4) becomes(2.5)According to (2.5), the contribution of P3 to Reynolds stress < —> was positiveabove z/h = 0.60 due to the positive wind speed gradient (Figure 2.6) and negative inthe layer between z/h = 0.12 and 0.60 due to the negative wind speed gradient. P,, canbe neglected provided that (1) there is negligible direct dissipation of mean kinematicenergy into heat by the canopy, and (2) the dispersive covariance and dispersive transportare both negligible (Raupach et al. 1986). If non-zero dispersive covariances exist, a littlemanipulation of the budget equation of <Ti”U”> (Raupach and Shaw 1982) yields (seeAppendix B for details)= —<‘‘> a <u> (2.6)9zEquation (2.6) means that P, if not zero, acts in a similar way as P3 in that both havethe same sign and that both are linear with the local wind speed gradient, aT is largely driven by the gradient of Reynolds stress (Shaw 1977). Because of thesmall magnitude of Reynolds stress in the lower part of the stand, this driving force wasprobably small, and T might therefore be small. On the other hand, the sum of P3 andP in the lower part of the stand were significant because of the very negative wind speedgradient. In other words, the sum of P and Pt,. was likely to dominate over T at z/h= 0.12 and 0.42, and result in the negative values of Reynolds stress. In fact, Reynoldsstress was found to have strong dependence on the wind speed gradient at the lowerChapter 2. Statistical Properties of the Velocity Field 30levels, the correlation coefficient being 0.70 at z/h = 0.12 for thirty seven 30-minute runsand 0.83 at z/h = 0.42 for twenty eight 30-minute runs.It should be pointed out that, although the non-local interactions represented byT are likely to be small compared to the local interactions represented by P3 and Pfor the Reynolds stress budget at lower heights of a plant canopy, they are generallysignificant for the flux budgets of scalars such as sensible heat and water vapour. Thisis well demonstrated by the phenomenon of counter-gradient flux frequently observed inthe lower parts of forest stands (Denmead and Bradley 1985, Amiro 1990, Leclerc 1987,Chapter 3). A comparison of the Reynolds stress budget (Raupach et al. 1986) and theheat flux budget (Coppin et al. 1986) in an artificial canopy in a wind tunnel shows that,while T is much smaller in magnitude than P3 in the Reynolds stress budget, T is inequal magnitude to P3 in the heat flux budget.Negative Reynolds stress indicates the upward flux of momentum and has been observed at the lower heights in vegetation canopies on a few other occasions (Raupachet al. 1986, Baldocchi and Hutchison 1987, Maitani and Shaw 1990, Appendix E). Themomentum conservation equation can be examined to shed some light on the origin of theupward momentum flux. For a stationary flow without buoyancy forces and advection,the conservation equation for momentum is<—u’w’> +-- <—‘‘>= CA<i>2+ <p> (2.7)azwhere Cd is the effective drag coefficient of the plant elements and A is the element areadensity (Raupach et al. 1986). Integration of (2.7) with respect to z yields[<—> + <—i””>] =jZ+ [<—u’w’> + <—ii’ w >] + I—dz (2.8)Jo p axThe first and second parts of the term on the LHS of (2.8) are spatially averaged ReynoldsChapter 2. Statistical Properties of the Velocity Field 31momentum flux (or Reynolds stress, assumed to equal the point measurement (Shaw1985)) and dispersive momentum flux (or dispersive stress), respectively; the first termon the RHS of (2.8) represents momentum absorption by the plant elements, the secondterm momentum absorption by the ground surface, and the third term the contributionof momentum divergence due to the longitudinal pressure gradient,. The onset ofthe sea/upslope breeze in the daytime was associated with a negative. Accordingto the estimates of Atkinson (1981, pp 125-127 and 217-219), the gradient due to theuneven radiative heating between land and sea was on the order of 0.2 kPa/100 km, andthe gradient due to the uneven radiation heating between slope and horizontal land wason the same order of magnitude. Using a value of —0.5 kPa/100 km for a >, thethird term on the RHS of (2.8) was estimated at —0.035 m2/s for z/h = 0.42. Momentumabsorption by the ground was probably negligible. Momentum absorption by the trunks(the main elements below z/h = 0.42) was estimated at 0.010 m2/s for the height z/h= 0.42, by using the value of Cd for a cylinder in turbulent flow (0.45, p 622 Schlichting1968). The sum of the terms on the RHS of (2.8) was thus on the order of —0.025 m2/s,which was similar to the average value of —0.033 m2/s for <—> measured at z/h =0.42. The result of this simple exercise suggests that the longitudinal pressure gradientmight, to a large extent, be responsible for the upward momentum flux. It is not feasibleto estimate the magnitude of the dispersive term from a point measurement, but resultsof earlier wind tunnel experiments suggested that this term might be negligible (Raupachet al. 1986, Mulhearn 1978).2.3.5 Quadrant Representation of Reynolds StressQuadrant-hole analysis, a conditional-sampling technique, is useful in identifying kindsof turbulent motion which dominate the vertical transfer of momentum represented byChapter 2. Statistical Properties of the Velocity Field 32the kinematic Reynolds stress, It was used in the experimental investigationsof momentum transfer in agricultural crops (Finnigan 1979b, Shaw et al. 1983), in analmond orchard (Baldocchi and Hutchison 1987), in deciduous forests (Baldocchi andMeyers 1988, Gao et al. 1989, Maitani and Shaw 1990), and in a wind tunnel modelcanopy (Raupach et al. 1986). These studies have shown the common features thatwithin a vegetation canopy, a large proportion of momentum transfer occurs in a smallfraction of time and that in the upper part of and immediately above the canopy, thetransfer is dominated by sweeps or gusts.The four quadrants in the u’w’ plane are conventionally labelled as outward interaction(i = 1; u’> 0, w’ > 0), ejection (i = 2; u’ < 0, w’ > 0), inward interaction (i = 3; u’ < 0,w’ <0), and sweep (i = 4; u’> 0, w’ <0). A stress fraction S,H and a time fraction tj,Hare defined, respectively, as1 1 tTS1,H——i—J u”(t)w’(t)I,HdtIUW IT oiTti,H = j 1,Hdtwhere T is the averaging time interval (30 minutes in this study), and ‘j,H is a conditioningfunction which equals one if the point (u’(t), w’(t)) is located in the jth quadrant andI u’(t)vY(t) is greater than H and zero otherwise. The dimensionless parameter,H, is called hole size.One 30-minute run at each level was selected for quadrant-hole analysis (Table 2.2).As shown in Table 2.2, the stability parameter (z — d)/L, was similar for all runs. Figure 2.12 shows the stress fraction S,H plotted against hole size H and Table 2.3 listsrelated information. In Table 2.3, H’ is the hole size above which half of the momentumtransfer occursI Si,H’ 1=0.5Chapter 2. Statistical Properties of the Velocity Field 33Table 2.2: Values of Reynolds stress standard deviations of the longitudinal andvertical velocity components (a and o,), and the mean longitudinal velocity component(z) at the indicated levels for the five runs selected for quadrant-hole analysis of Reynoldsstress for the Douglas-fir stand at Browns River. The stability parameter (z—d)/L wascalculated from the measurements at z/h = 1.38.Time interval z/h (z—d)/L o o zPST m2/s rn/s rn/s rn/s13:30—14:00 0.12 —0.26 —0.024 0.45 0.19 1.0019 July12:00—12:30 0.42 —0.25 —0.052 0.41 0.32 0.4227 July12:30—13:00 0.60 —0.35 0.036 0.34 0.33 0.5030 July13:30—14:00 1.00 —0.25 0.184 1.17 0.54 2.141 Aug12:00—12:30 1.38 —0.25 0.354 1.16 0.75 2.1927 JulyChapter 2. Statistical Properties of the Velocity Field 34I I Ii=2-Ejection*lj-Iiz. Inward interaction-I I I20 10 00 10 20 30HFigure 2.12: Stress fraction (S,H) plotted against hole size (H) for the Douglas-fir standat Browns River for five values of z/h: 1.38 (x), 1.00 (a), 0.60 (o), 0.42 (+), and 0.12(D).1.00.5000.51.0I IdinteractionSweep30Chapter 2. Statistical Properties of the Velocity Field 3551,0 + 53,0Table 2.3: Intermittence parameters (H’ and exuberance ( ) and thei=1 S2,0 + S4,054,0ratio of the contribution to Reynolds stress by sweeps to that by ejections (—) for theS2,0Douglas-fir stand at Browns River.2H’ 8.04ti,Hl 0.064i=1Si,o + S3,0—2.44S2,0 + 34,01.12.92,00.42 0.60 1.00 1.385.6 7.5 4.8 5.00.084 0.064 0.125 0.096—3.45 —0.36 —0.39 —0.260.90 2.20 1.30 0.86Chapter 2. Statistical Properties of the Velocity Field 36and is the corresponding time fraction. t,w and H’ are measures of intermittence. The intermittent nature of the momentum transfer can be readily seen: At alllevels, half of the momentum flux was contributed by the events with hole size greaterthan 4.8—8.0 which occupied small fractions of time (6.4—12.5%).The relative importance of the kinds of turbulent motion in momentum transfer canbe examined by forming ratios of stress fractions at zero hole size. The ratio of thecontributions by the interaction components (S1,0 + S3,0) to the contributions by theejection and sweep components (S2,0+ 54,0), called exuberance (Shaw et al. 1983), variedbetween —0.26 and —0.39 in the layer between z/h = 0.60 and 1.38, which is consistentwith the net downward momentum flux. At z/h = 1.38, ejections dominated over sweeps,the ratio S4,0/S2being 0.86. But sweeps gained strength at the tree tops and in thecanopy layer. The values of the ratioS4,o/52were 1.3 at z/h = 1.00 and 2.2 at z/h =0.60. The dominance of sweeps over ejections was even greater at these two heights ifonly larger events were considered, as shown in Figure 2.12. These results generally agreewith those of the experimental studies reviewed previously, but differ in some details. Forexample, the magnitudes of Sj,O (i = 1—4) in the present work were generally less than 1,while Baldocchi and Meyers (1988) reported the magnitudes to be 1 to 3 for a deciduousforest.At the lower heights of the stand, a different picture evolved. The interaction components played a major role in momentum transfer. The exuberance values were —2.44at z/h = 0.12 and —3.45 at z/h = 0.42. This is consistent with the upward transfer ofmomentum or negative Reynolds stress at these two heights as discussed in the previoussection. Baldocchi and Hutchison (1987) attributed the large contribution of the interaction components to either sloshing of the air near the forest floor or the existence ofa systematic wake circulation in tile lee of the tree upwind. However, it likely reflectsChapter 2. Statistical Properties of the Velocity Field 37a local interaction with the wind speed gradient: A downward/upward motion (negative/positive w’) would normally result in a decrease/increase in u (negative/positive u’)due to the negative wind speed gradient in the layer between z/h 0.12 and 0.42.2.4 Summary and ConclusionsDaytime turbulence statistics for the velocity field within and above a Douglas-fir foreston a 50 slope have been presented in this paper. The stability parameter, (z—d)/L variedmainly between —0.20 and —5.0 at z/h = 1.38. Eddy diffusivities under these moderatelyto strongly unstable conditions, calculated from the profile measurements at z/h = 1.00and 1.38 and the flux measurements at z/h = 1.38, were found to be enhanced by factorsof, on average, 1.3 for momentum flux and 1.9 for sensible heat flux, as compared tothe diffusivities calculated using the flux-gradient relationships pertaining to smoothersurfaces. However, the similarity functions for the standard deviations of the verticalvelocity component, air temperature and water vapour density were found to performwell at z/h = 1.38.The vertical profiles of the turbulence statistics reflect the influence of the verticalstructure of the stand. A marked secondary maximum in the wind speed profile occurredin the middle of the trunk space (around z/h = 0.12). The turbulence intensities for thelongitudinal and lateral velocity components increased with decreasing height, but theintensity for the vertical velocity component had a maximum at z/h = 0.60, where theleaf area density was highest. Magnitudes of the higher order moments (skewness andkurtosis) for the three velocity components were higher in the canopy layer than in thetrunk space and above the stand.There was a 20% reduction in Reynolds stress from z/h = 1.00 to 1.38, probablya result of topographic effects and land-sea/upslope-downslope circulations. NegativeChapter 2. Statistical Properties of the Velocity Field 38Reynolds stress persistently occurred at z/h = 0.12 and 0.42 (height of the base of thecanopy). Examination of the Reynolds stress budget revealed that the negative valuewas associated with negative wind speed gradients at the two heights. The longitudinalpressure gradient due to the land-sea/upslope-downslope circulations was believed to bethe main factor responsible for the upward momentum flux or negative Reynolds stress.Momentum transfer was highly intermittent. Sweep and ejection events dominatedthe transfer process at z/h = 0.60, 1.00 and 1.38, with sweeps playing the more importantrole of the two at z/h = 0.60 and 1.00 and the less important role at z/h 1.38. Butinteraction events were of greater magnitude than sweep and ejection events at z/h =0.12 and 0.42.2.5 ReferencesAllen, L.L.: 1968, ‘Turbulence and wind speed spectra within a Japanese larch plantation’, J. Appi. Meteorol. 7, 73-78.Amiro, B.D.: 1990, ‘Comparison of turbulence statistics within three Boreal forestcanopies’, Boundary-Layer Meteorol. 51, 99-121.Amiro, B.D. and Davis, P.A.: 1988, ‘Statistics of atmospheric turbulence within anatural black spruce forest canopy’, Boundary-Layer Meteorol. 44, 267-283.Atkinson, B.W.: 1981, Meso-scale Atmospheric Circulations, Academic Press, NewYork.Aylor, D.E.: 1989, ‘Aerobiology and atmospheric turbulence— examillig the interface’10th Conference on Biometeorology and Aerobiology, American Meteorological Society, Salt Lake City, UT. Preprint volume. pp 23-26.Chapter 2. Statistical Properties of the Velocity Field 39Baldocchi, D.D. and Hutchison, WA.: 1987, ‘Turbulence in an almond orchard: Verticalvariations in turbulence statistics’, Boundary-Layer Meteorol. 40, 127-146.Baldocchi, D.D. and Meyers, T.P.: 1988, ‘Turbulence structure in a deciduous forest’,Boundary-Layer Meteorol. 43, 345-364.Chen, F. and Schwerdtfeger, P.: 1989, ‘Flux-gradient relationships for momentum andheat over a rough natural surface’, Quart. J. R. Meteorol. Soc. 115, 335-352.Coppin, P.A.: 1982, ‘An examination of cup anemometer overspeeding’, Meteorol. Rdsch. 35, 1-11.Coppin, P.A., Raupach, M.R. and Legg, B.J.: 1986, ‘Experiments on scalar dispersionwithin a model plant canopy. Part II: An elevated plane source’, Boundary-LayerMeteorol. 35, 167-191.Denmead, O.T. and Bradley, E.F.: 1985, ‘Flux-gradient relationships in a forest canopy’,in Hutchison, B.A. and Hicks, B.B. (eds.), The Forest-Atmospheric Interaction, D.Reidel Publishing Co., Dordrecht, 421-442.Dyer, A.J.: 1974, ‘A review of flux-profile relationships’, Boundary-Layer Meteorol. 7,363-372.Finnigan, J.J.: 1979a, ‘Turbulence in waving wheat. Part I: Mean statistics andHonami’, Boundary-Layer Meteorol. 16, 181-211.Finnigan, J.J.: 1979b, ‘Turbulence in waving wheat. Part II: Structure of momentumtransfer’, Boundary-Layer Meteorol. 16, 213-236.Gao, W., Shaw, R.H. and Paw U, K.T.: 1989, ‘Observation of organized structure inturbulent flow within and above a forest canopy’, Boundary-Layer Meteo rot. 47,349-377.Chapter 2. Statistical Properties of the Velocity Field 40Garratt, J.R.: 1980, ‘Surface influence upon vertical profiles in the atmospheric near-surface layer’, Quart. J. Met. Soc. 106, 803-819.Garratt, J.R.: 1978, ‘Transfer characteristics for a heterogeneous surface of large aerodynamic roughness’, Quart. J. R. Met. Soc. 104, 491-502.Hogstrom, U., Bergstrom, H., Sedman, A.-S., Halidin, S. and Lindroth, A.: 1989, ‘Turbulent exchange above a pine forest, I: Fluxes and gradients’, Boundary-LayerMet eorol. 49, 197-217.Hogstrom, U. and Srnedman-Hogstrom, A.S.: 1974, ‘Turbulent mechanisms at an agricultural site’, Boundary-Layer Met eorol. 7, 373-389.Jarvis, P.G., James, G.B. and Landsberg, J.J.: 1976, ‘Coniferous forest’, in Monteith,J.L. (ed.), Vegetation and the Atmosphere II: Case Studies, Academic Press, NewYork, 171-240.Leclerc, M.Y.: 1987, ‘Turbulence and turbulent diffusion inside and above vegetation’,Ph.D. Thesis, University of Guelph, Guelph, Ontario.Leclerc, M.Y., Beissner, K.C., Shaw, R.H., den Hartog, 0, and Neumann, H.H: 1991,‘The influence of buoyancy on third-order turbulent velocity statistics within adeciduous forest’, Boundary-Layer Met eorol. 55, 109-124.Maitani, T. and Ohtaki, E.: 1987, ‘Turbulent transport processes of momentum andsensible heat in the surface layer over a paddy field’, Boundary-Layer Meteorol. 40,283-293.Maitani, T. and Shaw, R.H.: 1990, ‘Joint probability analysis of momentum and heatfluxes at a deciduous forest’, Boundary-Layer Met eorol. 52, 283-300.Monji, N.: 1972, ‘Budgets of turbulent energy and temperature variance in the transitionzone from forced to free convection’, Ph.D. Thesis, University of Washington.Chapter 2. Statistical Properties of the Velocity Field 41Muihearn, P.J.: 1978, ‘Turbulence over a periodic rough surface’, Phys. Fluids 21,1113-1115.Muihearn, P.J. and Finnigan, J.J.: 1978, ‘Turbulence over a very rough, random surface’, Boundary-Layer Meteorol. 15, 109-132.Ohtaki, E.: 1985, ‘On the similarity in atmospheric fluctuations of carbon dioxide, watervapor and temperature over vegetated fields’, Boundary-Layer Met eorol. 32, 25-37.Panofsky, H.A. and Dutton, J.A.: 1984, Atmospheric Turbulence: Models and Methodsfor Engineering Applications, John Wiley and Sons, New York.Panofsky, H.A. and Tennekes, H.: 1977, ‘The characteristics of turbulent velocity components in the surface layer under convective conditions’, Boundary-Layer Meteorol.11, 355-361.Raupach, M.R.: 1979, ‘Anomalies in flux-gradient relationships over forest’, Boundary-Layer Met eorol. 16, 467-486.Raupach, M.R., Coppin, P.A. and Legg, B.J.: 1986, ‘Experiments on scalar dispersionwithin a model plant canopy. Part I: The turbulence structure’, Boundary-LayerMet corol. 35, 21-52.Raupach, M.R. and Shaw, R.H.: 1982, ‘Averaging procedures for flow within vegetationcanopies’, Boundary-Layer Met eorol. 22, 79-90.Raupach, M.R. and Thom, A.S.: 1981, ‘Turbulence in and above plant canopies’, Ann.Rev. Mech. 13, 97-129.Raupach, M.R., Thom, A.S. and Edwards, I.: 1980, ‘A wind-tunnel study of turbulentflow close to regularly arrayed rough surfaces’, Boundary-Layer Met eorol. 18, 373-397.Chapter 2. Statistical Properties of the Velocity Field 42Sagar, R.M., Black, T.A., Lee, X. and Chen, J.M.: 1991, ‘Heat transfer relationshipsfor deer in Douglas-fir stands’, 10th Conference on Biometeorology and Aerobiology,American Meteorological Society, Salt Lake City, UT. Preprint volume. pp 129-132.Schlichting, H.: 1968, Boundary-Layer Theory, 6th Edition, McGraw-Hill Book Company, New York.Seginer, I., Muihearn, P.J., Bradley, E.F. and Finnigan, J.J.: 1976, ‘Turbulent flow ina model plant canopy’, Boundary-Layer Met eorol. 10, 423-453.Shaw, R.H.: 1985, ‘On diffusive and dispersive fluxes in forest canopies’, in Hutchison, B.A. and Hicks, B.B. (eds.), The Forest-Atmospheric Interaction, D. ReidelPublishing Co., Dordrecht, 407-419.Shaw, R.H.: 1977, ‘Secondary wind speed maxima inside plant canopies’, J. Appi.Met eorol. 16, 514-523.Shaw, R.H., den Hartog, G., King, K.M. and Thurtell, G.W.: 1974, ‘Measurements ofmean wind flow and three-dimensional turbulence intensity within a matured corncanopy’, Agric. Meteorol. 13, 419-425.Shaw, R.H., den Hartog, G. and Neumann, H.H.: 1988, ‘Influence of foliar densityand thermal stability on profiles of Reynolds stress and turbulence intensity in adeciduous forest’, Boundary-Layer Met eorol. 45, 391-409.Shaw, R.H. and Seginer, I.: 1987, ‘Calculation of velocity skewness iii real and artificialplant canopies’, Boundary-Layer Meteorol. 39, 3 15-332.Shaw, R.H., Tavangar, J. and Ward, D.P.: 1983, ‘Structure of Reynolds stress in acanopy layer’, J. Climate Appl. Meteorol. 22, 1922-1931.Shuttleworth, W.J.: 1989, ‘Micrometeorology of temperate and tropical forest’, Phil.Trans. R. Soc. Lond. 324B, 299-334.Chapter 2. Statistical Properties of the Velocity Field 43Takeuchi, K., Ohtaki, E. and Seo, T.: 1980, ‘Turbulent transport of water over paddyfields’, Ber. Ohara Inst. Landw. Biol. Okayama Univ. 18, 1-30.Tanner, C.B. and Thurtell, G.W.: 1969, ‘Anemoclinometer measurements of Reynoldsstress and heat transport in the atmospheric surface layer’, Research and Development Technical Report ECOM-66-G22-F, University of Wisconsin, Madison, Wisconsin.Tennekes, H.: 1973, ‘The logarithmic wind profile’, J. Atmos. Sci. 30, 234-238.Thom, A.S., Stewart, J.B., Oliver, H.R. and Gash, J.H.: 1975, ‘Comparison of aerodynamic and energy budget estimates of fluxes over a pine forest’, Quart. J. R.Meteorol. Soc. 101, 93-105.Wilson, R.N. and Shaw, R.H.: 1977, ‘A higher order closure model for canopy flow’, J.Appi. Meteorol. 14, 1197-1205.Wilson, J.D., Ward, D.P., Thurtell, G.W. and Kidd, G.E.: 1982, ‘Statistics of atmospheric turbulence within and above a corn canopy’, Boundary-Layer Met eorol. 24,495-519.Wyngaard, J.C.: 1981, ‘Boundary-layer modeling’, in Nieuwstadt, F.T.M. and vanDop, H. (eds.), Atmospheric Turbulence and Air Pollution Modelling, D. ReidelPublishing Company, Dordrecht, 69-106.Wyngaard, J.C., Cote, O.R. and Izumi, Y.: 1971, ‘Local free convection, similarity, andthe budgets of shear and heat flux’, J. Atmos. Sci. 28, 1171-1182.Chapter 3Eddy Fluxes of Sensible Heat and Water Vapour3.1 IntroductionMeasurements of the exchange of atmospheric scalar constituents such as heat and watervapour between forest communities and the atmosphere are needed to provide informationfor studies of global and regional water and CO2 balances, deposition of atmosphericpollutants, and productivity of forest ecosystems. Most micrometeorological studies ofthe exchange processes in forests over the past twenty years have been conducted abovethe stand (Verma et al. 1986, Shuttleworth et al. 1984, McNaughton and Black 1973,Jarvis et al. 1976, etc.). There have been fewer studies performed both within and abovethe stand (Denmead and Bradley 1985, Gao et al. 1989, Maitani and Shaw 1990). Yet,a complete picture can evolve only if the physical processes in both parts are considered.As reported in Chapter 2, an experiment to study the exchange processes within andabove a coniferous forest of Douglas-fir trees was conducted on Vancouver Island duringa two-week rainless period in July and August 1990. This Chapter reports the resultsof the analysis of eddy fluxes of sensible heat and water vapour within and above thisstand. As part of the analysis, energy budget closure above the stand and beneath theoverstory is examined. The big leaf model is used to calculate the canopy resistance andOmega factor of the stand for the purpose of describing the degree of coupling betweenthe atmosphere and the stand. The implications of measured flux profiles, namely, the44Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 45relationships between the flux and source distributions and the phenomenon of counter-gradient flux are addressed. Finally, the technique of quadrant-hole analysis is used toidentify the kinds of motion which dominate the exchange processes.3.2 Experimental Methods3.2.1 Site DescriptionThe experimental site was located on a slope with a 50 inclination angle near BrownsRiver approximately 10 km northwest of Courtenay on Vancouver Island, 125°10’W,49°42’N. The overstory species is Douglas-fir planted in 1962. In 1988 it was thinned to575 sterns/ha and pruned to a height of approximately 6 m. The height of the stand (h)was 16.7 ni. The average trunk diameter at the height of 1.3 rn was 0.20 m. The total(projected) leaf area index was 5.4. The forest floor was littered with dead branches andtrunks, with a little short understory vegetation less than 0.5 m tall. A more detaileddescription of the site can be found in Chapter 2.The experiment was conducted in late July and early August 1990. The most recentrainfall event prior to the experiment occurred on 6 July. The weather remained mostlyclear during the experimental period. The average water content of the root zone (0-60cm) was 0.19 on 27 July, 0.13 on 2 August and 0.11 kg/kg on 17 August on dry soil basis.During the late stage of the experiment, there was water stress of the trees as indicatedby some needle yellowing.3.2.2 InstrumentationPrimary instrumentation included two eddy correlation units mounted 1.5 m from a 25cm open-lattice triangular tower, which measured the fluctuations in the three velocityChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 46components, air temperature and water vapour density. One unit was operated permanently at a height of 23.0 m (z/h = 1.38). The other unit was operated at the followingheights (z/h in brackets): 2.0 (0.12), 7.0 (0.42), 10.0 (0.60), and 16.7 m (1.00), for 2—3eight hour periods at each height. The two units were operated in the daytime when thewind direction was favorable. The sampling rate was 9.9 Hz. About 120 hours of datawere collected for subsequent analysis.In the early stage of the experiment, three 1-dimensional sonic anemometer/thermocouple units (Campbell Scientific Inc., Logan, UT) were operated at 2 m above the forestfloor and located in the upwind direction of the main instrument tower. The main towerand the three 1-dimensional units were positioned approximately along a line with 15 mseparation from each other. The signals from the three units were sampled at 10 Hz by adata logger (Campbell Scientific Inc., 21X with extended software II), which gave on-linecalculations of sensible heat flux for every 30-minute period.Net radiation flux above the stand was measured with a net radiometer (SwisstecoInstruments, Oberriet, Switzerland, Model S-1) at a height of 24.0 m. Net radiationflux near the forest floor was measured at a height of 1.3 m (z/h = 0.08) with two netradiometers of the same type: one mounted on a tram and moving back and forth ata speed of 1.49 m/min along a 15.6 m pathway (Black et al. 1991) and the other at aheight of 1.3 in at a fixed position. Only data collected with the tram system were usedin the analysis of energy budget beneath the overstory. Soil heat flux was measured withtwo pairs of soil heat flux plates (one pair, Middleton Instruments, Australia, Model F;one pair, home-made following the design of Fuchs anf Tanner (1968)) placed at a depthof 3 cm and two nickel wire integrating thermometers to correct for the change in heatstorage in the surface soil layer.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 47Relative humidity was measured at heights of 24.0 and 1.5 m with two hygrometers (Physical-Chemical Corp., New York, NY, Model PRC). Both sensors were calibrated against an Assmman psychrometer (Casella Ltd., London, England) in the field.Air temperature and wind speed were measured with fine wire thermocouples (25 pmwelded chromel-constantan) and sensitive cup anemometers (C.W. Thornthwaite Associates, Centerton, NJ, Model 901-LED), respectively, at heights of 0.9, 2.0, 4.6, 7.0, 10.0,12.7, 16.7 and 23.0 m.Soil water content was measured once a week using gravimetric method. Soil watercontent of the root zone (0—60 cm) was measured at a 5 cm increment at two locations.Soil water content of the surface layer (0—3 cm) was measured at four locations and wasused to determine the volumetrical heat capacity of this layer for the calculations of soilheat flux.3.2.3 Theoretical ConsiderationsTurbulence statistics were calculated over 30-minute intervals. A two-way coordinaterotation was applied to the statistics measured at the heights of 16.7 m and 23.0 m,following the procedure of Tanner and Thurtell (1969), and a one-way coordinate rotationapplied to the statistics measured within the stand, following the procedure of Baldocchiand Hutchison (1987). Corrections were made to the measurements of water vapour fluxmade with the krypton hygrometers to account for the effect of oxygen (Massman et al.1990) and the effect of the air density due to the simultaneous transfer of heat and watervapour (Webb et al. 1980).Assuming horizontal homogeneity and neglecting the energy used in photosythesis,the energy budget of the forest stand can be expressed asR?l—S—G=H+\E (3.1)Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 48where R,1 is the net radiation flux above the stand, G is the soil heat flux, H is thesensible heat flux above the stand, AE is the latent heat flux above the stand, and Sis the rate of heat storage per unit ground area in the layer between the 0 and 23.0 mheights, all of which have units of W/m2.The rate of heat storage, S was separated into the following four components:S Ss+S1+Snb+Stwhere S is the rate of sensible heat storage in the air, S1 is the rate of latent heat storagein the air, Sb is the rate of heat storage in the needles and branches, and St is the rateof heat storage in the tree trunks. The first three components can be expressed asç23m öTa= J pc,—-dz (3.2)23m 8Si j idz (3.3)123m_____Snb = J mcb dz (3.4)cit8Ta 8Pv.where -—, --, and —— are the time rates of change in air temperature, water vapourdensity and temperature of the needles and branches; p is the air density, c is the specificheat of air at constant pressure, A is the latent heat of vaporization of water, m is themass of the ueedles and branches per unit volume of air, and Cnb is the specific heat of theneedles and branches. Using appropriate values for p, c, and A, (3.2) and (3.3) reduce to= 14.2LTaS1 = 31.2zwhere z (°C) and /7i (g/m3) are the changes over a 30-minute interval in air temperature and water vapour density averaged over the layer between the 0 and 23.0 mChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 49heights. /a was calculated from the measurements of air temperature made at theeight heights, and Loj was approximated by the measurement of water vapour densitymade at the height of 24.0 m. Using the measured mass of needles and branches anda value of 2647 J/(kg °C) for Cnb, based on the specific heat of dry wood (Cohen et al.1985) and corrected for the measured water content of the needles and branches, (3.4)reduces toSnb 4.3LTbwhere /Tnb (°C) is the change over a 30-minute interval in the average temperatureof the needles and branches, estimated to a good approximation from the change in airtemperature averaged over the four heights of 7.0, 10.0, 12.7 and 16.7 m. The rate of heatstorage in the trunk (Se) was estimated, using a method similar to that used by Denmeadand Bradley (1985), from a solution obtained by Herrington (1969) for radial heat flowin a semi-infiiite slab with a periodic surface temperature. Using the values for bulkdensity, specific heat and thermal diffusivity of Douglas-fir wood (Cohen et al. 1985) andthe average surface area of a trunk, and approximating the trunk surface temperatureby air temperature in the stand (assumed to vary sinusoidally), St is expressed as= 3•5ATa cos(wt— q + ir/4) (3.5)where ATa (°C) and are the amplitude and phase angle of the diurnal course of airtemperature in the stand, respectively, ‘ is the diurnal angular frequency which equals7r/12 (rad/h), and t is the time of the day.The bulk canopy resistance (re) can be obtained from the Penman-Monteith equation,i.e. the big leaf model (Monteith 1965)r = + ra[(s/7) 11 (3.6)where D is the saturation pressure deficit measured at the height of 24.0 m, y is thepsychrometric constant, s is the slope of the saturation vapour pressure curve at airChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 50temperature, ra is the aerodynamic resistance to water vapour and sensible heat diffusion between the reference height (23.0 m in the present study) and their effectivesource heights (assumed to be the same), and / is the Bowen ratio calculated from themeasured eddy fluxes. The aerodynamic resistance, ra was approximated by the aerodynamic resistance to momentum transfer (rm) without stability and roughness sublayercorrectionsra = U/Uwhere u is the mean wind speed at the reference height, and u. is the friction velocity.This simplification will not introduce much error in r since of the two terms on the RHSof (3.6), the first term is dominant.To perform the quadrant-hole analysis of the eddy fluxes of sensible heat and watervapour, the quantity cv (either air temperature or water vapour density) and the verticalvelocity component w are separated into means (, Y) and fluctuating parts (cv”, w’).The four quadrants in the cx’w’ plane are labelled as ejection (i = 1; cv’ > 0, w’ > 0),outward interaction (i = 2; cv’ < 0, W’ > 0), sweep (i 3; cv’ < 0, w’ < 0), and inwardinteraction (i 4; cv’ > 0, w’ < 0). A flux fraction F,ff and a time fraction ti,H with ahyperbolic exclusion zone set by the hole size H are defined as1 1 ,TF,H =— J w’(t)cv’(t)I,HdtIwaT oandiTti,H = j 1,Hdtwhere T is the average time interval (30 minutes in this study), and‘j,H is a conditioningfunction which equals one if the point (cv’(t), W’(t)) is located in the quadrant andI w’(t)cv’(t) is greater than H , and zero otherwise.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 513.3 Results and Discussion3.3.1 Eddy Fluxes above the Stand3.3.1.1 Energy Budget ClosureFigure 3.1 shows the sum of the eddy fluxes (H + )E) measured at z/h = 1.38 plottedagainst the available energy flux (R — S — G). On average, H + .XE accounted for83% of R — S — G. The correlation coefficient was 0.85 for a total of 118 thirty-minute runs. The following sources of error contributed to the energy imbalance and thescatter in Figure 3.1. First, neglect in (3.1) of the solar energy used in photosynthesiswould result in overestimating the available energy flux by 1—4% (Verma et al. 1986,Stewart and Thorn 1973). Second, estimating the heat storage component, S with themethod described above was subject to uncertainties. McCaughey (1985) showed thatin a dry, mixed forest, the temporal change in biomass temperature lagged behind thatin air temperature within the stand. Part of the effect of the time lag was incorporatedinto (3.5). But (3.5) was only a first order approximation, since the temporal courseof air temperature was not perfectly sinusoidal. Third, the heat flux into the soil wascharacterized by large horizontal uncertainties due to the high horizontal heterogeneityof the solar irradiance on the forest floor. Consequently, two pairs of heat flux plateswere insufficient to provide a good spatial average of G.The choice of averaging time interval is important for eddy correlation measurements.McMillen (1988) suggests a time constant of 200 seconds for the running mean removalfor the on-line computation of fluxes. Using the Reynolds averaging procedure, the fluxesand other statistics were first calculated over 5-minute intervals and averaged for each30-minute period. A large flux loss occurred, with H + \E being only 75% of R — G — S.This was due to the effect of low frequency cut-off and indicated the importance of eddiesChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 52I I a I,/600-rrVo °D a7a a —a a a4001:1 iine—4/ •u/b0 IO a a/2200- //OaOU/‘ 27/a0’ I I0 200 400 600R-S-G (W/m2)Figure 3.1: Comparison of the sum of the eddy flux densities (H + )E) measured at z/h= 1.38 and the available energy flux density (R — S — G) for the Douglas-fir stand atBrowns River during the entire experimental period in 1990. The dash line representsthe linear regression forced through zero with a slope of 0.83.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 53with periods exceeding 5 minutes. The atmosphere was moderately to strongly unstablein the daytime during the experimental period (Chapter 2). According to the estimateof McBean (1972) for the unstable surface layer, the loss of covariance resulting fromthe low frequency cut-off at 0.0033 Hz, a frequency corresponding to the period of 5minutes, is on the order of 10%. By changing the averaging time interval to 30 minutes,the energy budget closure was increased by 8% to 83%. Further increase in the averagingtime interval, however, had little effect on the computation of fluxes. The averaginginterval of 30 minutes therefore appears to be a good choice for the present study.Table 3.1 lists the daytime average components of the energy budget for the standfor the nine experimental days. The sky was clear except on 26 July and 1 August,when partly cloudy conditions occurred. The average values of R, H and AE duringthe measurement periods on the nine days were 449, 231 and 115 W/m2, respectively.On some days, energy budget closure was much better than on others. The values of theratio, (H + XE)/(R — S — G) ranged from 0.67 (31 July) to 0.96 (20 July).Figure 3.2 shows the daytime variation of the energy budget components on 1 Augustand on 28 July. On 1 August, it was partly cloudy. The fluctuations in R were closelyfollowed by the fluctuations in H and \E, and good closure was obtained. The threemain energy budget components of this day peaked at around 12:00 PST, the peak valuesof R, H and )..E being 669, 456 and 135 W/m2, respectively.It was perfectly clear on 28 July, as indicated by the smoothness of the R record. Butlarge fluctuations were observed in H and )E. There was a sigilificant energy imbalancearound noon. During the period between 11:30 and 13:00 PST, the average availableenergy flux (R— S — G) was 524 W/m2,while sensible and latent heat fluxes were only244 and 107 W/m2, respectively, with the ratio, (H + \E)/(R — S — G) being 0.66.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 54Table 3.1: Average values of the energy budget components, R, G, S, H and .\E (W/m2)during the indicated periods for the Douglas-fir stand at Browns River. Also shown arethe values of the ratio, (H + )E)/(R — S — G), and the daytime Bowen ratio, /3.Date 19 July 20 July 26 July 27 July 28 JulyHour (PST) 11:30—18:00 9:30—16:00 9:00—16:30 12:00—17:30 8:30—16:00R 462 533 444 460 512G 13 21 13 8 21S 7 23 20 15 36H 183 286 230 241 264\E 142 184 113 111 1130.76 0.96 0.83 0.81 0.83H+)ER-S-G/3 1.3 1.6 2.0 2.2Date 29 July 30 July 31 July 1 AugustHour (PST) 12:00—19:00 9:00—16:30 12:30—17:30 9:00—17:00R 376 469 319 469G 12 11 7 122.3MeanSHH+AER-S-G6171880.73222711100.873139690.6744913172311150.83182921070.911.9 2.5 2.0 2.7 2.1Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 550 I I800b0_____09 13 17Hour (PST)Figure 3.2: Energy budget closure as shown by the comparison of values of R (0) andH + \E + S + C (.) for the Douglas-fir stand at Browns River on (a) a partly cloudyday (1 August) and (b) a clear day (28 July 1990). Also shown are the variations of H(o), \E (.), G (Li) and S (x).Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 56The large imbalance did not appear to be related to the wind direction, since the daytime wind blew very constantly from the NE—NEE sector as a result of land-sea/upsiopedownslope circulations, and cannot be fully accounted for by the sources of error discussedabove. Furthermore, it was very unlikely that the imbalance was caused by instrumentmalfunction. This is demonstrated by the good agreement in the measurements madeby the two eddy correlation units. On 31 July and 1 August, the lower eddy correlationunit was operated at z/h = 1.00. In Chapter 2, it was shown that on these two days thecovariance of the vertical velocity and air temperature and the covariance of the verticalvelocity and water vapour density measured at z/h = 1.00 agreed very well with thosemeasured at z/h = 1.38. Figure 3.3 shows the daytime variation of the fluxes measured atthese two heights on 31 .July. The measurements at the two heights were almost identical.But, as on 28 July, there was a large energy imbalance around noon.The energy imba’ance is believed to be related to the cell-like structure of the flow under convective conditions in the planetary boundary layer (Thurtell, G.W. 1991, personalcommunication). In some areas there are ascending movements, which are compensatedby the descending movements in the surrounding areas (Deardorff 1973, Webb 1977).The vertical velocity at a single point, even though averaged over a certain time period,is likely different from zero. Because of the non-zero vertical velocity, the eddy correlationmeasurement made at a single point under convective conditions will tend to underestimate the vertical fluxes of sensible and latent heat. If the convection is very active, theunderestimation may be significant.3.3.1.2 Canopy Resistance and the Omega FactorThe daytime Bowen ratio increased with time during the 9-day experimental period from1.3 to 2.7 as the soil dried (Table 3.1). This is not surprising considering the steep waterretention curve for this coarse soil (Nnyamah and Black 1977) and the shallow root zone.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 57I I I600 -ej’30O-0 I I12 15 18Hour (PST)Figure 3.3: Comparison of eddy fluxes measured at z/h = 1.38 as indicated by H (.)and AE (A) and at z/h = 1.00 as indicated by H (o) and \E (A.) for the Douglas-firstand at Browns River on 31 July, 1990. Also shown are R (0) above the stand andH+,\E+G+S (.) for z/h = 1.38.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 58The canopy resistance of Douglas-fir stands has a strong dependence on the soilwater potential and saturation deficit of the air (D). It increases as soil water potentialdecreases and as D increases (Tan and Black 1976). Figure 3.4 shows the daytimevariation in r and D on 19 and 20 July. The value of r was about 300 s/rn in the midmorning, and tended to increase with time in the late afternoon as D increased. A similartime trend was also observed on the remaining days. The magnitude and the time trendreported here agree with those obtained with energy balance/Bowen ratio technique forconiferous stands of younger Douglas-fir trees under water stress (Price and Black 1990and 1991, Tan and Black 1976).Figure 3.5 shows the the courses of the daytime mean canopy resistance and saturationdeficit during the experimental period. The daytime mean canopy resistance wasobtained by weighting the half-hourly values of r by D as follows (Tan and Black 1976)— /-(D2/r)where D, and rj are the half-hourly values of D and r, and is the arithmetic averageof the daytime D. At very similar values of D, i was higher on 29 July than on 19 and20 July, a result of the steady decrease in soil water content during the experimentalperiod. During the period between 26 July and 1 August, was well correlated with .McNaughton and Jarvis (1983) and Jarvis (1985) introduced the concept of couplingbetween vegetation communities and the atmosphere in terms of the dimensionless decoupling factor=(8/7 + 1)/(s/7 + 1 + rc/ra)where IZ has values between zero and one. They suggested l values of about 0.1 to 0.2 forforests (strong coupling) and about 0.8 to 0.9 for grasslands (weak coupling). Based ontheir analyses, transpiration from trees is expected to follow closely the saturation deficitand to be controlled by the canopy resistance. Figure 3.6 shows the daytime variation ofChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 59:::.a1Hour (PST)Figure 3.4: Daytime variation of (a) canopy resistance r, and (b) saturation deficit Dfor the Douglas-fir stand at Browns River on 19 July (D) and 20 July, 1990 (s).Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 60I I I600- 6c30O-o.ozo 25°Date (July)Figure 3.5: Courses of daytime mean canopy resistance (o) and mean saturationpressure deficit i (.) for the Douglas-fir stand at Browns River in 1990.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 61Omega factor on 19 and 20 July. The mid-day value of Z was around 0.2, a value closeto those suggested by McNaughton and Jarvis (1983) and Jarvis (1985). Similar resultswere obtained on the remaining days.3.3.2 Eddy Fluxes beneath the Overstory3.3.2.1 Energy Budget ClosureAn advantage of the eddy correlation method in measuring fluxes from the forest floorand understory vegetation is that it is in situ so that the impact on the vegetation andthe environment is minimized. It is the only technique that can measure fluxes at variousheights within a forest stand. The technique is expected to give reasonable areal averagevalues of fluxes (Raupach 1989). It was used by Baldocchi and Meyers (1991) in a studyof evaporation and CO2 efflux near the forest floor of a deciduous forest. Its reliabilitycan be evaluated by examining the energy budget closure.Table 3.2 lists the daytime average value of the energy budget components beneaththe overstory of the stand. The rate of heat storage in the air and trunks was very small,and was neglected in the analysis. On 19, 20 and 26 July, eddy correlation measurementswere made at z/h = 0.12. Later, on 27 and 28 July, measurements were made at z/h =0.42, the approximate height of the canopy base. Divergence of the eddy fluxes betweenthese two heights was very small (Figure 3.9). The value of the ratio of the daytime totaleddy flux of sensible and latent heat (H + AE) to the available energy flux (R1. — G)ranged from 0.66 to 0.88, with an average value of 0.74. The large heterogeneities inR and G (see below) may be one of the reasons for the energy imbalance. But overallclosure was satisfactory, bearing in mind that each component of the energy budget wasof small magnitude.Although it was a small component in the energy budget of the whole stand, G wasChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 620.4Hour (PST)Figure 3.6: Daytime variation of Omega factor (Q) for the Douglas-fir stand at BrownsRiver on 19 July (La) and 20 July, 1990 (s).Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 63Table 3.2: Daytime average values of the energy budget components, R, G, H and \E(W/m2) beneath the overstory of the Douglas-fir stand at Browns River in July 1990.Also listed are the ratio, (H+)E)/(R —G), the daytime Bowen ratio, 3, and the relativeheight (z/h) of the measurement of H and \E.Date 19 20 26 27 28Hour (PST) 12:00-18:00 9:30-16:30 9:00-16:30 11:00-16:30 8:30-16:00z/h 0.12 0.12 0.12 0.42 0.42R 97 157 106 113 137G 11 21 13 10 21H 33 47 52 48 47E 29 48 29 26 34H+,\E 0.73 0.69 0.88 0.72 0.69/9 1.1 1.0 1.8 1.9 1.4Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 64significant in the energy budget beneath the overstory. As above the stand, H was thelargest output component of the energy budget, but was not as dominant. The value ofwas close to one on the first two days (19 and 20 July) and greater than one on thelater three days (26, 27 and 28 July), with a mean value of 1.4. The increase of /9 withtime was a result of soil drying and was consistent with the trend of the Bowen ratioabove the stand. However, the value of 3 beneath the overstory was smaller than thatabove the stand.3.3.2.2 Temporal and Horizontal Variations in the Energy Budget ComponentsFigure 3.7 presents the daytime variation of the energy budget components beneath theoverstory and the net radiation flux above the stand on 20 and 26 July. It was clear on20 July and partly cloudy on 26 July. The midday values of H and .AE were about 60and 70 W/m2 on 20 July and 90 and 40 W/m2 on 26 July, respectively. The trends ofH and \E was similar to the trend of the net radiation above the stand rather than Rmeasured near the forest floor.Considerable fluctuations occurred in R measured near the forest floor, even underclear sky conditions (Figure 3.7b). This means that the pathway of the tram systemwas not long enough to obtain a good spatially averaged value of R. Large fluctuationsalso occurred in C. To obtain more reliable measurements of R and C in this stand,the length of the tram pathway and the number of heat flux plates would have to beincreased.The optimal length of the pathway of the tram depends on crown closure. The sametram system has given satisfactory measurements of shortwave and longwave irradiancesin an unthinned Douglas-fir stand of similar age (Black et al. 1991). The pathwaylength/tree spacing ratio in that study was about 6.3. Using this ratio as a rule of thumb,Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 65300- ‘600200 400100- 2000 0300 ‘600b1R200- 400100 200Hour (PST)Figure 3.7: Variation of the energy budget components, R (D), H (o), )E (.) andG (Li) beneath the overstory of the Douglas-fir stand at Browns River on (a) a partlycloudy day (26 July) and (b) a clear day (20 July, 1990). Also shown is the variation ofthe net radiation flux density above the stand (.).Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 66the pathway length should have been increased to 26 m for a reliable measurement of Rin the present study.Figure 3.8 compares the kinematic sensible heat flux w’T’ near the forest floor measured at four positions with three 1-dimensional sonic anemometer/thermocouple unitsand one 3-dimensional sonic anemometer/thermometer unit. Good agreement was obtained among the measurements of the three 1-dimensional units: much of the scatter fellin the range of ±15%. The flux measured with the 3-dimensional unit was slightly lowerthan that measured with the 1-dimensional units. The results indicate that the eddycorrelation measurement made at the height of 2 m provided a good spatial average ofthe sensible heat flux from the forest floor and the understory in this pruned and thinnedstand.3.3.3 Profiles of Eddy FluxesFigure 3.9 shows the sensible heat and water vapour fluxes at various heights in thestand as fractions of the corresponding fluxes at z/h = 1.38. There appear to be twoconstant flux layers, one above the tree tops and the other in the trunk space. Withinthe canopy layer, the fluxes increased approximately linearly with height. This pattern ofvertical profiles, also observed by Denmead and Bradley (1985) in a pine forest, reflectsthe density distributions of the sensible heat and water vapour sources. The stand in thepresent study had two distinct sources: the forest floor (including a little short understoryvegetation) and the canopy, separated by the trunk space of approximately 6 m in height.While flux divergences in the trunk space were very small because of the negligible sourcedensity in the trunk space, the non-zero source density of the foliage resulted in large fluxdivergences in the canopy layer. But the divergences were not proportional to the leafarea density. For example, based on Figure 3.9, of the total flux divergence of sensibleheat in the canopy layer, 54% came from the layer between z/h = 0.60 and 1.00, whichChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 670.18 /(m°C/s) i:iZ0.12- Dd/ -V a v+v O -J•JJ LLI00 V‘4 1,-V 13. +DV//,r+ + +— I + I—-0.06 0 0.06 0.12 0.18w’T’, #1139Figure 3.8: Comparison of the kinematic sensible heat flux ?T7at 2 m (z/h = 0.12) abovethe forest floor of the Douglas-fir stand at Browns River measured at four positionsin July 1990 with three 1-dimensional sonic anemometer/thermocouple units (#1138,#1139, #1143) and one 3-dimensional sonic anemometer/thermometer unit (3-d): (D),#1138; (v) #1143; (+), 3-d.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 681.51.0N0.5-00 0.5 1.0Normalized eddy fluxFigure 3.9: Normahzed profiles of daytime averaged sensible heat flux (o) and watervapour flux (.) in the Douglas-fir stand at Browns River in 1990. The average values ofthe standard error of the mean was 0.085 at z/h = 0.60 and 0.025 at all other heights.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 69had 40% of the canopy leaf area (Chapter 2), and 46% came from the layer below z/h= 0.60, which had 60% of the canopy leaf area. In other words, for the same amount ofleaf area, the source density of sensible heat was higher in the upper canopy than in thelower canopy. This might be a result of higher radiation absorption per unit leaf area inthe upper canopy than in the lower canopy.The profiles of sensible heat and water vapour fluxes were somewhat dissimilar inthat the forest floor contributed less to the total sensible heat flux from the stand (19%)than to the total water vapour flux (26%). This may imply the inequality of the effectivesource heights for sensible heat and water vapour. By analogy to the centre-of-pressuretheorem (Thom 1971), the effective source height, d can be expressed asd = zS(z)dz (3.7)fS(z)dz+Fgwhere S(z) is the flux divergence or source density at height z and Fg is the flux fromthe forest floor. Physically, (3.7) defines the height of the zero-plane displacement. Withthe aid of the data in Figure 3.9, (3.7) gives an estimate of d = 9.6 m or d/h = 0.57for sensib]e heat and d = 8.7 m or d/h = 0.52 for water vapour. The difference in d/hbetween sensible heat and water vapour was small compared to the large uncertaintiesin the ratio d/h for forests (Jarvis et al. 1976), and seems to support the general use ofa single d for heat and water vapour (Thom 1972).Both sensible heat and water vapour fluxes within the stand were directed upward forthe majority of the runs. The numbers of the runs with upward sensible heat flux (totalnumbers of runs in brackets) at z/h = 0.12, 0.40 and 0.60 were 40 (42), 27 (28) and 26(29), respectively, and the corresponding figures for water vapour flux were 41 (42), 27(28) and 29 (29). The runs with downward fluxes occurred during the quiescent periodsin the late afternoon when the upslope wind was being replaced by the downslope wind,and the fluxes were very small. Daytime air temperature characteristically exhibited aChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 70maximum near the ground and an inversion in the layer between z/h 0.28 and 0.60(Chapter 4). In other words, sensible heat constantly flowed against the temperaturegradient in the inversion layer, a phenomenon termed counter-gradient flow that hasbeen frequently observed in forests (Denmead and Bradley 1985, Amiro 1990, Leclerc1987). The existence of counter-gradient flow is due in part to the sporadic penetrationof transporting eddies into the canopy and their large scales (Denmead and Bradley1985). In the context of a Lagrangian framework, it can be understood as a near-fieldeffect of the canopy heat source (Raupach 1987). The phenomenon of counter-gradientflow at these heights invalidates K-theory. However, K-theory appears to be able to givea reasonable prediction of fluxes near the forest floor (Chapter 4).3.3.4 Quadrant Representation of Eddy FluxesThe technique of quadrant-hole analysis has been widely used to reveal the structureof turbulent transfer of momentum and scalars in vegetation canopies (e.g. Shaw et al.1983, Finnigan 1979, Coppin et al. 1986, Chapter 2). In Chapter 2, it was shown thata major proportion of momentum transfer near the top of the stand and in the canopylayer occurred during intense intermittent sweep/ejection events. It was also shown thatthe magnitude of interaction contributions to the momentum transfer was greater thanthat of sweep/ejection contributions at the canopy base (z/h = 0.42) and in the middle ofthe trunk space (z/h = 0.12), which was consistent with the negative values of Reynoldsstress at these heights.Table 3.3 lists the set of the selected runs (same as used in Chapter 2) for performingthe quadrant-hole analysis of sensible heat and water vapour fluxes. The results aresummarized in Tables 3.4 and 3.5, where H’ is the hole size above which half of the fluxChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 71Table 3.3: Values of the covariances of the vertical velocity component and air tern—perature () and the vertical velocity component and water vapour densitystandard deviations of air temperature (0T), water vapour density (o,,) and the verticalvelocity component (am) at the indicated heights for the five runs selected for quadrant-hole analysis of eddy fluxes of sensible heat and water vapour for the Douglas-firstand at Browns River. The stability parameter (z — d)/L was calculated from the measurements at z/h = 1.38.Time interval z/h (z—d)/L w’T’ ‘P’ °T 0Pv WPST m0C/s g/(m2s) °C g/m3 rn/s13:30—14:00 0.12 —0.26 0.055 0.008 0.66 0.32 0.1919 July12:00—12:30 0.42 —0.25 0.112 0.015 0.75 0.15 0.3227 July12:30—13:00 0.60 —0.35 0.117 0.006 0.76 0.16 0.3330 July13:30—14:00 1.00 —0.25 0.217 0.017 0.77 0.12 0.541 Aug12:00—12:30 1.38 —0.25 0.335 0.033 0.78 0.17 0.7527 JulyChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 72occursIFi,HII=O.5and t,Hl is the corresponding time fraction. H’ and tI,HI are measures of intermittency. The intermittent nature of the turbulent transport is obvious at all levels: Half ofthe sensible heat flux was accounted for by events with a hole size larger than 5.7—3.5,which occupied a small fraction of time (6—11%), while for water vapour flux the valuesof H’ and tj,Hl were 34.6—5.2 and 1—10%, respectively.The relative importance of the kinds of turbulent motion in the transport of scalars canbe examined by calculating the ratios of the flux fractions at zero hole size. The variationof the ratio,F30/F1with height was related to the source distributions. For sensible heatflux, it had values less than one at the tree tops (z/h = 1.00) and above the stand (z/h =1.38), indicating that the ejection contribution to sensible heat flux exceeded the sweepcontribution. The sweep contribution exceeded the ejection contribution in the middleand at the base of the canopy (z/h = 0.60 and 0.42), with the ratioF3,0/F1greater thanone. Close to the ground, at z/h = 0.12, the ejection contribution again exceeded thesweep contribution. For water vapour flux, the ejection and sweep contributions wereof about equal magnitude at z/h = 1.38 and 1.00. At z/h = 0.60 and 0.42, the sweepcontribution was greater than the ejection contribution, but the ejection contributionexceeded the sweep contribution at z/h = 0.12.The ratio of the contribution of the interactions to that of the sweeps/ejections,(F2,9 +F4,0)/(F1+ F3,0), varied between —0.23 and —0.13 for sensible heat flux andbetween —0.67 and —0.30 for water vapour flux (Tables 3.4 and 3.5). In Chapter 2, itwas shown that the magnitude of this ratio for momentum flux exceeded one at z/h = 0.42and 0.12. This was not the case for sensible heat and water vapour fluxes. At z/h = 0.42,where the air temperature inversion occurred, the magnitude of the ratio was smaller thanChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 73Table 3.4: Summary of the results of quadrant-hole analysis for sensible heat flux of thefive runs in Table 3.3.z/h 0.12 0.42 0.60 1.00 1.38H’ 5.7 5.2 4.6 3.5 3.74Eti,H? 0.064 0.067 0.080 0.107 0.110i=1F2,0 + F4,0—0.21 —0.23 —0.19 —0.13 —0.16F1,0 + F3,00.81 1.20 1.39 0.82 0.75F1,0Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 74Table 3.5: Summary of the results of quadrant-hole analysis for water vapour flux of thefive runs in Table 3.3.z/h 0.12 0.42 0.60 1.00 1.38H’ 17.4 8.2 34.6 5.0 5.2>t1,H’ 0.047 0.050 0.009 0.102 0.101F2,0+F4,0-0.67 -0.37 -0.71 -0.30 —0.30F1,0 + F3,00.87 1.15 1.50 1.09 1.03F1,0Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 75one (0.23). This indicates that the transport of sensible heat at this height was of largescale and was no longer driven by the local temperature gradient.Figure 3.10 shows the sensible heat flux fraction at different heights plotted againstthe hole size. Unlike the case for momentum flux, there was very little contribution fromthe interactions beyond H = 6. For example, (F2,6 +F4,6)/(F1+ F3,6), the ratio of thecontribution of the interactions to that of sweeps/ejections at H = 6, was —0.003 at z/h= 0.60 for sensible heat flux, while the corresponding ratio for momentum flux was muchmore negative, with a value of —0.124. This difference, together with the difference in themagnitude of the ratio(F2,0+4)/(F13,indicates that the transfers of momentumand sensible heat are dissimilar due to different mechanisms and source distributions.These results agree broadly with the observations made in other experimental studiesin and immediately above vegetation canopies (Coppin et al. 1986, Gao et al. 1989,Maitani and Shaw 1990, Bergstrom and Hogstrom 1989), with some differences in thefine details. For example, the sweep dominated region for sensible heat flux for the standin the present study was confined below the tree tops, while the sweep dominated regionfor a mixed deciduous forest reached as high as z/h = 1.9 (Maitani and Shaw 1990).3.4 Summary and ConclusionsResults have been presented of the analysis of the daytime eddy fluxes of sensible heatand water vapour within and above a Douglas-fir stand under low soil water conditions.The sum of sensible and latent heat fluxes above the stand accounted for, on average, 83%of the available energy flux. But on some days, energy budget closure was far better thanon others. The occurrences of large energy imbalance on several occasions are believedto be associated with the possible non-zero value of the vertical velocity measured at asingle point and averaged over a short time interval under convective conditions.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapouri= 3SweepH76Figure 3.10: Flux fraction F,H plotted against hole size H for sensible heat flux at z/h= 1.38 (x), 1.00 0.60 (o), 0.42 (+), and 0.12 (D).1.00.500I I Ii=2Outward interactionI II Ii= 1Ejectioni=4Inward interactionI I0.51.0 -)30 20 10 0 0 10 20 30Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 77The sum of sensible and latent heat fluxes beneath the overstory accounted for 74% ofthe available energy flux. One of the reasons for the energy imbalance was that the smallnumber of soil heat flux plates and the short radiometer pathway of the tram systemwas unable to account for the large horizontal heterogeneity in the available energy fluxbeneath the overstory. The eddy flux of sensible heat, on the other hand, exhibited verylittle horizontal variation. Good agreement was obtained among the measurements ofsensible heat flux made at z/h = 0.12 at four positions 15 m apart.Sensible heat flux was the main output component of the energy budget both aboveand beneath the overstory. The average Bowen ratio had a value of 2.1 above the standand 1.4 beneath the overstory. The mid-morning value of the canopy resistance wasabout 300 s/m in the early stage of the experiment and mid-day value of the Omegafactor was about 0.20. The daytime mean canopy resistance showed a strong dependenceon the mean vapour saturation deficit during the two-week experimental period.The profiles of the eddy fluxes reflect source distributions. There was a constant fluxlayer in the trunk space, a large flux divergence in the canopy layer, and a constant fluxlayer above the stand. Counter-gradient flux of sensible heat constantly occurred at thebase of the canopy (z/h = 0.42).The transfer of sensible heat and water vapour was dominated by intermittent sweepand ejection events at all levels. The ratio of the sweep contribution to the ejectioncontribution was influenced to a large degree by the source distributions. For sensibleheat flux, the ratio was greater than one in the canopy layer and less than one above thestand and near the forest floor.3.5 ReferencesAmiro, B.D.: 1990, ‘Comparison of turbulence statistics within three Boreal forestChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 78canopies’, Boundary-Layer Met eorol. 51, 99-121.Baldocchi, D.D. and Hutchison, B.A.: 1987, ‘Turbulence in an almond orchard: Verticalvariations in turbulence statistics’, Boundary-Layer Met eorol. 40, 127-146.Baldocchi, D.D. and Meyers, T.P.: 1991, ‘Trace gas exchange above the floor of adeciduous forest. I: Evaporation and CO2 efflux’, J. Geophys. Res. 96(D4),727 1-7286.Bergstrom, H. and Hogstrom, U.: 1989, ‘Turbulent exchange above a pine forest. II:Organized structure’, Boundary-Layer Meteorol. 49, 231-264.Black, A.T., Chen, J.M., Lee, X. and Sagar, R.M.: 1991, ‘Characteristics of shortwaveand longwave irradiances under a Douglas-fir stand’, Can. J. For. Res. 21, 1020-1028.Cohen, Y., Kelliher, F.M. and Black, T.A.: 1985, ‘Determination of sap flow in Douglas-fir trees using the heat pulse technique’, Can. J. For. Res. 15, 422-428.Coppin, P.A., Raupach, M.R. and Legg, B.J.: 1986, ‘Experiments on scalar dispersionwithin a model plant canopy. Part II: An elevated plane source’, Boundary-LayerMeteorol. 35, 167-191.Deardorff, J.W.: 1973, ‘Three-dimensional numerical modeling of the planetary boundary layer’, in Haugen, D.A. (ed.), Workshop on Micrometeorology, American Meteorological Society, 271-311.Denmead, O.T. and Bradley, E.F.: 1985, ‘Flux-gradient relationships in a forest canopy’,in Hutchison, B.A. and Hicks, B.B. (eds.), The Forest-Atmospheric Interaction, D.Reidel Publishing Co., Dordrecht, 421-442.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 79Finnigan, J.J.: 1979, ‘Turbulence in waving wheat. Part II: Structure of momentumtransfer’, Boundary-Layer Met eorol. 16, 213-236.Fuchs, M. and Tanner, C.B.: 1968,’ Calibration and field test of soil heat flux plates’,Soil Sci. Soc. Am. Proc. 32, 326-328.Gao, W., Shaw, R.H. and Paw U, K.T.: 1989, ‘Observation of organized structure inturbulent flow within and above a forest canopy’, Boundary-Layer Meteorol. 47,349-377.Herrington, L.P.: 1969, ‘On temperature and heat flow in tree stems’, School of ForestryBulletin No.73, Yale University.Jarvis, P.G.: 1985, ‘Transpiration and assimilation of tree and agricultural crops: The‘Omega factor”, in Cannell, M.G.R. and Jackson, J.E. (eds.), Attributes of Trees asCrop Plants, I.T.E. (NERC), Monkswood Experimental Station, Abbots Ripton,Huntinghon, England, 460-480.Jarvis, P.G., James, G.B. and Landsberg, J.J.: 1976, ‘Coniferous forest’, in Monteith,J.L. (ed.), Vegetation and the Atmosphere II: Case Studies, Academic Press, NewYork, 171-240.Leclerc, M.Y.: 1987, ‘Turbulence and turbulent diffusion inside and above vegetation’,Ph.D. Thesis, University of Guelph, Guelph, Ontario.Maitani, T. and Shaw, R.H.: 1990, ‘Joint probability analysis of momentum and heatfluxes at a deciduous forest’, Boundary-Layer Met eorol. 52, 283-300.Massman W J, Fox, D.G., Zeller, K.F. and Lukens, D.: 1990, ‘Verifying eddy correlationmeasurements of dry deposition: A study of energy balance components of theChapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 80Pawnee Grasslands’, USDA Forest Service, Research Paper RM-288, Fort Collins,U.S.A, l4pp.McBean, G.A.: 1972, ‘Instrument requirements for eddy correlation measurements’, J.Appi. Meteorol. 11, 1078-1084.McCaughey, J.H.: 1985, ‘Energy balance storage terms in a mixed forest at Petawawa,Ontario: A case study’, Boundary-Layer Meteorol. 32, 1-24.McMillen, R.T.: 1988, ‘An eddy correlation technique with extended applicability tonon-simple terrain’, Boundary-Layer Meteorol. 43, 231-245.McNaughton, K.G. and Black, T.A.: 1973, ‘A study of evapotranspiration from aDouglas-fir forest using the energy balance approach’, Water Res. Res. 9, 1579-1590.McNaughton, K.G. and Jarvis, P.C.: 1983, ‘Predicting the effects of vegetation changeson transpiration and evaporation’, in Kozlowski, T.T. (ed.), Water Deficits andPlant Growth, Academic Press, New York, 1-47.Monteith, J.L.: 1965, ‘Evaporation and environment’, in Fogg, G.E. (ed.), The Stateand Movement of Water in Living Organisms, Academic Press, New York, 1-47.Nnyamah, J. U. and Black, T.A.: 1990, ‘Rate and patterns of water uptake in a Douglas-fir stand’, Soil Sci. Am. J. 41, 972-979.Price, D.T. and Black, T.A.: 1991, ‘Effects of summertime changes iii weather and rootzone soil water storage on canopy CO2 flux and evapotranspiration of two juvenileDouglas-fir stands’, Agric. For. Met eorol. 53, 303-323.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 81Price, D.T. and Black, T.A.: 1990, ‘Effects of short-term variation in weather on diurnalcanopy CO2 flux and evapotranspiration of juvenile Douglas-fir stand’, Agric. For.Meteorol. 50, 139-158.Raupach, M.R.: 1989, ‘Stand overstory processes’, Phil. Trans. R. Soc. Lond. B324,175-190.Raupach, M.R.: 1987, ‘A Lagrangian analysis of scalar transfer in vegetation canopies’,Quart. J. R. Meteorol. Soc. 113, 107-120.Shaw, R.H., Tavangar, J. and Ward, D.P.: 1983, ‘Structure of Reynolds stress in acanopy layer’, J. Climate Appl. Meteorol. 22, 1922-1931.Shuttleworth, W.J., Cash, J.H.C., LLoyd, C.R., Moore, C.J., Roberts, J., Filho, A.D.O.M.,Fuchs, G., Filho, V.D.P.S., Molin, L.C.B., Abreu Sa, L.D.D., Nobre, J.C.A., Cabral,O.M.R., Patel, S.R. and Moraes, J.C.D.: 1984, ‘Eddy correlation measurements ofenergy partition for Amazonian forest’, Quart. J. R. Meteorol. Soc. 110, 1143-1162.Stewart, J.B. and Thom, A.S.: 1973, ‘Energy budgets in pine forest’, Quart. J. R.Meteorol. Soc. 99, 154-170.Tan, C.S. and Black, T.A.: 1976, ‘Factors affecting the canopy resistance of a Douglas-firforest’, Boundary-Layer Met eorol. 10, 475-488.Tanner, C.B. and Thurtell, G.W.: 1969, ‘Anemoclinometer measurements of Reynoldsstress and heat transport in the atmospheric surface layer’, Research and Development Technical Report ECOM-66-G22-F, University of Wisconsin, Madison, Wisconsin.Chapter 3. Eddy Fluxes of Sensible Heat and Water Vapour 82Thom, A.S.: 1972, ‘Momentum, mass, and heat exchange of vegetation’, Quart. J. Roy.Meteorol. Soc. 98, 124-134.Thom, A.S.: 1971, ‘Momentum absorption by vegetation’, Quart. J. Roy. Meteorol.Soc. 97, 414-428.Verma, S.B., Baldocchi, D.D., Anderson, D.D., Matt, D.R. and Clement, R. J.: 1986,‘Eddy fluxes of C02, water vapor, and sensible heat over a deciduous forest’,Boundary-Layer Met eorol. 36, 71-9 1.Webb, E.K.: 1977, ‘Convection mechanisms of atmospheric heat transfer from surfaceto global scales’, in Bilger, R.W. (ed), Second Australian Conference on Heat andMass Transfer, The University of Sydney, 523-539.Webb, E.K., Pearman, G.I. and Leuning, R.: 1980, ‘Correction of flux measurementsfor density effects due to heat and water vapour transfer’, Quart. J. R. Meteorol.Soc. 106, 85-100.Chapter 4Observation and Lagrangian Simulation of Air Temperature Profiles4.1 IntroductionMany problems in agricultural and forest research require an understanding of the dispersion of atmospheric scalar constituents such as heat, water vapour, C02, trace gases,spores, pollen and other aerosols in vegetation canopies (e.g. Raupach et al. 1989a, Aylor1989, Di-Giovanni and Kevan 1991). It is well known that K-theory is not adequate todescribe the dispersion process in the canopy. In the search for alternatives, much attention has been focused on the simulation in a Lagrangian framework. Using the expressionof Taylor (1921) for the second moments of concentration distribution in homogeneousturbulence, Raupach (1987) demonstrated the near-field effect of the canopy source onthe concentration profiles of scalar quantities in a plant canopy and explained phenomenasuch as counter-gradient flux. Later, Raupach (1989b) developed a localized near-fieldtheory which expresses the mean scalar concentration as the sum of diffusive far-field andnon-diffusive near-field contributions. While these analytical models are relatively easyto use, the assumptions involved in the model development may limit their applications.Random flight models, on the other hand, can incorporate the inhomogeneity characteristic of the turbulent motion in the canopy environment. In these models, an ensemble ofparticle trajectories is constructed numerically from one or a set of stochastic differentialequations which determine the evolution of the Lagrangian velocity of a marked fluidparticle. Random flight models have been used for the dispersion of scalars in canopy83Chapter 4. Observation and Simulation of Air Temperature Profiles 84environments from elevated line sources (Legg et al. 1986, Leclerc et al. 1988), fromhypothetical elevated plane sources (Wilson et al. 1981b, Wilson et al. 1983) and fromhypothetical canopy sources (Raupach 1989b). However, there have been fewer studies performed to simulate the dispersion processes related to outdoor extensive canopysources/sinks.An experiment to study the exchange processes within and above an extensive coniferous stand of Douglas-fir trees was described in Chapters 2 and 3. The experimentprovides a data set for testing and further development of the Lagrangian theory ofscalar dispersion in the canopy environment. Accordingly, the specific objectives of thischapter are (1) to examine the profiles of air temperature in relation to the sensible heatsource/sink distributions in the stand, (2) to simulate the profile of air temperature usinga random flight model, and (3) to discuss the applicability of K-theory near the forestfloor.4.2 Experimental MethodsDetails of the experimental methods can be found in Chapter 2 and Chapter 3. Thefollowing is a brief summary of the information relevant to this Chapter.4.2.1 Site DescriptionThe experimental site was located near Browns River approximately 10 km northwest ofCourtenay on Vancouver Island, 125°10’W, 49°42’N. The overstory species is Douglasfir, planted in 1962. In 1988, it was thinned to a density of 575 stems/ha and pruneduniformly to a height of approximately 6 m. The height of the stand was 16.7 m, andthe total (projected) leaf area was 5.4. The forest floor was littered with dead branchesand trunks, with a sparse understory vegetation less than 0.5 m tall.Chapter 4. Observation and Simulation of Air Temperature Profiles 85The experiment was conducted in late July and early August 1990. The weatherremained mostly clear during the experimental period. There was water stress of thetrees as indicated by yellowing of the needles. Sensible heat flux was the main outputcomponent of the energy budget, with daytime average values of 230 W/m2 above thestand and 45 W/m2 beneath the overstory, and the daytime Bowen ratio of the standvaried from 1.3 to 2.7 during the course of the experiment (Chapter 3).4.2.2 InstrumentationEddy flux of sensible heat and other turbulence statistics were measured in the daytimewith two eddy correlation units mounted on an open lattice 25 cm wide triangular tower.One unit was operated permanently at a height of 23.0 m (z/h = 1.38), and the otherunit at various heights within the stand, with 2-3 eight hour periods at each height. Airtemperature and wind speed was measured continuously during the experimental periodwith fine wire thermocouples and sensitive cup anemometers, respectively, at heights of(z/h in brackets) 0.9 (0.05), 2.0 (0.12), 4.6 (0.28), 7.0 (0.42), 10.0 (0.60), 12.7 (0.76), 16.7(1.00), and 23.0 m (1.38). This Chapter focuses on the measurements made on 19, 20and 26 July, when the lower eddy correlation unit was operated at a height of 2.0 m (z/h= 0.12).4.3 The Model4.3.1 Construction of TrajectoriesThe dispersion of sensible heat can be represented by the random walk of ‘hot’ fluidparticles. Consider the dispersion in only the vertical direction, with w representingthe Lagrangian vertical velocity of a marked ‘hot’ particle at time t. Horizontally,the particle moves at the Eulerian streamwise velocity u. Neglecting dispersion in theChapter 4. Observation and Simulation of Air Temperature Profiles 86horizontal direction will cause only a small error (Raupach 1989b). The particle positionevolves according to the following equationsZn+ = Zn + 1n=1,2,... (4.1)Xri = Xn + U(Zn)Ltn Jwhere /tn is the time step at time t, and x and z, are the horizontal and verticalcomponents of the position vector at time tn, with (x1, Zi) being the position of theparticle at release. The sequence {w} is Markovian, and can be formed as= aw + ba,(z)+i + C Ti = 1,2, ... (4.2)where is a random number from a Gaussian distribution with zero mean and unitvariance, u(z) is the square root of the variance of the Lagrangian vertical velocity atheight Z,, and a, b, and c are coefficients specified asa = e_t1/TL()b = (1 — a2)u/2 (43)C = f(Zn)TL(Zn)(1 — a)with f(Zn) being the gradient of the variance of the Eulerian vertical velocity at heightZn‘2IJWJ Z) —and TL(Zn) being the Lagrangian integral time scale at height z,,. (Legg and Raupach1982). The third term on the RHS of (4.2) accounts for the effect of the mean force onthe marked particle due to the action of the mean pressure gradient. In the neutral surfacelayer, it is negligible. But it cannot be neglected in the vegetation canopy where thereis always a significant vertical gradient in w. A positive mean vertical velocity of theparticle, called biased velocity (Wilson et al. 1981b) or drift velocity (Legg and Raupach1982), arises from this term. For the special case of constant TL and f, an analyticalChapter 4. Observation and Simulation of Air Temperature Profiles 87solution has been derived, based on the differential form of (4.2), for air temperatureand vertical sensible heat flux from an elementary point source (Appendix D), which canthen be superposed to obtain the solutions for the plane and canopy sources. In general,however, air temperature and vertical heat flux can only be obtained using the randomflight technique.Before the construction of the particle trajectory, a set of 2000 Gaussian pseudo-random numbers with zero mean and unit variance are generated using= (_2lnui)h/2cos(2iruj i = 1—2000where {u,} is a set of uniform pseudo-random numbers in the range 0 to 1 (Abramowitzand Stegun 1964, pp 949-953). For each step of the flight, a Gaussian number is randomlydrawn from the set {,}. The initial vertical velocity is given by=As a common practice, the Lagrangian velocity variance, aj is assumed to be equal tothe Eulerian velocity variance, w at all positions (e.g. Wilson et al. 1981a). The timestep is chosen as= 0.2T(z,jThe ground surface is treated as being reflective.4.3.2 Simulation of Air Temperature and Vertical Sensible Heat FluxFor steady state conditions in an extensive horizontally homogeneous canopy (advectionfree) specified by a sensible heat source density 5(z) with dimensions of W/m3, theconservation of sensible heat requires (Raupach 1 989b)dH(z)/dz = S(z) (4.4)Chapter 4. Observation and Simulation of Air Temperature Profiles 88where H is the vertical sensible heat flux (with dimensions of W/m2). Integration of(4.4) with respect to z givesH(z) = H9 + j S(z’)dz’ (4.5)where H9 is the sensible heat flux from the ground-level source. Equations of the formof (4.4) and (4.5) also apply to scalars other than sensible heat. For an extensive foreststand with a trunk space relatively free of branches and needles, or sources/sinks, theflux profiles of scalars typically exhibit a constant flux layer in the trunk space, a largeflux divergence in the canopy layer and a constant flux layer above the stand (Chapter 3,Denmead and Bradley 1985, Denmead and Bradley 1989). This feature is consistentwith (4.5). The total flux above the stand or the total source density of the stand canbe expressed asHT H9 + j S(z’)dz’ (4.6)where h is the height of the stand (h = 16.7 m in the present study).Potential air temperature, 0 is separated into two parts, the contribution from thecanopy source (O) and the contribution from the ground-level source (Os), as0(z) = 0(z) + 09(z)The simulation technique for 0 is that of Raupach (1989b). In the simulation, M particles(M 2000 in the present study) are released at the leading edge (x = 0) of the canopysource. The initial height, z1 of particle m is chosen from a distribution with the shapeof S(z). The particle moves according to (4.1) and (4.2) until it reaches the streamwiseposition x = x, (‘horizontal fetch’). It can be shown that the potential temperature andthe vertical heat flux at x = areM0(z)= pu(z) Mz , <Xm > (z, z + z)Chapter 4. Observation and Simulation of Air Temperature Profiles 89andH’(z) = Hg + (HT — Hg)MC5respectively, where < Xm > (z, z + Liz) is the total streamwise distance traversed byparticle m while it lies between height z and z + /-z and Mcross(z) is the net number ofparticles that cross height z between x = 0 and x = x. As the fetch x increases, H’(z)converges to H(z).The simulation technique for °g is based on the assumption that the dispersion fromthe ground-level source is basically diffusive (Hunt and Weber 1979, Raupach 1983), thusHg=PcPKf0 (4.7)where Kf is a far-field eddy diffusivity expressed as (Raupach 1989b)Kf = O,(z)TL(z) (4.8)Integrating (4.7) and using (4.8), °g is found to beOg(z)— Og(zr)= jrwhere Zr is a reference height (Zr = 23.0 m in the present study).The source density of sensible heat in the canopy, S was estimated from the measuredprofiles of leaf area density and sensible heat flux. According to the measurementsreported in Chapter 3, of the total source density of the canopy, 54% was from the layerbetween z/h 0.60 and 1.00 and 46% was from the layer below z/h = 0.60. Thesepercentages were further partitioned into values as a function of height assuming thatthe source density was proportional to the measured leaf area density. The S profileobtained in this manner is well represented by a beta function as follows— 5 5 0.80— 5 1.446.9( 55) (1— 55) 5.5 < z < hS(z) = (4.9)0 z<5.5 and z>hChapter 4. Observation and Simulation of Air Temperature Profiles 90where z is in metres and the height of the stand is h = 16.7 m.The velocity field is specified byz—11.7 z7—11.7ln 0.21 / in 0.21 z> hU(Z)/U(Zr) = (4.10)0.8sinh(3.5)/sinh3.5 + 1.7(.)°(1 — Z)36 z < h1 z>hJw(Z)/0w(Zr) = (4.11)()° z < hand0.43 z>houj (zr)TL(z) (4.12)0.43 h 0<zho•w (z,.)where the reference height z. was 23.0 m. Equation (4.10) fits well with the measuredwind speed profile in the Douglas-fir stand presented in Chapter 2. Equation (4.11) isbased on the fact that the variance of the vertical velocity component was approximatelylinear with height (Chapter 2). The Lagrangian time scale has the same form as that usedby Leclerc et al. (1988), with the value of the constant adjusted slightly to obtain goodpredictions for sensible heat flux from the forest floor. Experimental evidence appears tosupport the use of constant TL within the stand (Legg et al. 1986, Leclerc et al. 1988).It follows from (4.11) and (4.12) that K increases linearly with height. Figure 4.1 showsthe plots of (4.9—4.12).Chapter 4. Observation and Simulation of Air Temperature Profiles 911.5hT1.0-_/Gw0.5-aw(zr)____________________ _________I I00 0.2 0.4 0 0.5 1.0Figure 4.1: Profiles of S(z), u(z), u(z) and TL(z) used as model inputs. See Equations (4.9—4.12) for analytical forms.Chapter 4. Observation and Simulation of Air Temperature Profiles 924.4 Results and Discussion4.4.1 Observation of Air Temperature Profiles4.4.1.1 Diurnal Changes in the Air Temperature ProfileIn the context of Lagrangiari theories, potential temperature 9 in a vegetation canopyis determined by the combination of the sensible heat source/sink density distributionS and the statistics of the velocity field. The effect of S on 0 can be examined qualitatively without the precise knowledge of the velocity field. The stand in the presentstudy consisted of two distinct sensible heat sources/sinks separated by a trunk space ofapproximately 6 m in height: the ground-level forest floor source/sink (including somesparse short understory) and the elevated canopy source/sink. At night, the canopy wasa sensible heat sink due to the radiative cooling of the foliage, and the forest floor waseither a sensible heat source or sink depending on whether or not the heat flux fromthe soil exceeded the net radiation flux from the forest floor. In the daytime, both thecanopy and the forest floor were sensible heat sources.Figure 4.2 shows the diurnal change in the 0 profile observed on 26 July. Beforesunrise, the net radiation flux at z/h = 1.38 was very small in magnitude, with an averagevalue of —5 W/m2 for the period between 00:00 and 05:00 PST. This was because therewas complete cloud cover during this period. Consequently, the magnitude of S wassmall, and so 0 at 00:00 and 03:00 PST showed only a little change with height. Theground was probably acting as a heat source during this period, resulting in a smallnegative 0 gradient near the forest floor.After sunrise, both the canopy and the forest floor acted as sensible heat sources. Thedaytime 0 profile during the experimental period always exhibited a negative gradientin the layer between z/h = 0.05 and 0.28, a positive gradient (inversion) in the layerChapter 4. Observation and Simulation of Air Temperature Profiles 930 6:00 13:001.5- 3:00 10:00 15:00 17:30 19:30 23:301.0N0.5hod0—Potential temperature—>Figure 4.2: Diurnal change in the profile of the 30-minute averaged potential temperatureobserved in the Douglas-fir stand at Browns River on 26 July 1990. The time shown abovethe profiles marks the end of each 30-minute run.Chapter 4. Observation and Simulation of Air Temperature Profiles 94between z/h = 0.28 and 0.60, and a peak at z/h = 0.60 where the leaf area density washighest (Chapter 2). The peak of the potential temperature can be viewed as a resultof the near-field effect of the canopy sensible heat source. On 26 July, the inversion wasstrongest between 12:30 and 15:00 PST.The sky was clear in the evening of 26 July, with an average value of —65 W/m2for the net radiation flux at z/h = 1.38 for the period between 20:00 and 24:00 PST.The intensive radiative cooling caused the canopy as well as the forest floor to be strongsensible heat sinks. The 0 profile at 23:30 PST showed the typical features under clearsky conditions at night: 0 decreasing rapidly and monotonically with depth into thestand.4.4.1.2 Normalization of Air Temperature ProfilesThe measured sensible heat flux can be used to reveal further the effect of the sourcedensity distribution on the 0 profile. There were simultaneous measurements of H (at z/h= 0.12) and HT (at z/h = 1.38) in the daytime of 19, 20 and 26 July. According to (4.6),the ratio Hg / HT, hereafter called relative source density, is the density of the ground-levelsource normalized against the total source density of the stand, while (1— Hg/HT) is therelative density of the canopy source. It has been found that the potential temperaturedifference, z0(z) = 0(z)— O(zr), where O(zr) is the potential temperature at height zr,can be normalized by a characteristic potential temperature 0 defined as0 HT*— pCpJw(Zr)Figure 4.3 plots /0/0 against Hg/fIT for three measurement levels, two in the trunkspace (z/h= 0.05 and 0.28) and one in the canopy layer (z/h= 0.60). It can be seen thatmost of the variation in 0/0 resulted from the variation in Hg/HT, with the correlationcoefficient of 0.63 at z/h = 0.60, 0.82 at z/h = 0.28 and 0.83 at z/h = 0.05, for 36 runs.Chapter 4. Observation and Simulation of Air Temperature Profiles 95Figure 4.3: Dimensionless daytime potential temperature, O/O versus relative sourcedensity, Hg/HT in the Douglas-fir stand at Browns River measured on 19, 20 and 26 July1990: (a), z/h = 0.60; (b), z/h = 0.28; (c), z/h = 0.05.aaaa DIaaID aa•aaaa aa*630630630•baaaa a aaa a aIa0 aa0aa.c a.Iaaa a aaa0a a0U• a aaIPa Ua0 2 4Hg/HTChapter 4. Observation and Simulation of Air Temperature Profiles 96Good correlations also existed at other heights within the stand. The variation in M/Ofor the runs of similar Hg/HT can be interpreted as the result of the difference in thevelocity field among the runs. But this variation was much smaller than the variationdue to the change in the relative source density. In other words, the source densitydistribution was the primary factor influencing the potential temperature profile, whilethe statistics of the velocity field were secondary factors. Figure 4.3 also shows that 04.was a temperature scale that collapsed the temperature profiles of similar relative sourcedensity reasonably well onto a single line.Figure 4.4 shows the profiles of M/O averaged for four ranges of H9/HT. The fourprofiles share some common features, namely a peak at z/h = 0.60 and an inversion inthe layer between z/h = 0.28 and 0.60. The profile shifted to higher values of O/O asH2/HT increased, which is most evident below z/h = 0.60. It can also be seen that thegradient in zO/O in the trunk space increased with increasing Hg/HT. Daytime sensibleheat flux was directed upward at all heights within the stand, indicating occurrence ofcounter-gradient flux in the inversion layer (Chapter 3).4.4.2 Simulation Results4.4.2.1 Validation of the Numerical SchemeTo test the numerical scheme of the random flight technique, air temperature and verticalsensible heat flux were simulated for the downwind edge of a 100 m long elevated planesource placed in homogeneous turbulence and were compared with those obtained bysuperposing the exact solutions of Taylor (1921) for a large number of elementary linesources. The velocity field was specified asu = 1 rn/s= 0.25 rn/sChapter 4. Observation and Simulation of Air Temperature Profiles 971.5Hg /HT range (%)0-1515-251.0- ° 25-35. >350.5 -0 I I0 2 4 6Figure 4.4: Profiles of the dimensionless daytime potential temperature, O/O averagedover the four ranges of relative source density, Hg/HT in the Douglas-fir stand at BrownsRiver. The measurements were made on 19, 20 and 26 July 1990.Chapter 4. Observation and Simulation of Air Temperature Profiles 98andTL=lsThe kinematic heat flux from the plane source was specified as=1°Cm/sThe agreement between the numerical scheme and the analytical solutions is excellent,both for the temperature and the vertical sensible heat flux (Figure 4.5).4.4.2.2 Simulation of the Potential Temperature in the StandFigure 4.6 shows the comparison of the profile of the potential temperature simulated forHg/Hr = 0.2 with the observed profile averaged over the runs with 0.15 < Hg/Hr <0.25.In the simulation, the wind speed and the square root of the vertical velocity variance atthe reference height were ‘U(Zr) = 2.0 rn/s and w(zr) = 0.6 m/s, corresponding to themeasured values averaged over the above runs. The fetch was = 960 m. There wassome random noise in the simulated profile, but overall the agreement between the simulated and the measured profiles was satisfactory. The simulated vertical flux was veryclose to that calculated from (4.5) and (4.9) for advection-free conditions (Figure 4.7),indicating that a fetch of 960 m was sufficient to minimize the effect of horizontal advection. There was a sharp decrease in O with height near the ground. This shows thewall effect: Once a particle wanders into the layer very close to the ground, it has thetendency to stay there because of the very small velocity variance. The accumulation of‘hot’ fluid particles in this layer resulted in the high air temperature. A similar patternwas also reported by Wilson et al. (1983) for a hypothetical plane source placed at thetop of a corn canopy. Unlike their study, the wall effect in the present study was confinedto a very thin layer of approximately 0.5 m or 0.03h.Chapter 4. Observation and Simulation of Air Temperature Profiles 99H’/pc (°Cm/s)0.40 0.45 0.50O.4\I \H’IPc0NNO.2o0 I I0.18 0.22 0.26 0.309 (°C)Figure 4.5: Comparison of air temperature, 0 and vertical kinematic heat flux, H’/pcsimulated using the random flight technique (lines) with those obtained from the analytical solutions of Taylor (1921) (squares) at the downwind edge of a 100 m long planesource placed at height z0 in homogeneous turbulence.Chapter 4. Observation and Simulation of Air Temperature Profiles 1001.5simulated 0‘SiO.c-• measured 0 ...N •• (• /0.5 -: -( ..)< c..•._——__ —00 4 8Figure 4.6: Comparison of the profile of the potential temperature simulated forH2/HT = 0.2 with the observed profile averaged over the the runs with Hg/HT in therange 0.15—0.25 in the Douglas-fir stand at Browns River.Chapter 4. Observation and Simulation of Air Temperature Profiles 1011.5H/HT and H’/HTFigure 4.7: Comparison of normalized vertical heat flux simulated using the randomflight technique with a fetch x = 960 m (H’/HT, dash line) with that calculated fromEquations (4.5) and (4.9) for advection-free conditions (H/HT, solid line).Chapter 4. Observation and Simulation of Air Temperature Profiles 102It is a common practice to treat sensible heat as a passive scalar in random flightsimulations of sensible heat dispersion. In other words, it is assumed that the dispersionof sensible heat does not modify the velocity field. For an isolated line source, this is true.For an extensive plane or canopy source, however, sensible heat is not a completely passivescalar, since the extensive source will result in the stratification of air temperature. Thestratification, in turn, will affect the movement of the air (including the marked fluidparticles). It is possible that the results of the simulation can be improved by taking intoaccount the effect of the source-induced buoyancy.4.4.2.3 Test of the Effect of the Wind Speed ProfileIn a forest stand with a trunk space relatively free of branches and needles, wind speedtypically exhibits a maximum in the trunk space and a minimum in the canopy layer(e.g. Shaw 1977, Chapter 2). In contrast, wind speed in agricultural plant canopiesor artificial canopies in wind tunnels usually decreases monotonically with depth (e.g.Wilson et at. 1982, Seginer et at. 1976). Numerical tests suggest that velocity skewnesshas only a small effect on the dispersion of passive scalars (Legg 1983, Raupach 1989b).Yet it is unclear how sensitive simulated results are to the wind speed profile. To testthe effect of the wind speed profile, simulations were performed using the profile withinthe stand described by (4.10) as well as the profile described byU(Z)/U(Zr) = 0.8z/h z < Ii (4.13)which satisfies the boundary conditions but does not accurately match the actual profile.Other input parameters remained the same as in the previous section.Figure 4.8 shows the comparison of the simulated results for three fetches. It canbe seen that the two sets of profiles are similar in magnitude and in shape, with slightdifferences in the layer 0.05 < z/h < 0.35, where the actual wind speed was much higherChapter 4. Observation and Simulation of Air Temperature Profiles 1031.5x, = 60m 240m 960mNo.:0 4iXOIOFigure 4.8: The effect of the wind speed profile on the simulation of potential temperatureresulting from the canopy sensible heat source for three fetches (xv): (—) wind speedwithin the stand defined by Equation (4.10); (- - - -) wind speed within the stand definedby Equation (4.13). Other parameters are the same as in Figure 4.6Chapter 4. Observation and Simulation of Air Temperature Profiles 104than that described by (4.13) because of the existence of the secondary maximum. Thissuggests that the wind speed profile is not critical in the simulation. For the purpose ofLagrangian simulation, efforts should therefore be directed toward a better understandingof the velocity variance and Lagrangian time scale of the velocity field.4.4.2.4 Flux-Gradient Relationships near the Forest FloorTheoretically, the ground-level flux (including the contribution from the short understoryvegetation) can be calculated from K-theory expressed by (4.7) and (4.8). In reality,however, only 0 instead of °g can be measured. If the separation between the overstorycanopy and the ground is large, as in the present study, it may be hypothesized that thegradient in 0g in the layer close to the ground is well approximated by the gradient ino or that the overstory canopy does not contribute much to the gradient in 9. If thiswere the case, this simple model, which requires only the measurements of 0 and o nearthe ground and an estimate of TL as the inputs, would be applicable. Furthermore, thishypothesis would support the application of the aerodynamic approach, although notvalid at higher levels in a forest stand, to the exchange between the forest floor (with itsunderstory) and the adjacent air layer (Black and Kelliher 1989, Raupach 1989a).Figure 4.9 shows the comparison of Hg calculated using (4.7) and (4.8), with 0 substituted for O, and Hg measured at z/h 0.12. In the calculation, the potential temperaturemeasured at z/h = 0.05 and 0.28 was used to compute ö0/öz. Although some randomnoise is evident in the simulated profile of 0 (Figure 4.6), it appears that 0 does not varymuch with height in the layer 0.05 < z/h < 0.28. This suggests that ÔO/öz is a goodapproximation for OOg/OZ in this layer. The vertical velocity variance was measured atz/h = 0.12. The estimate of the Lagrangian time scale, TL was based on (4.12), using themeasurements of the vertical velocity variance at the reference height Zr (z/h = 1.38).Although the model for TL was rather primitive, the modelled and the measured fluxesChapter 4. Observation and Simulation of Air Temperature Profiles 105Hour (PST)Figure 4.9: Comparison of modelled (U) kinematic sensible heat flux, Hg/(pcp) with thatmeasured (.) at z/h = 0.12 in the Douglas-fir stand at Browns River on (a) 19, (b) 20,and (c) 26 July 1990.0.100.0500.100.0500.100.050Eb .—oI I Iab10 14 18Chapter 4. Observation and Simulation of Air Temperature Profiles 106showed good agreement.4.5 Summary and ConclusionsThe profile of potential temperature in the Douglas-fir stand was influenced to a greatextent by the distribution of sensible heat source/sink density. The daytime profile alwaysexhibited an inversion in the layer between the middle of the trunk space (z/h = 0.28)and the middle of the canopy (z/h = 0.60), and a peak in the middle of the canopy asa result of the near-field effect of the canopy sensible heat source. The daytime profilesof the dimensionless potential temperature, /O/O were found to be well stratified bythe relative source density, Hg/HT. As H9/HT increased, the profile of zO/O shifted tohigher values.The daytime profile of tO/O was simulated by adding the contribution from thecanopy source, calculated using the random flight technique, and that from the ground-level source, calculated from gradient-diffusion theory with a far-field eddy diffusivity.The simulated profile appeared to agree reasonably well with the measured one. Thesimulated results suggested that the profile of /O/O was not sensitive to the shape ofthe wind speed profile. There was good agreement between the sensible heat flux fromthe forest floor calculated using the gradient-diffusion theory and that measured near theground (z/h = 0.12). This supports the application of the aerodynamic approach to theexchange process between the forest floor and the adjacent air layer.4.6 ReferencesAbramowitz, M. and Stegun, l.A.: 1964, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, United States Department of Commerce,U.S. Government Printing Office, Washington, D.C.Chapter 4. Observation and Simulation of Air Temperature Profiles 107Aylor, D.E.: 1989, ‘Aerial spore dispersal close to a focus of disease’, Agric. ForestMeteorol. 47, 109-122.Black, T.A. and Kelliher, F.M.: 1989, ‘Processes controlling understory evapotranspiration’, Phil. Trans. R. Soc. Lond. B324, 207-231.Denmead, O.T. and Bradley, E.F.: 1985, ‘Flux-gradient relationships in a forest canopy’,in Hutchison, B.A. and Hicks, B.B. (eds.), The Forest-Atmospheric Interaction, D.Reidel Publishing Co., Dordrecht, 421-442.Denmead, O.T. and Bradley E. F.: 1989, ‘Eddy-correlation measurement of the CO2 fluxin plant canopies’, in Heat and Mass Transfer ‘90, Fourth Australian Conferenceon Heat and Mass Transfer, University of Canterbury, Christchurch, New Zealand,183-191.Di-Giovanni, F. and Kevan, P.G.: 1991, ‘Factors affecting pollen dynamics and itsimportance to pollen contamination: a review’, Can. J. For. Res. 21, 1155-1170.Hunt, J.C.R. and Weber, A.H.: 1979, ‘A Lagrangian statistical analysis of diffusionfrom a ground-level source in a turbulent boundary layer’, Q. J. R. Meteorol. Soc.105, 423-443.Leclerc, M.Y., Thurtell, G.W. and Kidd, G.E.: 1988, ‘Measurements and Langevinsimulations of mean tracer concentratioll fields downwind from a circular line sourceinside an alfalfa canopy’, Boundary-Layer Met eorol. 43, 287-308.Legg, B.J. and Raupach, M.R.: 1982, ‘Markov-chain simulation of particle dispersionin inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerianvelocity variance’, Boundary-Layer Meteorol. 24, 3-13.Chapter 4. Observation and Simulation of Air Temperature Profiles 108Legg, B.J., Raupach, M.R. and Coppin, P.A.: 1986, ‘Experiments on scalar dispersionwithin a plant canopy. Part III: An elevated line source’, Boundary-Layer Meteorol.35, 277-302.Raupach, M.R.: 1989a, ‘Stand overstory processes’, Phil. Trans. R. Soc. Loud. B324,175-190.Raupach, M.R.: 1989b, ‘A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies’, Q. J. R. Meteorol. Soc. 115,609-632.Raupach, M.R.: 1987, ‘A Lagrangian analysis of scalar transfer in vegetation canopies’,Quart. J. R. Met eorol. Soc. 113, 107-120.Raupach, M.R.: 1983, ‘Near field diffusion from instantaneous sources in the surfacelayer’, Boundary-Layer Meteorol. 27, 105-113.Seginer, I., Mulhearn, P.J., Bradley, E.F. and Finnigan, J.J.: 1976, ‘Turbulent flow ina model plant canopy’, Boundary-Layer Met eorol. 10, 423-453.Shaw, R.H.: 1977, ‘Secondary wind speed maxima inside plant canopies’, J. Appi.Meteorol. 16, 514-523.Taylor, 0.1.: 1921, ‘Diffusion by continuous movements’, Proc. Lond. Math. Soc. A20,196-211.Wilson, J.D., Legg, B.J. and Thomson, D.J.: 1983, ‘Calculation of particle trajectories in the presence of a gradient in turbulent-velocity variance’, Boundary-LayerMet eorol. 27, 163-170.Chapter 4. Observation and Simulation of Air Temperature Profiles 109Wilson, J.D., Thurtell, G.W. and Kidd, G.E.: 1981a, ‘Numerical simulation of particle trajectories in inhomogeneous turbulence. I: Systems with constant turbulentvelocity scale.’, Boundary-Layer Met eorol. 21, 295-313.Wilson, J.D., Thurtell, G.W. and Kidd, G.E.: 1981b, ‘Numerical simulation of particle trajectories in inhomogeneous turbulence. II: Systems with variable turbulentvelocity scale’, Boundary-Layer Met eorol. 21, 423-442.Wilson, J.D., Ward, D.P., Thurtell, G.W. and Kidd, G.E.: 1982, ‘Statistics of atmospheric turbulence within and above a corn canopy’, Boundary-Layer Meteorol. 24,495-519.Chapter 5ConclusionsResults have been presented of the analysis of the daytime velocity statistics, air temperature, sensible and latent heat fluxes based on the measurements within and abovethe thinned and pruned Douglas-fir stand, and of the random flight simulations of airtemperature profiles. The most important findings are summarized as follows:(1) The vertical structure of the stand affected, to a great extent, the vertical distributions of the velocity statistics (wind speed, variance, turbulence intensity, Reynoldsstress, skewness and kurtosis), air temperature, sensible and latent heat fluxes. Theprofile of wind speed showed a minimum in the canopy layer and a marked maximumat the middle of the trunk space. The profile of potential temperature always exhibitedan inversion between the middle of the trunk space and the middle of the canopy and amaximum in the middle of the canopy. The profiles of daytime sensible and latent heatfluxes in the stand showed the features as described by the scalar conservation equationunder advection free conditions: constant flux layers in the trunk space and above thestand and large flux divergences in the canopy layer. The effect of the stand structurewas also evident in the quadrant representation of the fluxes of momentum, sensible heatand water vapour.(2) Negative Reynolds stress, or upward transport of momentum, persistently occurred at the lower heights of the stand, the magnitude being 0.03 m2/s. The examination of the Reynolds stress budget revealed that the negative values are likely associatedwith the negative velocity gradients at these heights. It is believed that the longitudinal110Chapter 5. Conclusions 111pressure gradient due to larid-sea/upslope-downslope circulations was the main factorresponsible for the upward transport of the momentum.(3) Energy budget was examined above and beneath the overstory of the stand. Thesum of the sensible and latent heat fluxes above the stand accounted for, on average, 83%of the available energy flux. Beneath the overstory, the corresponding figure was 74%.On some days, energy budget closure was much better than on others. The measuredsensible heat flux near the forest floor showed very little horizontal variations. Thedaytime Bowen ratio of the stand increased from 1.3 to 2.7 during the experimentalperiod as the soil dried. The daytime mean canopy resistance showed strong dependenceon the mean saturation deficit. The mid-day value of the Omega factor of the standwas about 0.2, indicating a strong coupling between this stand and the atmosphere asexpected for forests.(4) Counter-gradient flux of sensible heat constantly occurred at the canopy base,invalidating the conventional gradient-diffusion model or K-theory at this height. However, K-theory with a far-field eddy diffusivity appeared to be valid near the ground. Thesensible heat flux from the forest floor calculated using this modified K-theory agreedreasonably well with the measured one. This supports the application of the aerodynamicapproach to the exchange process between the forest floor and the adjacent air layer.(5) The daytime profiles of the dimensionless potential temperature, where zOis the difference in potential temperature between the height of interest and the referenceheight, and O was a characteristic temperature defined as the ratio of the kinematicsensible heat flux to the square root of the vertical velocity variance, both measuredabove the stand, were found to be well stratified by Hg/HT, the ratio of the sensibleheat flux measured near the forest floor to that measured above the stand (the relativesensible heat source density). As Hg/HT increased, the profile of zO/O shifted to highervalues.Chapter 5. Conclusions 112(6) The daytime profile of zO/O, simulated by combining the random flight techniquefor the dispersion of sensible heat from the elevated canopy source and the gradient-diffusion relationship (K-theory) with a far-field diffusivity for the dispersion from theground-level source, agreed reasonably well with the measured one. The simulationresults suggested that the profile of zO/O was not sensitive to the shape of the windspeed profile. This, together with the simulation results of other studies, indicates thatfor the purpose of Lagrangian simulation of the dispersion in canopies, efforts shouldbe directed toward a better understanding of the velocity variance and Lagrangian timescale of the velocity field.Appendix APhotographs of the Site and Instrumentation113Appendix A. Photographs of the Site and Instrumentation 114Figure A.1: Eddy correlation unit operated permanently at the height of 23.0 m (z/h =1.38) in the Douglas-fir stand at Browns River. It consisted of one 3-dimensional sonicanemometer, one krypton hygrometer and one fine wire thermocouple and was pointedin the NNE direction. The daytime wind direction was NE to NNE.Appendix A. Photographs of the Site and InstrumentationFigure A.3: Main instrument tower used in the Browns River experiment.116•1•Appendix A. Photographs of the Site and Instrumentation 115Figure A.2: Eddy correlation unit operated at various heights in the Douglas-fir standat Browns River. It consisted of one 3-dimensional sonic anemometer/thermometer andone krypton hygrometer. The photograph was taken when it was mounted at a height of10.0 m (z/h = 0.60).Appendix A. Photographs of the Site and Instrumentation 117Figure A.4: Forest floor and truilk space of the Douglas-fir stand at Browns River.Appendix BWake Production in the Reynolds Stress BudgetFrom the TKE budget equation in the canopy, Raupach and Shaw (1982) derived thebudget equation for <Z’Z’>, the dispersive kinetic energy. By replacing one of thetwo subscripts i with k, we transform the budget equation for <Z’ii’> to the budgetequation for <Z’7>, the dispersive stress, thus(+ <>,,,, 8 8 <Uj>—<Uk’ttj>(1)!I(JU+<UU7 ><uu >(2)a—I,——(<z%u ><iu >)(3)a <i’T?’!>— (<‘> +2p3(4)(5)1 1+— <U>< > + <Uk><>8Xk p(6) (B.1)118Appendix B. Wake Production in the Reynolds Stress Budget 119where u and x are velocity and position vectors, t is time, p is pressure, v is the kinematicviscosity; triangular brackets and double primes denote, respectively, horizontal averagesand departures therefrom; and overbar and single prime denote, respectively, temporalaverages and departures therefrom. The six groups of the terms on the RHS of (B.1) are(1) production of the dispersive stress due to wind shear(2) wake production of Reynolds stress. When i = 1 and k = 3, this term becomes—P.m in Equation (2.4).(3) & (4) transport terms, assumed to be negligible. Physically this assumption meansthat the dispersive stress (or TKE if i k) arising from work against drag on elementswithin an averaging volume is produced within the same averaging volume.(5) viscous terms accounting for direct dissipation of the dispersive stress. They canbe further separated into two parts as(5) =(B.2)Provided that there is negligible direct viscous dissipation by the canopy of the dispersivestress without prior conversion to wake turbulence, and using fyi = —v < V2z’ >, wherefyi is the viscous drag force vector exterted on a unit mass of air, (B.2) reduces to(5) fvk+ <Uk> fyi (B.3)(6) wake production of the dispersive stress due to the form drag. It can be re-writtenas(6) =<> fFk+ <Uk> fFi (B.4)where fF, is the form drag vector exerted on a unit mass of air.We replace the tensor notation by the meteorological notation, writing x = (x, y, z)Appendix B. Wake Production in the Reynolds Stress Budget 120and u = (u, v, w) with the x-coordinate in the mean streamwise direction and the zcoordinate normal to the ground surface. To an excellent approximation, horizontallyaveraged flow properties within the canopy are functions of z only. Substituting 1 forsubscript i and 3 for subscript k into (B.1) and making use of the above simplificationsgive—“—-II_____= —<ww>9= (B.5)9zwhere we have used the fact that (fvz + fFz) (vertical drag) is negligible.Appendix CComparison of the Two Eddy Correlation Units over a Bare FieldUpon the completion of Chapters 2—4 of this dissertation, concern was expressed aboutthe aerodynamic shadow effect of the rings of the 3-dimensional sonic anemometer (Applied Technologies Inc., Model SWS-211/3V) used in the Browns River Experiment onthe measurements of the two horizontal velocity components. Wind tunnel tests showedthat this effect might result in an underestimation of mean wind speed by 20% (G.A.Zimmerman 1991, Applied Tecnologies Inc., personal communication). By applying tothe Browns River data the algorithms obtained in laminar flow in a wind tunnel to correctthe shadow effect, it was found that the wind speed measured with this sonic anemometerwas about 22% higher than the wind speed measured with the cup anemometers. Furthermore, the streamwise velocity measured with this sonic anemometer at the tree topswas about 13% higher than that measured with another 3-dimensional sonic anemometer(Applied technologies Inc., Model BH-478B/3, probe without rings) 6.33 m above thetree tops. It is clear that the algorithms obtained in laminar flow can not be applieddirectly to turbulent flow.In order to assess the shadow effect in outdoor turbulent environments, an experimentwas performed over a bare field on level ground on George Reynolds’ farm in Delta,British Columbia on 3 and 5 October 1991 with the two eddy correlation units used inthe Browns River Experiment: unit 1 (called the upper unit in Chapters 2 and 3, withModel BH-478B/3 sonic anemometer) and unit 2 (called the lower unit in Chapters 2and 3, with Model SWS-211/3V sonic anemometer). The field had been laser levelled121Appendix C. Comparison of Eddy Correlation Units over a Bare Field 122and harrowed to improve drainage. The potato crop of the previous season had beencompletely incorporated into the soil and no crop residue remained at the surface. Onlyone krypton hygrometer (Campbell Scientific Inc., Model K20, 1.021 cm path length)was available for this experiment and was used as part of unit 1. The two units wereoriented toward the northwest, the direction of the daytime sea breeze. They weremounted at the same height of 2.25 m. The horizontal separation between the two unitswas approximately 1.2 m. For comparison, a sensitive cup anemometer (ThornthwaiteAssociates, Model 901-LED) was also mounted at the height of 2.25 m. Net radiationflux, R was measured using a net radiometer (Swissteco Instruments, Model S-i) at aheight of 1.5 m. Heat flux into the soil, G was measured with a heat flux plate (MiddletonInstruments, Model F) buried at a depth of 1.5 mm. The fetch was at least 600 m. Theweather was mostly clear. The stability parameter, z/L, where L is Monin-Obukhovlength calculated from the measurements of unit 2, had values in the range —4.42 to0.011.Statistics were calculated over 30-minute intervals. A two-way coordinate rotationwas performed in the same manner as discussed in Chapter 2. Only runs after the onsetof the sea breeze were used in the data analysis.C.1 Comparison of VelocitiesFigure C.i compares the streamwise velocity and the equivalent cup wind speed definedin Chapter 2. Unit 2 appeared to underestimate both variables by about 4%. On thewhole, the agreement was very good.Figure C.2 compares the vertical velocity variance, w’2 for the two units. Unit 2appeared to overestimate w’2 by about 11%.Figure C.3 compares the equivalent cup wind speed measured with the 3-dimensionalAppendix C. Comparison of Eddy Correlation Units over a Bare Field 1236 /i:1Z2--0 I0 2 4 6mis, unit 1Figure C.1: Streamwise velocity (0) and equivalent cup wind speed (.) measured withunit 2 versus those measured with unit 1 over the bare field in Delta on 3 and 5 October1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 1240.15VD -‘oo 7000.10- i -!O.05 - -0 I I0 0.05 0.10 0.15w’2 (m Is ), unit 1Figure C.2: Vertical velocity variance, w’2 measured with unit 2 versus that measuredwith unit 1 over the bare field in Delta on 3 October 1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 12560El..04-E 1•1 ICQ-0oo 2 4 6mIs, cup anemometerFigure C.3: Equivalent cup wind speed measured with the 3-dimensional sonic anemometers versus wind speed measured with the cup anemometer over the bare field in Deltaon 3 and 5 October 1991: unit 1 (D); unit 2 (I).Appendix C. Comparison of Eddy Correlation Units over a Bare Field 126sonic anemometers with the wind speed measured with the cup anemometer. There wasa good correlation between the sonic and cup anemometer measurements, but the cupanemometer tended to overestimate the wind speed by about 15%, probably resultingfrom the overspeeding of cup anemometers in turbulent environments (Coppin 1982).The results shown in Figure C.3 were similar to those obtained within and above theDouglas-fir stand at Browns River (Chapter 2).C.2 Comparison of Momentum FluxFigure C.4 compares the kinematic momentum flux, It appears that the ring-induced shadow effect of the 3-dimensional sonic anemometer in unit 2 resulted in asystematic underestimation of the magnitude of the kinematic momentum flux. Theaverage value of the ratio of —7 measured with unit 2 to measured with unit 1was 0.80. However, there existed a good correlation between the two measurements, thecorrelation coefficient being 0.966 for 14 runs.Despite this difference, some derived aerodynamic quantities from the measurementsof the two units were rather similar. For example, the average value of the ratio, u/u,where u is the square root of the vertical velocity variance and u,. is the friction velocity, was 1.28 from the measurements of unit 2 for the runs with I z/L 1< 0.09. Thecorresponding value for unit 1 was 1.25. Both ratios were very similar to the commonlyobserved value of 1.25±0.03 in the neutral surface layer (Panofsky and Dutton 1984).Figure C.5 shows —Z as a function of i2, where i is the mean streamwise velocitycomponent. The correlation coefficient was 0.956 for unit 1 for 14 runs and 0.957 forunit 2 for 26 runs. The scatter in the plot for the runs with the same i was mostly aresult of varying stability among the runs. The average drag coefficients (defined as theratio of kinematic Reynolds stress to the square of the horizontal velocity component)Appendix C. Comparison of Eddy Correlation Units over a Bare Field 1270.10a0.05--0 0.05 0.10- u’w’ (m2/s), unit 1Figure C.4: Kinematic momentum flux, measured with unit 2 versus that measuredwith unit I over the bare field in Delta on 3 October 1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 1280.1000I•0005 aI..•0..IIII •• • ••0 I0 10 20 30—2 2 2u (mis)Figure C.5: Kinematic momentum flux, as a function of the square of the averagestreamwise velocity component, 2 for unit I (U) and unit 2 (a) over the bare field inDelta on 3 and 5 October 1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 129at 2.25 m were 0.0035 and 0.0033, for units 1 and 2, respectively. The roughness lengthof the field was estimated to be 2.7 mm from the measurements of unit 2 and 3.0 mmfrom the measurements of unit 1, both values being about 1/10 of the mean height ofthe roughness elements.C.3 Comparison of Scalar FluxesOn 3 October, the output signal from the amplifier used to amplify the thermocouplevoltage of unit 1 was severely contaminated by the noise created by a nearby AC voltagesource. The resulting temperature variance was unrealistically high, the magnitude being3 °C2. Because of the noise, the plot of kinematic sensible heat flux, showed somescatter, but overall the agreement between the two units was very good (Figure C.6).In order to compare the two units further in regard to scalar flux measurements,the covariance between the vertical velocity component measured with unit 1 (wi) andair temperature measured with unit 2 (T2), was calculated for each 30 minute run andwas compared with (?T)2, the kinematic sensible heat flux measured with unit 2. Anexcellent correlation existed between wT and (?T7)2,with R2 0.997. The regressionequation waswçT = O.75()2 (R2 = 0.997, n = 16) (Ci.)Because some of the flux contribution from eddies of small wave-length was lost due tothe horizontal separation between the two units, the regression coefficient was smallerthan unity. A similar result was obtained for water vapour flux, as shown by the followingregression equationwp = 0.77() (R2 = 0.990, n = 16) (C.2)where wp1 is the covariance between the vertical velocity component measured withunit 2 (w2) and water vapour density measured with unit 1 (pvi) and is theAppendix C. Comparison of Eddy Correlation Units over a Bare Field 1300.200.1-71:1VI I0 0.1 0.2w ‘T’ (°C m Is), unit 1Figure C.6: Kinematic sensible heat flux, measured with unit 2 versus that measuredwith unit 1 over the bare field on 3 October 1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 131water vapour flux measured with unit 1. The fact that the values of the coefficient inthe regression equations (C.1) and (C.2) are almost identical is another indication of theconsistency between the two units in measuring scalar fluxes.On 5 October, the noise of the amplifier was eliminated by grounding the amplifierproperly and removing the AC power source. However, the electronics for the verticalvelocity component of unit 1 failed. Although there was no comparison available for i?Ton this day, there was a comparison for air temperature variance, T’2 (Figure C.7). Thetwo units measured the fluctuation in air temperature in very different ways: Unit 1measured it directly with a fine wire thermocouple (chromel-constantan, 13 um in diameter), while unit 2 measured it indirectly using the sonic signal of the vertical velocitycomponent. There was excellent agreement between the two measurements of.The consistency check can also be done by examining the energy budget closure.Figure C.8 shows the comparison of the sum of turbulent fluxes, H + AE with theavailable energy flux, R — G. Sensible heat flux, H was measured with unit 2 on bothdays. Latent heat flux, AE was measured with unit 1 on 3 October and was estimatedfrom wp using (C.2) on 5 October. Figure C.8 shows that very good energy budgetclosure was achieved during the experimental period.C.4 SummaryThe rings of the sonic anemometer probe of unit 2 had little effect on the measurementsof scalar fluxes. The ring-induced shadow effect resulted in an underestimation of meanwind speed by about 4%, much smaller than the value observed in laminar flow in awind tunnel. The effect on the measurement of momentum flux was more noticeable. Onaverage, unit 2 underestimated the magnitude of momentum flux by 20%.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 1320.8aa0.4--hE-00___0.4 0.8T’2 (°C2), unit 1Figure C.7: Air temperature variance, T’2 measured with unit 2 (sonic signal) versus thatmeasured with unit 1 (thermocouple signal) over the bare field in Delta on 5 October1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 133300 •-•,,Vi:i-+0-zv-70 100 200 300R- G (W/m2)Figure C.8: The sum of the turbulent heat fluxes, H + \E versus the available energyflux, R — G over the bare field in Delta on 3 (D) and 5 (•) October 1991.Appendix C. Comparison of Eddy Correlation Units over a Bare Field 134It should be pointed out that the probe of the sonic anemometer in unit 2 was designedprimarily for turbulence measurements in crop and forest canopies where the wind speedis very low and wind direction highly unpredictable. According to Kaimal (Kaimal, J.C.,1991, personal communication), occasional sweeps by the wakes across an acoustic paththat result from the constantly changing wind speed and direction in a plant canopy,will have minimal shadow effect on the measurement. The wind direction during thisexperimental period, on the other hand, was rather steady and was mainly directed alongthe central axis of the probe (the worst-case scenario, Kaimal 1991). No attempt wasmade to correct the data obtained in the Browns River Experiment for the ring-inducedshadow effect. But even with the correction based on these worst-case scenario results,the conclusions made in previous chapters will not be altered.ReferencesCoppin, P.A.: 1982, ‘An examination of cup anemometer overspeeding’, Meteorol. Rdsc/i. 35, 1-11.Panofsky, H.A. and Dutton, J.A.: 1984, Atmospheric Turbulence: Models and Methodsfor Engineering Applications, John Wiley and Sons, New York.Appendix DAn Analytical Expression for Legg and Raupach’s ModelD.1 A Modified Langevin Equation for the Canopy EnvironmentConsider dispersion in only the vertical direction, writillg Z(z0,t) for the position andw(z0,t) = OZ(z0,t)/öt for the Lagrangian velocity of a marked fluid particle, where tis time and z0 is the height of the source. Legg and Raupach (1982) expressed w as aMarkovian process which obeys a modified Langevin equationöw(z0,t)= —aw(z0,t) + (t) + f (D.1)where a, \ and f are coefficients to be specified below, and is a Gaussian white noisewhich has the properties(t) = 0, (s)(t) = — t) (D.2)where the overbar denotes ensemble averaging. The first term on the RHS of (D.1)represents a retarding force per unit mass, the second term is a random acceleration, andthe third term is a mean force per unit mass on the marked particle due to the meanpressure gradient. In a steady, horizontally homogeneous flow over a level surface, Leggand Raupach (1982) showed thatf=Ow/öz (D.3)where w is the variance of the Eulerian vertical velocity.135Appendix D. An Analytical Expression for Legg and Haupach ‘s Model 136The solution of (D.1) has been found by Legg and Raupach (1982) to bew(z0,t) = w(z0,O)e_at + Ajea(s_t)(s)ds + fa’ (1 — et) (D.4)which represents a random process with mean (called mean vertical drift velocity),(z0,t) = W(z0,O) + fc(1 — c_at) (D.5)variance,[w’(z0,t)]2 = [w’(z0,0)]2e_2at+ (1 — e_2at) (D.6)and covariance,w’(z0,O)w’(z0,t) = [w’(z0,O)]2e_at (D.7)It is apparent from (D.7) that= 1/Tiwhere1TL= J w’(z0,O)w’(zt dt[w’(z0,O)12 ois the Lagrangian integral time scale.In their derivation, Legg and Raupach (1982) assumed that w was a stationary process. From this assumption they simplified the form of UY and fixed the coefficient A.They used the above equations to perform a random flight simulation for scalar dispersion in canopies. It turns out that for the special case of constant f (corresponding tothe case of /3i 1/2 in the simulations of Raupach (1989) for scalar concentration in thecanopy and to the case of the simulation of Legg and Raupach (1982) for the evolutionof scalar profiles in the canopy) and constant TL within the canopy (Leclerc et al. 1988,Legg et al. 1986), an analytical solution can be derived for the single particle transitionprobability based on these equations.Appendix D. An Analytical Expression for Legg and Raupach’s Model 137We begin the derivation with two more simplifications. First, the initial statistics ofthe Lagrangian and the Eulerian velocities are thought to be identical (Raupach 1983),i.e.iY(z0,0) = UJE(zo) = 0 (D.8)[w’(z, 0)]2 = [w(z)]2We further assume that the Lagrangian velocity variance is not a function of time. Thissimplification fixes ,\ from (D.6) as= u(z0) (D.9)whereu(z0) = V(zo,0)]2 = [w(z0,t)]2Using (D.8), (D.5) reduces toUY(z0,t) = fTL(1 — e_t’TL) (D.10)It is interesting that Y in (D.10) has an asymptotic behavior similar to that of thevertical drift velocity of a tracer particle released from an elevated source in the neutralsurface layer (Raupach 1983). In the near field where t << TL, approximately equalszero, while at t >> TL, iY approaches its far field limit of fTL. A visual inspection ofthe w profile generalized from the experimental studies in a variety of plant canopies(Raupach 1989) givesf1.4u/h (D.11)where u is the friction velocity measured above the canopy and h is the height of thecanopy. Furthermore, if TL is related to u. and h in the form (Legg et al. 1986)TL = 0.3h/u (D.12)Appendix D. An Analytical Expression for Legg and Raupach’s Model 138then it follows from (D.11) and (D.12) thatfTL 0.42u (D.13)which is remarkably close to ku, the far field vertical drift velocity for a marked particlein the surface layer or in the layer above the canopy (Hunt and Webber 1979, Raupach1983), where k = 0.4 is the von Karman constant.D.2 Single Particle Transition ProbabilityThe height of the marked particle isZ(z0,t) =0+jw(z,s)ds (D.14)From (D.10) and (D.14), the mean height can be shown to beZ(z0,t) = z0 + fTLt — fT(1 — e_t’TL) (D.15)To find uz(zo, t) = /(Z — )2, the mean depth of plume or the square root of thevariance of particle position, we use (D.14), (D.4) and (D.5), thus[UZ(zo, t)]2= {{J w(z0,t1)dt + z0] — [j (z0,t1)dt + z0]}2= J J [w(z0,ti)—(z,ti)][w(zt2—Y(z0,t2)jd idt= it it[w’(z0,0)J2e t1+t2)dt dt2+2\ j f e°’’ dt1 dt2 [w’(z0,0) j e*t2L(u)duJIIj dt1 f dt2 e_t1)ds f2 ea(u_t2)(s)(u)duIII (D.16)Appendix D. An Analytical Expression for Legg and Raupach ‘s Model 139Term I can be evaluated easily asTerm I = [w’(z0,0)12(1 — e_Yt)2/cr= o,(z0)T 1 — e_t/TL)2 (D.17)Using the fact that is uncorrelated with w, Term II reduces toTermII=0 (D.18)Term III can be evaluated, using (D.2) and (D.9), as followsTerm III= 2 f dt1 f dt2 e(8_t1)ds ft2 e_t2)S(s — u)du2ftdt1fti€_t1)d5jSdt2ft2ea(L_t2)6(s— u)du +ftdt2ft2ett2(s— u)du}=dti ft’ ea(s_t1)ds{O + f edt2}= —(at— 1 + et) — —-(1 — et)2= 20 (z)T(t/TL — 1 + et/T1) — o(z0)T(1 — et/T)2 (D.19)where the following property of the S function has been used10 b<xf y(u)S(x — u)du = y(x) b>x(with x > 0 and b> 0). Substitution of (D.17)—(D.19) into (D.16) reduces (D.16) too(z0,t) = 2J(z0)T(t/TL — I + et) (11.20)The mean depth specified by (11.20) has the same form as that of a plume in homogeneousturbulence (Taylor 1921).Appendix D. An Analytical Expression for Legg and Raupach ‘s Model 140Because is Gaussian and (D.1) is linear, w is also Gaussian (Durbin 1983). By thesame argument, Z is also Gaussian because it is linear with w according to (D.14). Hencethe single particle transition probability density is1 (zZ)2P(z,t;z0,O) = ,-_ exp[— 2 1 (D.21)V2’Jruzwhere and z are given in (D.15) and (D.20), respectively. P(z, t; z0, 0) is a conditionalprobability density that Z(z0,t) = z, given Z(z0,0) = z0.For a point source of instantaneous release of unit mass of scalar at height z0 andtime 0, the ensemble averaged scalar concentration at height z and time t is (Batchelor1964)Ce(z,t;zo,0) = P(z,t;z0,0) (D.22)where the subscript e stands for this special elementary source. For the special case off = 0 or Z(t) z9, (D.21) reduces to the single particle transition probability densityin homogeneous turbulence, and Ce satisfies phenomenologically the diffusion equation(Batchelor 1964)öCe--= {K(zo,t)ã_} (D.23)with the diffusivity K given by2K(z0,t) (D.24)and the vertical flux Fe given explicitly byFe(z,t;zo,0) = _J (D.25)For the general case of non-zero f, however, no form of K can be found to make Cesatisfy the diffusion equation (D.23). To find Fe for the general case, we use the scalarconservation equation for the elementary sourceOCe — OFe—(.6)Appendix D. An Analytical Expression for Legg and Raupach’s Model 141Equation (D.26) can be integrated with respect to z as followsFe(z,t;zo,0)= —J (z00)dY (D.27)Figure D.1 shows the comparison of the concentration profiles from an elementarysource calculated using (D.21-D.22) and those simulated using the random flight technique.One gram of mass was released at time zero into the velocity field specified byo(z0) = 0.4 m/sf = 0.012 rn/s2andTL = 12 sIn the random flight simulation, a total of 20,000 particles were released and the timestep was Lt = 0.2TL. It can be seen that the agreement is excellent.D.3 Profiles of Concentration and Flux for a Plane SourceThe analytical solution obtained for the elementary source can be superposed for morecomplicated sources. As an example, consider a horizontal plane source located at heightz = z0 with flux density S (with dimensions of unit mass per unit surface area per unittime) and the horizontal position of the leading edge at x = x. The observation is madeat horizontal position x = 0 and height z. For simplicity, we assume the horizontal windspeed u to be constant with height. Using Taylor’s hypothesis of frozen turbulence, theparticles released at position (x, z0) always have a migration time of t = x/u when theyreach the observing position (0, z). The contribution to the mean concentration at (0, z)from the portion of the source located between x and x + dx is (Wilson et al. 1981)SCe(Z, t; z0,Appendix D. An Analytical Expression for Legg and Raupach’s Model 14260Ct=1OTL30:It=4TLN 03OL0 0.05 0.10 0.15Ce (g/m)Figure D.1: Comparison of concentration profiles resulting from the release of 1 gram ofmass at height z0 and time zero: (—) calculated using the analytical solution (D.21) and(0) simulated using the random flight technique.Appendix D. An Analytical Expression for Legg and Raupach’s Model 143orS’Ce(z,t;zo,O)dt (D.28)C(z; z0), the total contribution from the plane source, can be found by integrating (D.28)C(z; z0) = gj Ce(Z, t; z0, O)dt= sjvzexP[_24)1dt (D.29)where tf = xf/u and subscript p stands for this plane source. This integral can only beevaluated numerically.Similarly, F(z; z0), the total contribution to the vertical flux at observing position(0, z) from the plane source, can be found by integrating (D.27) with respect to t andmultiplying by S, thusF(z; z0) = Sj Fe(z, t; Zo, o)dt (D.3o)To evaluate (D.30), we use (D.27), (D.21) and (D.22) a new dummy variable ç definedas(D.31)Jz(Zo, t)With some lengthy algebra, it can be shown thatI S[1-(j z >F(z; z0) = (D.32)( —S() z < z0where— z —(z0,tf)Cif—oz(z0,tf)and1 Ctf 2=et/2d2irEquations (D.29) and (D.32) show the evolution of the profiles of concentration andvertical flux as the fetch increases. Further work is needed to compare the results obtainedAppendix D. An Analytical Expression for Legg and Raupach ‘s Model 144from these equations with measurements (e.g. the experiment on the plane source dispenon reported by Coppin et al. 1986) or those obtained from the conventional boundarylayer theory.The analytical expressions (Equations D.21, D.27, D.29 and D.32) enable the computation of the dispersion process to be carried out more rapidly, as compared to randomflight techniques, and make some of the physical aspects of the dispersion process apparent. However, one should be aware of the simplifications made in the derivation (constantTL, f, and u).D.4 ReferencesBatchelor, G.K.: 1964, ‘Diffusion from sources in a turbulent boundary layer’, Archiv.Mechaniki Stosowanj. 3, 661-670.Coppin, P.A., Raupach, M.R. and Legg, B.J: 1986, ‘Experiments on scalar dispersionwithin a plant canopy. Part II: An elevated plane source’, Bonndary-Layer Meteorol. 35, 167-192.Durbin, P.A.: 1983, ‘Stochastic differential equations and turbulent dispersion’, NASAReference Publication 1103.Hunt, J.C.R. and Webber, A.H.: 1979, ‘A Lagrangian statistical analysis of diffusionfrom a ground level source in a turbulent boundary layer’, Q. J. R. Met eorol. Soc.15, 423-443.Leclerc, M.Y., Thurtell, G.W. and Kidd, G.E.: 1988, ‘Measurements and Langevinsimulations of mean tracer concentration fields downwind from a circular line sourceinside an alfalfa canopy’, Botndary-Layer Met eorol. 43, 287-308.Appendix D. An Analytical Expression for Legg and Raupach ‘s Model 145Legg, B.J. and Raupach, M.R.: 1982, ‘Markov-chain simulation of particle dispersionin inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerianvelocity variance’, Boundary-Layer Meteorol. 24, 3-13.Legg, B.J., Raupach, M.R. and Coppin, P.A.: 1986, ‘Experiments on scalar dispersionwithin a plant canopy. Part III: An elevated line source’, Boundary-Layer Meteorol.35, 277-302.Raupach, M.R.: 1989, ‘A practical Lagrangian method for relating scalar concentrationsto source distributions in vegetation canopies’, Q. J. R. Meteorol. Soc. 115, 609-632.Raupach, M.R.: 1983, ‘Near field diffusion from instantaneous sources in the surfacelayer’, Boundary-Layer Met eorol. 27, 105-113.Taylor, G.I.: 1921, ‘Diffusion by continuous movements’, Proc. Lond. Math. Soc. A20,196-211.Wilson, J.D., Thurtell, G.W. and Kidd, G.E.: 1981, ‘Numerical simulation of particle trajectories in inhomogeneous turbulence. I: Systems with constant turbulentvelocity scale.’, Boundary-Layer Met eorol. 21, 295-313.Appendix EWind and Turbulence Regimes in an Old Growth Douglas-fir Stand on aSouth-Facing SlopeXuhni Lee and T. Andrew Black 1‘Presented at the Annual Meeting of Canadian Society of Agrometeorology held on 24 July, 1990 inPenticton, British Columbia and submitted to Forest Science.146Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 147AbstractThis paper reports the results of the analysis of measured wind and turbulence regimesnear the forest floor in an old growth Douglas-fir stand on a south facing slope in northernVancouver Island. Primary instrumentation included one eddy correlation unit, whichconsisted of a 3-dimensional sonic anemometer, a krypton hygrometer and a fine wirethermocouple, and four home-made hot wire anemometers.Anabatic and katabatic winds were observed within and outside the stand duringclear weather. The high value of the ratio of the wind speed inside the stand to thatoutside (0.28) suggests the existence of a secondary maximum in the stand wind profile.The profile of the wind speed near the forest floor was well approximated by a logarithmicequation with an effective roughness length of 0.005 m. Turbulence intensity was found tobe 0.7 for wind speed greater than 0.3 rn/s. Skewness of the vertical velocity componentwas positive near the forest floor. Power spectra for the streamwise and lateral velocitycomponents exhibited a bimodal distribution in contrast with a unimodal distributionfor the spectrum of the vertical component. Latent heat flux near the forest floor wasdirected upward for all daytime and nighttime runs and was the main energy outputcomponent of the energy budget of the forest floor.Keywords: eddy correlation, velocity statistics, energy budgetAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 148E.1 IntroductionThroughout much of Canada, old growth forests are important winter ranges for ungulates. For example, in the provincial and national parks and the ecological reserves ofBritish Columbia, old growth forests occupy approximately 185,600 ha, covering 22% ofthe total area of the parks and reserves (Roemer et gil. 1988). Yet little is known aboutthe microclimate in the environment of old growth forests. As a part of the microclimate,wind and turbulence regimes are important in several respects. Wind speed and turbulence intensity affect both boundary layer and coat resistances of animals (McArthurand Monteith 1980, Campbell et al. 1980). High turbulence intensity coupled with thepredominant eddy sizes (the turbulence length scale) similar to those of objects in theflow can greatly enhance heat and mass transfer from the objects (Chen et al. 1988).Knowledge of turbulent transfer processes near the forest floor is needed to understandthe competitive role of understory vegetation (the food supply for many species of wildanimals) in terms of water use and CO2 uptake (Black and Kelliher 1989).In order to understand the characteristics of air movement in old growth forests, anexperiment was conducted in an old growth Douglas-fir stand (Pseudotsuga menziesiiMirb. Franco) on a south facing slope in 1989. The main objective of this paper is todescribe the wind and turbulence regimes near the forest floor of this stand. Some specific concerns to be addressed included wind pattern, turbulence statistics, and spectralcharacteristics of the velocity components. In addition, the measurements of the energybudget will be briefly examined. The information documented in this report will be usedin assessing the magnitude of heat loss from black tailed deer in old growth forests (Sagaret al. 1991).Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 149E.2 Experimental MethodsE.2.1 Site DescriptionThe experimental site was located on an extensive south facing, 30-40% slope in theNimpkish Valley near Woss in northern Vancouver Island (50°65’N, 126°38’W). The valleyis oriented approximately in an east-west direction and the valley sides reach an elevationof 5 00-700 in above sea level. The lower part of the slope was occupied by a second growthDouglas-fir stand, roughly 20 m tall, and the upper part by an old growth Douglas-firstand over 200 years old, with dominant trees of about 30 m tall. The density of the oldgrowth stand was 500-700 stems/ha. The understory vegetation was patchy, less than0.7 m tall and mainly composed of salal (Gaultheria shallon Pursh.) and huckleberry(Vaccinium parvifolium).Two locations were selected for the experiment: one approximately 100 m into the oldgrowth stand, and the other, which served as a reference, at the outer edge of a widenedportion of a logging road 50 m outside the old growth stand.E.2.2 InstrumentationAt the interior location, an eddy correlation unit was mounted at a height of 2 m. Itconsisted of a 3-dimensional sonic anemometer (Applied Technologies Inc., Boulder, CO,Model BH-478B/3), a krypton hygrometer (Campbell Scientific Inc., Logan, UT, ModelKH2O, 1.021 cm path length) and a fine wire thermocouple (chromel-constantan, 13m in diameter). Profiles of wind speed and air temperature near the ground surfacewere measured using four home-made hot wire anemometers and four thermocouples(chromel-constantan, 26 um in diameter), respectively, at heights of 0.2, 0.4, 0.8 and 2.0m. For comparison and in situ calibration of the hot wire anemometers, a sensitive cupanemometer (C & F Casella Co., London, Model 3106/TO) was also mounted at theAppendix fri Turbulence in an Old Growth Douglas-fir Stand on a Slope 150height of 2 m. The horizontal separation among the three types of wind speed sensorswas approximately 5 m. A wind vane (Met One Inc., Grants Pass, OR, Model 024A)was mounted at a height of 2 m to monitor wind direction.The hot wire anemometers were calibrated individually before the experiment usinga turn-table system. The design of the hot wire anemometers was an improved versionthat of Kanemasu and Tanner (1968). The vertical supporting rod (1.7 mm in diameter)was 20 mm away from the vertically oriented heated ceramic tube (0.8 mm in diameter)so that measurements could be made for winds from all directions. The operating voltagewas 2 V instead of the original 12 V. The voltage from a 12 V recreational vehicle batterywas regulated down to four 2 V outputs in series so that 4 anemometers could be operatedsimultaneously. The heating wire had a resistance of about 10 Q, the time constant wasabout 1 second, and the minimum detectable wind speed was about 0.05 m/s. Thetemperature difference between the ceramic tube and the air was on the order of 80 °C.Because of the robust construction and low power consumption (0.20 A), the hot wireanemometers were operated continuously.Net radiation was measured with a net radiometer (Swissteco Instruments, Oberriet,Switzerland, Model S-1) mounted parallel to the slope surface at a height of 1.3 m.Another net radiometer of the same type was mounted on a tram system of 20 m pathlength for measuring spatially averaged net radiation (Black et al. 1991). The operationof the tram system was intermittent, but the results showed that the daytime total netradiation measured at a point with the first net radiometer well estimated the spatialaverage value. Heat flux into the soil was measured using four soil heat flux plates(two made by Middleton Instruments, South Melbourne, Model F, and two home-made)placed at a depth of 3 cm and two nickel wire integrating thermometers to correct forthe change in heat storage in the surface soil layer.The signals from the eddy correlation unit were sampled at 10 Hz by a data loggerAppendix F. Turbulence in an Old Growth Douglas-fir Stand on a Slope 151(Campbell Scientific Inc., Model 21X with extended software II). The data logger wasoperated in two modes, mean and burst. In the former, statistics such as means, varianceand covariance were calculated over 5 minute intervals and output every half hour. In thelatter, the raw signals were sent via the data logger to a lap-top micro-computer (ZenithData Systems Corp., St. Joseph, MI, Model ZWL-184-02 Supersport with a 20 Mb harddrive) for subsequent analysis. Sixty-seven 30-minute runs was made in the mean mode,fifty of which were in the daytime. Three 60-minute runs were made in the burst mode.Signals from the supplementary instruments were sampled by another data logger of thesame type at 0.1 Hz. An array of means were generated every 5 minutes.At the reference location, a vaned propeller anemometer (R.M. Young Company,Traverse City, MI, Model 05031) was operated at a height of 4.2 m. Wind speed anddirection were averaged over 5-minute intervals.The experiment started in late July and ended in the middle of August, 1989. Theexperiment was interrupted by three moderate to heavy rainfall events. Consequently,the forest floor was very wet during the experimental period.E.2.3 Comparison of AnemometersFigure E.1 compares measurements by the hot wire and the cup anemometers at theheight of 2 rn over the whole experimental period. In the low wind speed range, the hotwire sensor was superior to the cup sensor because of the inertial problem of the cup.Good agreement was achieved in the high wind speed range. Figure E.1 also shows thatthe calibration of the hot wire sensor did not shift during the experimental period.To make the comparison between the hot wire sensor and the sonic sensor, ‘cup’speed was calculated from the burst data for the sonic anemometer. The ‘cup’ speed wasAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 152I1.51.00.500Cup wind speed (mis)Figure E. 1: Comparison of the 30-minute average wind speed measured with a hot wireanemometer with that measured with a cup anemometer at a height of 2 m in the oldgrowth Douglas-fir stand near Woss during the entire experimental period of 1989.0.5 1.0 1.5Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 153defined asV=u?+v?where u and v1 are the two instantaneous horizontal velocity components and the overbardenotes temporal average. The results are shown in Table E.1. There was a slightdifference of 0.04 to 0.11 m/s, which might be a result of the underestimation by thesonic anemometer due to the shading effect of its transducers (Kaimal 1979, Baker 1989,Conklin et al. 1989).On 14 and 16 August, the four hot wire sensors were mounted at the same height of2 rn for inter-comparison. The 5-minute average wind speeds agreed within 0.10 rn/s.Generally, the hot wire system was reliable in measuring wind speed in low wind speedconditions.E.2.4 Data ProcessingE.2.4.1 Coordinate RotationCoordinate rotation was made in order to interpret properly the measurements of theeddy correlation unit. The new coordinate system was defined such that u was thestreamwise component of the velocity vector, v the lateral component of the vector, andw the component of the vector normal to the slope surface. The statistical properties ofturbulence were expressed in the new coordinate system.E.2.4.2 Spectral AnalysisThe power spectrum q of the a component of the velocity (i.e. u, v, in) is defined as00 1—J &a(n)dnwhere n is natural frequency in cycles per second (Hz) and cv’2 is the variance of a. Thepower spectra were calculated using a fast Fourier transform procedure written in PascalAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 154Table E.1: Comparison of the wind speed (m/s) at a height of 2 m measured by a hotwire anemometer (U) with the ‘cup’ speed measured by a sonic anemometer (V) on 9August 1989 in the old growth Douglas-fir stand near Woss.Run Time (PST) U Vla 10:00—10:30 0.76 0.73lb 10:30—11:00 1.18 1.122a 13:15—13:45 1.39 1.312b 13:45—14:15 1.31 1.253a 22:15—22:45 0.50 0.413b 22:45—23:15 0.49 0.38Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 155(Brigham 1988). The DC component and slope of the time series were removed beforeusing the procedure.E.3 Results and DiscussionE.3.1 Wind RegimesE.3.1.1 Daily PatternOn clear days there was a well defined anabatic (upsiope, approximately 1800) and katabatic (downslope, approximately 00) wind pattern both inside and outside the stand onthis south-facing slope, as shown in Figures E.2 and E.3 for 9 August 1991. Driven bysolar heating, the anabatic wind was well developed by around 08:00 PST. Wind speedincreased with time and reached peak values of 3.5 and 1.9 rn/s at the reference locationand inside the stand, respectively, at 13:30 PST, when solar heating was greatest. Afterthat wind speed decreased gradually. A transition occurred at 17:30 PST, when the ups-lope wind was replaced by a light downslope breeze. The nighttime wind speed fluctuatedaround 0.8 and 0.5 rn/s at the reference location and inside the stand, respectively.E.3.1.2 Comparison of Wind Speed inside and outside the StandThe wind inside the stand was well coupled with that outside the stand despite the heavyoverstory coverage, the correlation coefficient being 0.87 for 249 runs (Figure E.4). Thepositive offset of the regression equation shown in the figure was probably caused bythe inertia of the vaned propeller anemometer at the reference location. Wind speedinside the stand was on average 28% of that outside the stand. This value is ratherhigh, suggesting the existence of a secondary maximum in the profile of wind speed inthe stand. Secondary maxima in the wind profiles have been frequently observed in thetrunk space of forests (e.g. Shaw 1977). As a consequence of this maximum, gas andAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 156100— I I I I I0 6 12 18 24Hour (PST)Figure E.2: Daily pattern of 5-minute average wind speed and direction observed on aclear day (9 August 1989) at a height of 4.2 m on the logging road outside the old growthDouglas-fir stand near Woss.Appendix F. Turbulence in an Old Growth Douglas-fir Stand on a Slope 157I3OO -1824Hour (PST)Figure E.3: Same as in Figure E.2 except at a height of 2 m inside the stand. The windvane was stalled during the period between 0:00 and 7:00 PST.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 158I I I1.5 Y=O.16+O.28XD.‘-4.EDD0 I I I0 1.0 2.0 3.0Wind speed outside stand (mis)Figure E.4: Comparison of 30-minute average wind speed at a height of 2 m inside theold growth Douglas-fir stand near Woss with that at a height of 4.2 m outside the standduring the period from July 29 to August 19, 1989. Also shown is the equation for thebest fit line.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 159heat exchange between the understory vegetation and the air, and the heat loss fromanimals are likely to be enhanced. In this sense, the old growth stand is not as good an‘insulating’ environment as one may expect.E.3.1.3 Wind Speed Profiles near the Forest FloorFor practical purposes, wind speed near the ground surface beneath a vegetation canopyis commonly described by (Wilson and Shaw 1977)Z ZrU(z)/Ur = ln(—)/ln(—) (E.1)Z0where U(z) is the wind speed at height Z measured with the hot wire anemometer,Ur is the wind speed at a reference height Zr (Zr = 2.0 m in this case), and Z0 is aneffective roughness length of the ground surface. In this study, the daytime wind speedincreased approximately logarithmically with height (Figure E.5). As shown in thisfigure, the prediction of (E.1) with a value of 0.005 m for Z0 agreed well with the daytimemeasurements. This value of Z0 was smaller than expected, considering that there werescattered understory vegetation and dead debris on the forest floor. In other words, theforest floor was aerodynamically smoother than it appeared to be.The nighttime wind speed was generally low. The nighttime profiles were slightlydifferent in shape from the daytime profiles. For most of the nighttime runs, the windspeeds at 0.8 m and 0.4 m were of similar magnitude, while for some runs the wind speedat 0.4 m exceeded that at 0.8 m. This feature may be an indication of the thermallyinduced drainage flow on the slope during the nighttime.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 160I I19:30 13:30- 6:00 23:30 10:00 15:00I’llI’llI) III?/ ‘I!/ ‘I /hi /I /‘/0—_ I I0 0.5 1.0 1.5Wind speed (mis)Figure E.5: Profiles of 30-minute average wind speed during the period from 09:30 PST9 August to 06:00 PST 10 August 1989 near the forest floor of the old growth Douglas-firstand near Woss. The time shown above each profile marks the end of the 30-minuterun. The dashed line represents a logarithmic profile calculated from Equation(E.1) witha value of 0.005 rn for z0 and a value of 1 rn/s for Ur.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 161E.3.2 Turbulence StatisticsE.3.2.1 Variance and Momentum FluxInformation regarding variance of the velocity components is helpful for developingcanopy flow models (e.g. Wilson and Shaw 1977, Wilson 1988) and for understanding of dispersion and diffusion processes in a plant canopy (Raupach 1987). The daytimeaveraged values for the u variance (), v variance (v12) and w variance () were 0.111,0.094 and 0.008 m2/s, respectively. The corresponding figures for the nighttime were0.017, 0.014 and 0.004 m2/s. The daytime ratios of v’2/u’ and w’2/u were, on average,0.87 and 0.07, respectively. While the ratio v’2/u’ was similar to that observed in theneutral surface layer (Panofsky and Dutton 1984) and in some other forest stands (e.g.Amiro 1990a and Baldocchi and Meyers 1988), the ratio of w’2/u in the present studywas much smaller. The small value was likely a consequence of the measurement beingclose to the ground (our sensor height/canopy height ratio was 0.07), and might havebeen related to the stratification of the air layer in the lower part of the stand. As pointedout later in this paper, daytime air temperature exhibited characteristically a moderateto strong inversion in the 0< z < 2 m layer. It is well established that in the surfacelayer the main contribution to w variance comes from smaller eddies and that the maincontributions to u and v variances come from much larger eddies. Consequently, w variance obeys Monin—Obukhov scaling, i.e. a similarity theory that applies to the exchangeprocesses in the atmospheric surface layer, while u and v variances do not (Panofsky andDutton 1984). The spectral analysis presented later in this paper shows that the energycontaining frequencies of the w variance were higher than those of the u and v variancesby a factor of 10. In other words, turbulent energy was fed into the w component andthe u and v components from eddies of quite different sizes. Vertical fluctuations weremore subject to the local stratification in the lower part of the stand, because the size ofAppendix F. Turbulence in an Old Growth Douglas-fir Stand on a Slope 162the energy containing eddies was small, and hence were suppressed. On the other hand,streamwise and lateral fluctuations might be affected more by the external environmentwhich was not necessarily stable, because the energy containing eddies were large.Values of tangential momentum flux —7 varied from 0.035 to —0.015 m2/s. Halfthe runs had negative values. Other researchers (Baldocchi and Hutchison 1987, Raupach et al. 1986, Chapter 2) have also reported negative momentum flux at the lowerheight within plant canopies. They suggested that the negative values, if real, mightbe associated with dispersive flux. Dispersive flux arises from the spatial correlation ofquantities averaged in time but varying with horizontal position (Raupach and Shaw1982). However, it is possible that the negative momentum flux reported here was aresult of errors in the measurements or in performing the coordinate rotation on a steepslope.E.3.2.2 Turbulence IntensityTurbulence intensity is defined asi=Ju+v2+w2where i is the mean value of the streamwise velocity component. Figure E.6 plots theintensity (i) as a function of wind speed (z). Much of the scatter occurred at wind speedless than 0.3 m/s, with the value of i occasionally exceeding 3.0. At higher wind speed,the intensity approached a constant value of approximately 0.7. This value was lowerthan that obtained by Baldocchi and Hutchison (1987) and Moritz (1989) near the forestfloors of a deciduous forest and a pine forest, respectively, but similar to that obtainedby Allen (1968) in a Japanese larch plantation.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 16340aU2Uri 0a—0 0a DO00 osai.o 1.5i (mis)Figure E.6: Turbulence intensity (i) as a function of mean streamwise velocity (i1) at aheight of 2 m inside the old growth Douglas-fir stand near Woss.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 164E.3.2.3 Higher Order MomentsSkewness and kurtosis were calculated from the the burst mode data obtained on 9August 1989 (Table E.2). Skewness expresses the degree of asymmetry about the meanof a probability distribution. The values of skewness for the velocity components werenot equal to zero, a value for the Gaussian distribution, and exhibited variability inmagnitude for all three components and uncertainties in sign except for w component.The skewness of the w component was positive for all six 30-minute runs, implying activeupdraft motions. This seems to contradict the general picture that large scale downwardmovements are dominant in the plant canopy, making w skewness negative (e.g. Shawand Seginer 1987, Raupach et al. 1986, Amiro and Davis 1988, Moritz 1989, Baldocchiand Hutchison 1987, Kelliher et al. 1991). However, Leclerc et al. (1991) found that wskewness in a deciduous forest canopy could become positive in strongly stable conditions.Kurtosis is a measure of peakness or flatness of a probability distribution. For mostof the runs, the values of the kurtosis of the velocity components were higher than 3,the value for the Gaussian distribution, but much smaller than those observed by otherworkers (e.g., Amiro and Davis 1988 and Raupach et al. 1986).E.3.3 Power SpectraThe power spectrum of a quantity reveals the relative importance of eddies of differentsize in its variance. The spectra of the velocity components were calculated for the period13:15—14:15 PST on 9 August (Figure E.7). The spectrum of the u component showsdouble peaks, the dominant one at 0.01 Hz and the less developed one at 0.5 Hz. Asimilar pattern was also found for the v component. This bimodal distribution is similarto the observations made by Allen (1968) for the streamwise velocity in a Japanese Larchplantation, with peaks occurring at 0.05 and 0.3 Hz, and the main contribution beingAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 165Table E.2: Turbulence statistics at a height of 2 m on 9 August 1989 in the old growthDouglas-fir stand near Woss, where i is the mean streamwise component of the velocityinside the stand and Uref is the wind speed at the reference location outside the stand.The time of the runs is given in Table E.1.wind speed variance skewness kurtosisRun u Uref ‘Lt V W U V W U V Wrn/s m2/sla 0.67 2.38 0.14 0.12 0.01 0.58 0.17 0.12 3.99 2.79 3.53lb 1.09 2.65 0.18 0.17 0.01 —0.54 —0.05 0.30 3.11 3.59 4.122a 1.28 2.91 0.29 0.18 0.02 —0.56 —0.08 0.47 4.39 3.23 4.502b 1.20 3.11 0.30 0.29 0.02 —0.26 0.72 0.82 2.62 4.10 4.673a 0.48 0.86 0.01 0.02 0.00 0.20 0.19 0.02 3.34 3.01 3.053b 0.43 0.86 0.02 0.02 0.00 —0.68 —0.22 0.08 3.95 2.51 3.09Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope(%C,,n (Hz)166Figure E.7: Power spectra of the streamwise (u) and vertical (w) velocity componentsfor the period 13:15—14:15 PST on 9 August 1989 at a height of 2 m in the old-growthDouglas-fir stand near Woss. Also shown is the slope predicted for the inertial subrange.0.0010.00010.010.001.•e.:•: -2/3-’- •iiiil •• I IIIIII I III II III I I I I I iiil I I-•.•.• : ‘-.•-U-.••iiiil I I iiiiiil I III iiiil I I iiiiiil I0.001 0.01 0.1 1Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 167from the lower frequency peak. This means that near the forest floor there was lessvariance on small scales and that most of the streamwise and lateral variations of the airflow was associated with eddies of large scale.Some researchers have suggested that turbulent wakes generated by the plant elementsare responsible for the higher frequency peak in the power spectra inside canopies (Allen1968, Seginer et al. 1976, Raupach et al. 1986, Amiro and Davis 1988). Some of themfound that the secondary peak frequency could be predicted using (Seginer et al. 1976,Amiro and Davis 1988)Si = nd/ri (E.2)where d is an effective dimension of the plant elements, n is the frequency of the wakes,and St is the Strouhal number, which has a value of 0.21 for cylinders for Reynoldsnumbers between 6 x 102 and 6 x iO (Schlichting 1968). In the present study, treetrunks were the main elements in the lower part of the stand. The diameter of thedominant trees was about 0.4 m. Using (E.2) with the value of 0.21 for St and a valueof 1.2 rn/s for F1, the frequency of the wakes of the tree trunks was found to be about0.4 Hz, which is quite close to the secondary peak frequency. The vortices shed by thevertical cylinders, i.e. tree trunks, were mainly of vertical vorticity (Seginer et al. 1976),which would more likely show up in the u and v energy spectra. The u and v energyspectra may therefore be viewed as spectra combining the effects of wake production ofthe tree trunks and the low frequency fluctuations associated with large eddies.The ratio of the size of vortices in the wake of the trunks to the characteristic dimension of the body of ungulates, e.g. mature black tailed deer, is approximately 1.0—2.3.According to the studies of Zijnen (1958) on heat transfer from cylinders in turbulentflow, ratios in this range would result in maximum heat loss. This implies that the sizeof vortices in the wake would be optimum to enhance heat transfer from the body of theAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 168deer.In contrast, only one peak can be identified in the w power spectrum. The main contribution was from high frequencies, suggesting that the fluctuations in the w componentwere related to much smaller eddies. The peak of the w power spectrum occurred ataround the secondary peak frequency of the u and v spectra. The separation betweenthe energy containing frequencies of the u and v components and the w component nearthe forest floor has also been observed in several other cases (Baldocchi and Hutchison1987, Amiro 1990h).Besides resulting in the production of turbulent wakes, the drag force imposed on thecanopy flow by plant elements short-circuits the energy cascade process, i.e. the continuous transfer of turbulence kinetic energy from larger to progressively smaller eddies(Shaw and Seginer 1985). The short circuit in the cascade, in combination with the invalidity of Taylor’s frozen turbulence hypothesis in plant canopies and the energy loss dueto the averaging over the path length between the transducers of the sonic anemometer,caused the power spectra to deviate from Kolmogorov’s local isotropy law (Amiro andDavis 1988). This is evident from the slope of the high frequency range in Figure E.7being steeper than —2/3, the slope predicted for the inertial subrange (Tennekes andLumley 1972).E.3.4 Energy Budget near the Forest FloorThe magnitudes of the energy budget components near the forest floor were rather small.The half-hourly values for net radiation flux (R,j, heat flux into the soil (C), sensibleheat flux (H) and latent heat flux ()E) varied between —3 and 58, —5 and 10, —11 and2 and 1 and 21 W/m2, respectively. \E was positive (upward) for all 67 runs, whichwas expected since the forest floor was fairly wet during the experimental period. Hwas slightly positive in the nighttime and was negative (downward) for the majorityAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 169of the runs (39 out of 50) in the daytime. The temperature profile near the forest floorconstantly exhibited a moderate to strong inversion in the daytime, the gradient being ashigh as 0.3 0C/m, and a slight lapse in the nighttime. The directions of the temperaturegradient resulted mainly from the radiative heating of the overstory in the daytime andcooling at night. These results suggest that very close to the floor of the tall forest, thescalar fluxes generally flowed down their respective gradients, although the phenomenonof counter-gradient flow has been frequently observed in the middle and upper parts ofthe forest stands (Denmead and Bradley 1985, Leclerc 1987, Amiro 1990a, Chapter 3). Infact, there existed a fair correlation between H and the temperature gradient calculatedfrom the measurements at the heights of 2 m and 0.2 m, the correlation coefficient being0.76 for the 67 runs.Table E.3 shows the averaged values of the energy budget components for five periods.It can be seen that )E was the main output component of the energy budget of the forestfloor during the daytime. The sum of the eddy fluxes (H + )E) was slightly lower thanthe available energy flux (R,,— G), but overall the energy budget closure was satisfactoryconsidering the small magnitudes of the components. The daytime courses of the energybudget components shown in Figure E.8 for 17 August 1989 are typical of those duringthe experimental period.E.4 Concluding RemarksOn clear days, anabatic and katabatic winds were observed inside and outside the stand.The high value of of the ratio of wind speed inside the stand to that outside the stand(0.28) suggests that there existed a secondary maximum in the stand wind profile. Thismeans that the old growth stand was not as good an ‘insulating’ environment as might beexpected. The wind speed near the forest floor was well approximated by the logarithmicAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 170Table E.3: Components (W/m2)of the energy budget of the forest floor of the old growthDouglas-fir stand near Woss in August 1989. R is net radiation flux, G is the heat fluxinto the soil, H and AE are the eddy fluxes of sensible and latent heat, respectively. Alsolisted are the measure of energy budget closure (Rn—G—Hm\E) and the average value ofthe global (horizontal surface) solar irradiance (S, W/m2)outside the stand.Date 9 9 to 10 10 17 18Period (PST) 11:30—17:00 20:30—6:00__10:30—14:00__9:30—17:00__9:30—16:30S 588 0 568 501 627R 24 —3 21 23 26G 3 —4 2 5 6H —3 1 —1 —2 —3AE 17 1 13 8 13R—G—H—,\E 7 —1 7 12 10Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 1716O-20--I I I10 13 16Hour (PST)Figure E.8: Daytime courses of the energy budget components of the forest floor of theold growth Douglas-fir stand near Woss on 17 August 1989: () J?, — G, (o) H, and (.)AE. The sky was overcast.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 172wind profile equation with an effective roughness length of 0.005 rn.Turbulence intensity was a function of wind speed. The value of the intensity wasabout 0.7 for wind speed higher than 0.3 rn/s. The skewness of the vertical velocitycornponent was positive, implying active updraft movements near the forest floor. Thepower spectra for the streamwise and lateral velocity components exhibited a bimodaldistribution, the main contribution being at the lower frequency peak. The sizes of theeddies corresponding to the higher frequency peak, probably the result of wakes producedby the tree trunks, were comparable to the trunk diameter of mature black-tailed deer.This may have implications in the turbulence enhancement of heat loss from the animal.Only one peak was identified in the spectrum for the vertical velocity component.Latent heat flux was the main output component of the energy budget of the forestfloor and was directed upward. Results showed that that eddy fluxes of sensible heat andwater vapour near the forest floor generally flowed down their respective gradients.E.5 Literature CitedALLEN, L.J. 1968. Turbulence and wind speed spectra within a Japanese larch plantation. J. Appi. Meteorol. 7:73-78.AMIRO, B.D. 1990a. Comparison of turbulence statistics within three boreal forestcanopies. Boundary- Layer Meteorol. 51:99-121.AMIRO, B.D. 1990b. Drag coefficients and turbulence spectra within three boreal forestcanopies. Boundary- Layer Meteorol. 52:227-246.AMIRO, B.D. and P.A. DAVIS. 1988. Statistics of atmospheric turbulence within anatural black spruce forest canopy. Boundary-Layer Meteorol. 44:267-283.BAKER, C.B. 1989. Experimental determination of transducer shadow effects on a sonicAppendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 173anemometer. Eighth Symposium on Turbulence and Diffusion, Preprint volume,American Meteorological Society, San Diego, CA, pp 104-107.BALDOCCHI, D.D. and B.A. HUTCHISON. 1987. Turbulence in an almond orchard:Vertical variations in turbulent statistics. Boundary-Layer Meteorol. 40:127-146.BALDOCCHI, D.D. and T.P. MEYERS. 1988. Turbulence structure in a deciduousforest. Boundary-Layer Meteorol. 43:345-364.BLACK, T.A., J.M. CHEN, X. LEE, and R.M. SAGAR. 1991. Characteristics of shortwave and longwave irradiances under a Douglas-fir forest stand. Can. J. For. Res.21:1020-1208.BLACK, T.A. and F.M. KELLIHER. 1989. Processes controlling understory evapotranspiration. Phil. Trans. R. Soc. Lond. B324:207-231.BRIGHAM, E.O. 1988. The Fast Fourier Transform and Its Applications, EnglewoodCliffs, NJ.CAMPBELL, G.S., A.J. McARTHUR, and J.L. MONTEITH. 1980. Windspeed dependence of heat and mass transfer through coats and clothing. Boundary-LayerMeteorol. 18:485-493.CHEN, J.-M., A. IBBETSON, and J.R. MILFORD. 1988. Boundary-layer resistancesof artificial leaves in turbulent air: I. Leaves parallel to the mean flow. BoundaryLayer Meteorol. 45:137-156.CONKLIN, P.S., K.R. KNOERR, T.W. SCHNEIDER, and C.B. BAKER. 1989. Awind tunnel test of probe shadow effects on a sonic anemometer in two orientation. Eighth Symposium on Turbulence and Diffusion, Preprint volume, AmericanMeteorological Society, San Diego, CA, pp 108-110.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 174DENMEAD, O.T. and E.F. BRADLEY. 1985. Flux-gradient relationships in a forestcanopy. The Forest-Atmospheric Interaction, HUTCHISON, B.A. and B.B. HICKS(eds.). D. Reidel Publishing Co., Dordrecht, pp 421-442.KAIMAL, J.C. 1979. Sonic anemometer measurement of atmospheric turbulence. Proceedings of Dynamic Flow Conference. Skovlunde, Denmark, DISA Electronic A/S,pp 551-565.KANEMASU, E.T. and C.B. TANNER. 1968. A note on a heat transport anemometer.BioScience. 18:327-329.KELLIHER, F.M., D. WHITEHEAD, K.J. McANENEY, AND M.J. JUDD. 1991. Partitioning evapotranspiration into tree and understorey components in two youngPinus radiata D. Don stands. Agric. Forest Meteorol. 50:211-227.LECLERC, M.Y. 1987. Turbulence and turbulent diffusion inside and above vegetation.Ph.D. Thesis. University of Guelph, Guelph, Ontario.LECLERC, M.Y., K.C. BEISSNER, R.H. SHAW, C. den HARTOG, and H.H. NEUMANN. 1991. The influence of buoyancy on third-order turbulent velocity statisticswithin a deciduous forest. Boundary-Layer Meteorol. 55:109-124.McARTHUR, A.J. and J.L. MONTEITH. 1980. Air movement and heat loss fromsheep. I: Boundary layer insulation of a model sheep, with and without fleece.Proc. R. Soc. Loud. B209:187-208.MORITZ, E. 1989. Heat and momentum transport in an oak forest canopy. BoundaryLayer Meteorol. 49:317-329.PANOFSKY, H.A. and J.A. DUTTON. 1984. Atmospheric Turbulence: Models andMethods for Engineering Applications, John Wiley & Sons, New York.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 175RAUPACH, M.R. 1987. A Lagrangian analysis of scalar transfer in vegetation canopies.Quart. J. R. Meteorol. Soc. 113:107-120.RAUPACH, M.R. and R.H. SHAW. 1982. Averaging procedures for flow within vegetation canopies. Boundary-Layer Meteorol. 22:79-90.RAUPACH, M.R., P.A. COPPIN, and B.J. LEGO. 1986. Experiments on scalar dispersion within a model plant canopy. Part I: The turbulence structure. Boundary-Layer Meteorol. 35:21-52.ROEMER, H.L., .1. POJAR, and K.R. JOY. 1988. Protected old-growth forests incoastal British Columbia. Natural Areas Journal. 8:146-159.SAGAR, R.M., T.A. BLACK, X. LEE, and J.M. CHEN. 1991. Heat transfer relationships for deer in Douglas-fir stands. 20th Conference on Agricultural and ForestMeteorology and 10th Conference on Biometeorology and Aerobiology, AmericanMeteorological Society, Salt Lake City, UT. Prepririt volume. pp 129-132.SCHLICHTING, H. 1968. Boundary-Layer Theory. 6th Edition, McGraw-Hill BookCompany, New York.SEGINER, I., P.J. MULHEARN, E.F. BRADLEY, and J.J. FINNIGAN. 1976. Turbulent flow in a model plant canopy. Boundary-Layer Meteorol. 10:423-453.SHAW, R.H. 1977. Secondary wind speed maxima inside plant canopies. J. Appl.Meteorol. 16:514-523.SHAW, R.H. and I. SEGINER. 1985. The dissipation of turbulence in plant canopies.Seventh Symposium on Turbulence and Diffusion, Preprint volume, American Meteorological Society, Boston, Massachusetts, pp 200-203.Appendix E. Turbulence in an Old Growth Douglas-fir Stand on a Slope 176SHAW, R.H. and I. SEGINER. 1987. Calculation of velocity skewness in real andartificial plant canopies. Boundary-Layer Meteorol. 39:315-332.TENNEKES, H. and J.L. LUMLEY. 1972. A First Course in Turbulence, The MITPress, Massachusetts.WILSON, J.D. 1988. A second-order closure model for flow through vegetation. BoundaryLayer Meteorol. 42:371-392.WILSON, R.N. and R.H. SHAW. 1977. A higher order closure model for canopy flow.J. Appl. Meteorol. 14:1197-1205.Van der HEGGE ZI.JNEN, B.G. 1958. Heat transfer from horizontal cylinders to aturbulent air flow. Appl. Sci. Res. A7:205-223.Appendix FMaps of the Browns River Research Site177Appendix F. Maps of the Browns River Research Site 1784Contour elevations are in thousands of feet above mean sea level. The forest surroundingthe site is second growth Douglas-fir of similar age which extends at least 5 km in alldirections.Appendix F. Maps of the Browns River Research Site 179200Figure F.2: Positions of the instruments used in the Browns River experiment: maininstrument tower (s), tower for measuring diffuse solar irradiance above the stand(A), tram for radiation measurements (—), model deer (.), and one-dimensional sonicanemometer/thermometer units (.). Contour elevations are in metres above mean sealevel.0 metres
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Atmospheric turbulence within and above a coniferous forest Lee, Xuhui 1992
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Title | Atmospheric turbulence within and above a coniferous forest |
Creator |
Lee, Xuhui |
Date Issued | 1992 |
Description | An experiment to study the exchange processes within and above an extensive coniferous forest of Douglas-fir trees was conducted on Vancouver Island during a two-week rainless period in July and August 1990. The stand, which was planted in 1962, thinned and pruned uniformly in 1988, had a (projected) leaf area index of 5.4 and a height of h = 16.7 m. The experimental site was located on a 5° gentle slope. The primary instrumentation included two eddy correlation units which were operated in the daytime to measure the fluctuations in the three velocity components, air temperature and water vapour density. One unit was mounted permanently at a height of 23.0 m (z/h = 1.38) and the other at various heights of (z/h in brackets) 2.0 (0.12), 7.0 (0.42), 10.0 (0.60), and 16.7 m (1.00) with two to three 8-hour periods of measurement at each level. Profiles of wind speed and air temperature were measured continuously during the experimental period at heights of 0.9, 2.0, 4.6, 7.0, 10.0, 12.7, 16.7 and 23.0 m using sensitive cup anemometers and fine wire thermocouples, respectively. Radiation regimes and air humidity were measured both above and beneath the overstory of the stand. The vertical structure of the stand affected, to a great extent, the vertical distributions of the velocity statistics (wind speed, variance, turbulence intensity, Reynolds stress, skewness and kurtosis), air temperature, sensible and latent heat fluxes. The effect was also evident in the quadrant representation of the fluxes of momentum, sensible heat and water vapour. Negative Reynolds stress persistently occurred at the lower heights of the stand (z/h = 0.12 and 0.42). The negative values were related to the local wind speed gradients and it is believed that the longitudinal pressure gradient due to land-sea/upslope-downslope circulations was the main factor responsible for the upward transport of the momentum at these heights. Energy budget was examined both above and beneath the overstory of the stand. The sum of sensible and latent heat fluxes above the stand accounted for, on average, 83% of the available energy flux. Beneath the overstory, the corresponding figure was 74%. On some days, energy budget closure was far better than on others. [more abstract] |
Extent | 3821316 bytes |
Genre |
Thesis/Dissertation |
Type |
Text |
FileFormat | application/pdf |
Language | eng |
Date Available | 2008-12-18 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0086620 |
URI | http://hdl.handle.net/2429/3154 |
Degree |
Doctor of Philosophy - PhD |
Program |
Soil Science |
Affiliation |
Land and Food Systems, Faculty of |
Degree Grantor | University of British Columbia |
GraduationDate | 1992-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
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