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On nighttime turbulent exchange within and above a sloped vineyard Everard, Kelsey 2017

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On Nighttime Turbulent Exchange within and abovea Sloped VineyardbyKelsey EverardB.S., University of Virginia, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Geography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2017c©Kelsey Everard, 2017AbstractHigh frequency three-dimensional wind and distributed temperature measurements were taken over a ∼7◦vineyard slope in the Southern Okanagan Valley, British Columbia, Canada, during three weeks in July2016. Approximately 17% of the nighttime is characterised by drainage flow along the local slope. Drainageconditions are characterised by inverted temperatures beginning around z/hc = 0.39, where z is the heightabove ground level (AGL) and hc is the canopy height (∼ 2.3 m AGL), and near-surface lapses. A jetmaximum is observed around z/hc = 1.65, while a weak inflection point is observed near the canopy top,suggesting influence from both drainage layer and canopy layer dynamics on the turbulent field. The greatestobserved fluxes in both the stream-wise momentum flux and the sensible heat flux are near the top ofthe canopy, consistent with the location of the inflection point. Calculated two-point length scales fromdistributed temperature measurements reveal that turbulent structures are smallest near the canopy top.Conditional sampling of the 3-D ultrasonic wind components and acoustic temperature indicate that a largefraction of canopy layer transport is driven by canopy-top turbulence, with sweeps dominating over ejections,particularly at z/hc = 0.65. Results presented here are important both for nighttime vineyard managementtechniques and for further understanding on particle dispersion.iiLay SummaryIn the following work, the exchange of heat and momentum within a vineyard environment during thenighttime is investigated. It is shown that two regimes dictate the turbulent dynamics of the system, boththe nighttime drainage regime and the canopy layer regime. This work furthers current understanding onthe interface and communication between the surface and the atmosphere, and is integral to the continuedefforts to improve the representation of near-surface processes in current and future climate and weathermodels.iiiPrefaceField site set-up was conducted by myself, Dr. Andreas Christen (hereafter referred to as AC), Dr. AndyBlack, and Paul Skaloud (hereafter referred to as PS). Soil moisture measurements were made and recordedby PS during the campaign. Scripting of the logger programs was completed in part by my supervisor, AC.All data processing was scripted and completed by myself. Part of the introduction section of this thesis wascompleted as part of a required course for all first year graduate students in the Department of Geography(GEOB 500). Sonic inter-comparison data was acquired from Liss et al. (2009).ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviDedications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Canopy Layer Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Canopy Turbulence in Near Neutral Conditions . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Advances in CSL Understanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Common Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 Drainage Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Brief Theory and Characteristics of Drainage Flow . . . . . . . . . . . . . . . . . . . . 61.2.2 Typical Drainage Onset Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 Observational Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 Study Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Field Site Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Measurement Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.1 Campbell Scientific 3D Sonic Anemometer . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Post-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.1 CSAT-3D Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.2 CSAT-3D Wind Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.3 CSAT-3D Acoustic Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20v2.4.4 Thermocouple Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Case Study Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5.1 Time Series Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.2 K-Means Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.6 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1 Graphical Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 General Case Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3.1 The Flux-Gradient Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4 Characterising Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4.1 Profile of Third Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4.2 Connectivity between Heat and Momentum . . . . . . . . . . . . . . . . . . . . . . . . 473.4.3 Event Size and Transfer Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.5 Characteristic Turbulent Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1 Drainage Flow Characteristics within the Vineyard . . . . . . . . . . . . . . . . . . . . . . . . 594.1.1 Thermal Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.1.2 Mechanical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2 Fluxes, Gradients, and their Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2.1 Flux-Gradient Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2.2 Momentum Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2.3 Sensible Heat Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.3 Turbulent Scales and Coherent Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3.1 Coherent Structure Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684.3.2 Structure Scale and Behaviour Dependence on Wind Direction . . . . . . . . . . . . . 694.3.3 Similarity to Plane Mixing Layer Theory . . . . . . . . . . . . . . . . . . . . . . . . . 705 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81viAppendix A: CSAT Rotation Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Appendix B: Thermocouple Corrections - Sample Calculation . . . . . . . . . . . . . . . . . . . . . 85viiList of Tables2.1 Time line of field campaign in the southern Okanagan Valley in July 2016. . . . . . . . . . . . 112.2 Table of CSAT-3D instrument uncertainty, as calculated from reported standard deviationsin Liss et al. (2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Corrections obtained through ultrasonic anemometer zero-wind calibration tests. ultrasonicanemometers are identified by serial number, and their vertical placement on the flux towerindicated (z/hc; z = height AGL, hc = height of canopy). Corrections for x- y- and z- weresubtracted from all CSAT-3D measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4 Calculated mean difference between CSAT-3D acoustic temperature and the mean thermo-couple temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 Summary of selection criteria during initial visually based clustering methods. . . . . . . . . . 262.6 Summary of selected drainage events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.7 Octants necessary for the calculation of quadrant stress fractions for common quadrant anal-ysis for both the stream-wise vertical momentum flux (u′w′) and the cross-stream verticalmomentum flux (w′T ′). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.1 Measured soil volumetric water content at the tower and at 32 m up-slope from the tower(near Mast H). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37A1 Mean absolute error (MAE) for vertical momentum and heat fluxes associated with ±1◦ slopeangle measurement errors. MAE is calculated from 211 5-minute case study time series. . . . 82A2 Percent contribution of fluxes (potentially) affected by over or under rotation (6◦ or 8◦, re-spectively) to the total calculated flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82A3 Percentage of time that the flux is above the threshold hole size of 3 or 1 . . . . . . . . . . . 84viiiList of Figures1.1 Schematic of typical temperature, wind, and turbulent kinetic energy (TKE) vertical profilesfor the nighttime drainage wind, modified from the image provided in Zardi and Whiteman(2013). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Topographic map of the southern Okanagan Valley. Map of British Columbia was obtainedfrom ESRICanadaED (https://www.arcgis.com/home/item.html?id=dcbcdf86939548af81efbd2d732336db). Map projection is BC Albers 1984. Scale provided is for the coloured topo-graphic map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Elevation (m above sea level) transects between the ultrasonic tower and 2 km (a) east and(b) north. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Schematic of field site set-up. Bird’s eye view provides to-scale spacing of thermocouple(TC) masts and the ultrasonic tower. The side-view provides a to-scale visual of the verticalalignment of CSAT-3D’s on the pump-up tower and the TCs on respective masts. . . . . . . . 122.4 Photos of the field site. (a) is a panorama view from east (90◦) over south to west (270◦)of the vineyard plot where the study slope is located, position of thermocouple (TC) mastsand ultrasonic tower are labelled (see also Figure 2.3). (b) is a close-up view looking up-slope(east) of the ultrasonic tower, with labelled vertical positions of the individual CSAT-3D’snormalised by the canopy height hc = 2.3 m AGL. (c) provides a close-up of TC mast set-up,the position of some of the TCs and the infrared thermometers (IRTs) that were mounted onthe tower. Credit: A. Christen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Schematic of fine-wire thermocouple (TC) deployed on slope for air temperature measure-ments. A: Polyvinyl shielded Chromel-Constantan (Chr-Con) extension grade wire (EXPP-E-24S-SLE) is connected to B: female connector which connects to C: male connector whichconnects to 30-gauge Chr-Con wire which feeds into D: a small brass protection tube of length15.24 cm. E: the 30-gauge wire is then soldered to F-G: the 0.001" factory-welded bare Chr-Con TC junction. F represents the Chr-Con 0.001" wires, and G represents the factory-weldedjunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14ix2.6 (a) Soil thermocouple (TC) array, located in the centre between the N-vegetation row andthe adjacent row the the N of the study site. Six TCs constructed from polyvinyl shieldedChromel-Constantan (Chr-Con) extension-grade wire are spaced at 1 cm, with the topmostmeasurement at 1 cm below the soil surface. Note that photo was taken during installation;soil was filled in afterwards. (b) Diagram of soil TC. A: Extension-grade Chr-Con wires; B:Polyvinyl-shielded extension-grade Chr-Con wire. Soil TCs are constructed by twisting theends of the Chr-Con wires to create a ’junction’. Chromel wires are coloured purple, and arethe positive legs; Constantan wires are coloured red, and are the negative legs. . . . . . . . . 152.7 Photos of CSAT-zeroing set-up. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.8 Vertical profiles of mean wind speed for case study on the night of 06/07/2017. Ui =1N∑Nt=1√x¯i(t)2 + y¯i(t)2, where N = number of 30-minute records in case study night (18),x¯i(t) is the 30-minute mean of component x for record t, and index i indicates the CSAT-3Dat which the average is calculated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.9 Comparison between the CSAT-3D acoustic temperatures and the thermocouple (TC) tem-peratures before (a) and after (b) applied acoustic temperature corrections. . . . . . . . . . . 212.10 Example of a drainage flow night (DF). Five minute averages of variables are plotted for thenight of 07 July 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.11 Example of a valley drainage or other flow type (VOF). Five minute averages of variables areplotted for the night of 07 July 2016. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.12 Five-minute block averaged turbulent kinetic energy (TKE) versus five-minute block averagedgradient Richardson number (Ri) for all nighttime cases with outgoing net radiation (Q∗)< −30 W m−2 at z/hc = 1.01 and z/hc = 2.05. (a) cases with a five-minute averaged winddirection at z/hc = 1.02 outside of the down-slope domain (between 45◦ and 135◦; (b) caseswith a five-minute averaged wind direction at z/hc = 1.02 within the down-slope domain.Valley or other flow (VOF) clusters are coloured red; Drainage flow (DS) clusters are colouredblue. TKE and Ri at z/hc = 2.06 are denoted by asterisks, and that at z/hc = 1.02 by opencircles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.13 Diagram of octants. The numbers identify the octants. . . . . . . . . . . . . . . . . . . . . . . 313.1 Diagram describing the statistics represented by the box plots presented in this study. Q1represents the 25th percentile, Q2 is the median, Q3 is the 75th percentile, and the IQR is theInter-Quartile Range, defined as Q3 - Q1. The notches in the box plots represent the 95%confidence interval for the calculated median, and a represents the parameter described bythe box plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35x3.2 Measured and calculated components of the energy balance for the drainage layer as a functionof time after sunset (Sunset is approximately 21:05 LST) . . . . . . . . . . . . . . . . . . . . . 363.3 Relationship between volumetric water content and the soil thermal conductivity for a mineralsoil. Red star indicates value used for soil in study. . . . . . . . . . . . . . . . . . . . . . . . . 383.4 Ensemble average of nighttime case study soil temperature with depth. Surface temperatureis measured by the IRT (red dot), whereas soil temperatures are measured by extension-gradeTCs (black dots). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5 Box plots of the 211 five-minute averaged potential temperature profiles as measured by fine-wire TCs (dark-gray) and infrared thermal sensor (light-gray; labelled IRT). For box plotstatistics definitions, see Figure 3.1 at the beginning of Section 2.6. The translucent greenshading provides approximate location of the vegetated portion of the vineyard canopy at thesite; hc denotes the approximate top of the canopy; hb denotes the approximate bottom ofthe vegetated portion of the vineyard canopy. Ensemble average is given by red line. . . . . . 393.6 Profiles of side wall temperature (north (a) and south (b)) and the average horizontal gradientbetween the centre of the gap and the vineyard rows (c). Box plot statistical definitions areprovided by Figure 3.1 at the beginning of Section 2.6. . . . . . . . . . . . . . . . . . . . . . . 403.7 Boxplots of the 211 five-minute averaged profiles of turbulent kinetic energy (a), normalisedwind speed (b), and wind direction (c). (a) Turbulent kinetic energy (TKE), ensemble averageis given by red line; (b) wind speed (ms−1) measured by CSAT-3D’s normalised by the windspeed at hc, ensemble average is given by red line; (c) Wind direction (WD ◦) measured byCSAT-3D’s, wind coming from the east (90◦; down-slope) is given by dark green line. Boxplot statistical definitions are provided by Figure 3.1 at the beginning of Section 2.6 . . . . . 413.8 Vertical profiles of (a) stream-wise vertical, (b) cross-stream vertical, and (c) cross-vine mo-mentum fluxes. Box plot statistical definitions are provided by Figure 3.1 at the beginning ofSection 2.6. Asterisk at z/hc = 1.65 in (a) gives location of interpolated jet-height. . . . . . . 423.9 Kinematic sensible heat flux with height. Box plot statistical definitions are provided byFigure 3.1 at the beginning of Section 2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.10 Relationship between the vertical gradient in u-momentum and the vertical flux u′w′. . . . . 443.11 Relationship between the vertical gradient in v-momentum and the vertical flux v′w′. . . . . 453.12 Relationship between the vertical gradient in T and the vertical heat flux w′T ′. . . . . . . . . 45xi3.13 Vertical profiles of ensemble averaged skewness in the 5 minute data blocks for all three velocitycomponents and for temperature during the selected case study nights. Error bars representthe standard deviation of the skewness data, and the grey shading represents the uncertaintydue to instrumentation errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.14 (a) Octant heat flux stress fractions. Blue colours are associated with −T ′ and red colourswith +T ′. Solid lines represent gradient transport of stream-wise momentum, and dashedline represent counter-gradient transport of stream-wise momentum. (b) Separation of thestream-wise momentum flux exuberance into instances of gradient (red) and counter-gradient(black) sensible heat flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.15 〈u′w′〉 quadrant stress fractions (a) and time fractions (b) as a function of hole size, H . . . . 483.16 (a) 〈u′w′〉 quadrant stress fractions as a function of normalised height for a hole size, H = 3;(b) Ensemble averaged exuberance of the u′w′ flux; (c) the ejection sweep ratio for the u′w′ flux 493.17 Flux fractions (a) and exuberance (b) for the heat flux as a function of height. . . . . . . . . 513.18 Normalised two point length scales (a), time scales (b) and normalised, ensemble averaged,wind speed and convection velocity (c) with height. . . . . . . . . . . . . . . . . . . . . . . . . 523.19 Dependence of two point, L¨ and shear, Ls, length scales on the incident wind angle at canopytop. WD = 90◦ corresponds with row-parallel flow. . . . . . . . . . . . . . . . . . . . . . . . . 533.20 Median convection velocity for parallel wind (a; 12 five minute cases) and oblique wind (b; 5five minute cases) normalised by average canopy top wind speed . . . . . . . . . . . . . . . . 543.21 (Time) ensemble averaged two-point correlations between all possible TC distance combina-tions. Correlations made up-slope are positive x−distances, and correlations made upwardsare positive z−distances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.22 (Time) ensemble averaged two-point correlations between all possible TC distance combina-tions for cases during which the five-minute averaged wind direction was within 90◦ ± 2.5◦.Distance definitions are provided in Figure 3.21 . . . . . . . . . . . . . . . . . . . . . . . . . . 573.23 (Time) ensemble averaged two-point correlations between all possible TC distance combina-tions for cases during which the five-minute averaged wind direction was less than 47.5◦ orgreater than 132.5◦. Distance definitions are provided in Figure 3.21 . . . . . . . . . . . . . . 584.1 Measure surface temperature of vegetation to the north and south sides of the instrumentedtower as a function of time since sunset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2 Relationship between length scales - shear, Ls, and integral, L¨ - and δ . . . . . . . . . . . . . 61xii4.3 Hourly averaged potential temperature profiles through night of 07-06 - 07-07, 2016. Timesare displayed in LST for each profile. Over bars in the present plot indicate hourly averagesas opposed to five-minute averages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66A1 Inclination angles with varying wind direction with height. . . . . . . . . . . . . . . . . . . . . 81A2 Density plot of contribution of flux associated with a sign change to the total flux. solid linesrepresents the contribution associated with an over rotation, and dashed lines represent thecontribution associated with an under rotation. When the lines reach zero, there is no longerany contribution of the flux to the mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83A3 Sketch of problem set-up and variables used in example calculation of the temperature cor-rections for Mast F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85xiiiSymbol Units Descriptiona Five-minute mean of a〈a〉 Ensemble average of a in time (i.e., average of mul-tiple five-minute averaged a){a} Ensemble average of a in spacea′ Deviation of instantaneous a from aa Dummy variable for definitionsb Dummy variable for definitionsdz m change in height above ground levelhb m Height of the bottom of the canopy crown-spacehc m Height of the canopyhi m Height of velocity inflection pointH Quadrant analysis hole sizek W m−1 K−1 Soil thermal conductivityLc m Obukhov length at the canopy top, hcMAE Mean Absolute ErrorN2 s−2 Brunt Väisälä frequencyQ∗ W m−2 Net RadiationRi Gradient Richardson numberRf Flux Richardson numberSka units of a Skewness in aT ◦ C Air temperature (acoustic and/or fine-wire)Ts◦ C Soil temperatureTKE m2 s−2 Turbulent kinetic energyu m s−1 Stream-wise wind velocityuc m s−1 Stream-wise wind velocity at hcuc m s−1 Convection velocityUa units of a Measurement uncertaintyv m s−1 Cross-stream wind velocityw m s−1 Slope-normal wind velocityxivWD ◦ Wind directionx m Along-slope distancey m Cross-slope distancez m Height above ground levelα ◦ Slope angleδ ◦ Difference between above-canopy wind vector andorientation of vineyard rowsΘ K Potential (air) temperatureAcronym Units DescriptionAGL m Above Ground LevelAM25T Campbell Scientific MultiplexerBOV Burrowing Owl VineyardsCSAT-3D Campbell Scientific 3D sonic anemometerCSL Canopy sub-layerDS Drainage wind clusterIRT Infrared temperature sensorLST Local Standard TimeRSL Roughness sub-layerTC Thermocouple (fine wire, unless otherwise stated)VOF Valley flow or otherwise clusterVWC % Volumetric (soil) Water ContentxvAcknowledgementsI would like to acknowledge first and foremost, my advisor Dr. Andreas Christen, who was supportiveand enthusiastic of my research during the program, and without whom my research would not have beenpossible. Management at the Burrowing Owl Estate Winery, who granted us free access to the study siteand accommodation during the campaign. Dr. Andy Black, who lent a Campbell Scientific CSAT-3D sonicanemometer to us during the campaign. Dr. Holly Oldyroyd and Dr. Marco Giometto, who have continuallyacted as mentors to me. Dr. Dan Moore, who has provided aid with data analysis in R. Dr. Rob Stoll whohas provided invaluable information on observed canopy sub-layer dynamics in other vineyards. Dr. AndySturman who found the best slope for the field measurements, and was an invaluable help in initial set-up.My committee members, Dr. Ian McKendry and Dr. Phil Austin, who took the time to edit and respondto my thesis draft. Paul Skaloud, the superior undergraduate field assistant, without whom my campaignwould have been near impossible. Jose Aparicio, who kindly helped me navigate ArcMap. Zoran Nesic, whowas of vital help during instrumentation tests. Finally, my parents, who were a constant emotional supportthroughout the process.This research was funded by several grants and awards. Selected equipment was supported by the CanadaFoundation for Innovation (Grant 33600, Christen) and NSERC RTI (Christen). Financial support throughscholarships and training were provided by UBC Faculty of Graduate and Postdoctoral Studies and UBCGeography. Funding for undergraduate field assistance was provided via a Work Learn International Un-dergraduate Research Award. Funding for the purchase of thermocouple materials and travel expenses wasprovided in part by UBC Faculty of Arts via a Graduate Student Research Award.xviThis work is dedicated to my dad, who sparked my interest in buoyancy and encouraged me to pursuescience; and to my mom, who challenged my knowledge by asking incredibly in depth questions about myresearch and its relevance.xvii1 IntroductionFor decades, researchers have sought to characterise the turbulent transfer of momentum and scalars withinand above canopies. The presence of vegetation influences both the mechanical and thermal aspects of theflow, including the behaviour of drag near the surface (e.g. Garrett, 1983; Gross, 1987; Yi et al., 2005; Oldroydet al., 2014) and radiative cooling, heat storage, and sensible heat transfer (e.g. Froelich and Schmid, 2006;Froelich et al., 2011). While a substantial amount of work has elucidated the mean and turbulent natureof flow within and above dense, homogeneous canopies over flat terrain and under near-neutral stability(e.g. Finnigan, 2000; Finnigan et al., 2009), understanding is far from complete for the more complex casestypical of the Earth’s surface. For agricultural crops, knowledge on the turbulent field reveals the potentialfor particle dispersion (e.g. Bailey et al., 2014; Miller et al., 2015), which can include spread of disease,insecticides, and pesticides. In a vineyard, the impact of the canopy on particle dispersion becomes furthercomplicated by the canopy organisation (Miller et al., 2015).For the present case, a complex situation arises as a row-oriented vineyard canopy interacts with a nighttimedrainage flow. The following introduction includes a section on the canopy sub-layer (CSL), a section ondrainage flow, and a final section discussing the objectives of the thesis.1.1 Canopy Layer DynamicsThe roughness sub-layer, normally defined as the layer between the ground surface and at least twice theheight of the canopy (e.g. Finnigan, 2000; Katul et al., 2013), is the layer in which the presence of the canopyinfluences the mean and turbulent nature of the flow. The RSL contains the canopy sub-layer (CSL), whichis defined as the layer between the ground surface and the height of the canopy, and is the region wherethe environment is dictated by the micro-scale properties of the various surfaces present within the domain(e.g. Oke et al., 2017). Canopy height is usually defined as either the physical height AGL of the canopy, hc(e.g. Thomas and Foken, 2007a; Katul et al., 2013), or as the height of the velocity inflection point, hi (e.g.Raupach et al., 1996), which is near hc. Extensive work has allowed for the description of the mean andturbulent nature of flow at near-neutral stability within the CSL for a variety of homogeneous canopies (i.e.,more-or-less horizontally homogeneous at the canopy height), such as a tall forest canopy (e.g. Cava et al.,2006; Launiainen et al., 2007) or an agricultural crop, like corn or wheat (e.g. Paw U et al., 1992). While ourunderstanding of the ’simple’ CSL dynamics are strong, our understanding of more complex CSL situationsis far from complete. Even when more complex situations are considered, the canopies investigated aretypically tall forest canopies (e.g. Launiainen et al., 2007), due to current efforts to address carbon balance1closure issues at long-term flux measurement sites (e.g. Aubinet et al., 2003; Heinesch et al., 2007; Belcheret al., 2008). In the following sub-section, typical CSL dynamics under near neutral stability are summarised,recent advances in CSL studies are discussed, and the various observational and analysis techniques employedin CSL studies are briefly reviewed.1.1.1 Canopy Turbulence in Near Neutral ConditionsIt is well known that under near-neutral stability, for fairly horizontally homogeneous canopies, the canopy-top dynamics behave similarly to the plane-mixing layer dynamics, whereby the hydrodynamic instabilityinduced by an inflection in the velocity profile generates large turbulent structures near the canopy top(Raupach et al., 1996; Finnigan, 2000; Finnigan et al., 2009; Bailey and Stoll, 2016). While the turbulentfield is known to be three dimensional, the coherent structures generated via the shear instability have beenshown to be quasi two-dimensional (Bailey and Stoll, 2016). These structures scale well with canopy height(e.g. Finnigan, 2000) and are responsible for a large fraction of the total turbulent flux within the canopy(e.g. Thomas and Foken, 2007a). The predominance of larger, non-locally generated coherent structures con-trolling the flux within the canopy then invalidates the applicability of simple flux-gradient transport theory(K-theory, see Stull (1988) for details) (Cellier and Brunet, 1992; Raupach et al., 1996; Katul et al., 2013),necessitating either canopy-relevant corrections to K-theory (Cellier and Brunet, 1992) and/or higher-orderclosure (e.g. Wilson and Shaw, 1977). The speed at which the structures propagate through the flow isthought to be determined by the mean wind speed at the height of the core of the structure (Bailey andStoll, 2016). For an in depth consideration of the behaviour of coherent structures within homogeneous,dense canopies under near-neutral stability, see Bailey and Stoll (2016).Conditional sampling of the Reynolds stress (see Section 1.1.2 and 2.6 for details) in the CSL reveals fairlyexuberant flow, with sweeps - the movement of above canopy air (i.e. typically higher momentum, colder,fluid) downwards into the canopy - dominating over ejections in the canopy environment (e.g. Raupach, 1981;Finnigan, 2000; Finnigan et al., 2009). Above the roughness sub-layer, the sweep/ejection ratio returns tounity as is expected for classical rough-wall boundary layer flow (e.g. Raupach, 1981; Bailey and Stoll, 2013),acting as an indication of the depth of the CSL.1.1.2 Advances in CSL UnderstandingMany authors have worked to extend known turbulent dynamics for the simple near-neutral case to thosewith further complexities, like varying stability (Leclerc et al., 1990; Launiainen et al., 2007; Thomas andFoken, 2007a; Dupont and Patton, 2012; Francone et al., 2012), varying canopy density (Poggi et al., 2004),2in regions of hilly terrain (e.g. Finnigan and Belcher, 2004; Francone et al., 2012), near canopy discontinu-ities, like forest edges (e.g. Irvine et al., 1997; Gash, 1986), and in canopies with specific orientations likethe classical row-gap trellised vineyard environment investigated in the present study (Francone et al., 2012;Chahine et al., 2014; Miller et al., 2017).Increased stability has been found to decrease shear length scales (Dupont and Patton, 2012; Miller et al.,2017), however, has no effect over the characteristic sweep/ejection cycle observed under near-neutral condi-tions (Miller et al., 2017). With stability comes the increased potential for wave motions, and wave breaking(e.g. Lee and Mahrt, 2005), which could introduce scales potentially on the order of coherent structures thusaffecting measurements and analysis. Additionally, under stable conditions over slopes, the development of adrainage wind can occur (e.g. Lee and Mahrt, 2005), which further complicates the flux-gradient relationship(and corrections to it due to vegetation), among other things like advection (e.g. Aubinet et al., 2003; Aubi-net, 2008; Belcher et al., 2008; Thomas, 2011) and the coupling between the canopy and the outer-canopyenvironment (for tall forest canopies) (e.g. Turnipseed et al., 2003; Froelich and Schmid, 2006; Sun et al.,2006; Rebman et al., 2010).As for canopy density, there are two extremes under consideration, 1) the very dense case in which the mixing-layer analogy is expected to hold (e.g. Finnigan, 2000), and 2) the completely bare case in which rough-wallboundary layer theory is expected to hold. Using a canopy model in a flume, Poggi et al. (2004) describethe turbulent nature within a sparser canopy as a three-layered system, whereby deep-canopy turbulence isdominated by von-Kármán streets, the canopy-top region is influenced by both mixed-layer and boundarylayer dynamics, and the above-canopy environment returns to the classical boundary-layer dynamics.Dispersive flux, or transfer due to dispersion from high to low concentration, within the canopy is related tocanopy density, whereby dispersive fluxes are largest for sparser canopies (Poggi and Katul, 2008). Böhmet al. (2013) show that the heterogeneity and geometry of the canopy can also affect whether or not thereare general wake and/or non-wake regions, which can then add an additional spatial heterogeneity to thebehaviour of turbulence within the canopy. Miller et al. (2017) show that for a row-gap aligned canopy, thedirection of the above-canopy wind also affects whether or not the canopy behaves more like a dense canopy(i.e., row-perpendicular wind vectors) or a sparse, open canopy (i.e., row-parallel wind vectors). In eithercase, flow channelling by the canopy is present, making the direction of the approaching above-canopy windin relation to the direction of row-orientation an important influence on the CSL turbulence (Miller et al.,2017). Miller et al. (2017) investigate this directional dependence in depth, revealing a further influence of3stability in the amount of wind-vector turning due to a trellised vineyard canopy, with the influence of thecanopy-orientation extending higher into the atmosphere under moderately stable conditions compared withnear-neutral conditions. The added turning of wind vectors then increases shear, depending on the winddirection. For example, when the above-canopy wind is angled more obliquely to the canopy-rows, the shearlength scales are smaller, implicating higher shear near the canopy top (Miller et al., 2017). This dependenceon the above-canopy wind vector and stability also holds implications for the location of the inflection point,and thus on the definition of the canopy height (Miller et al., 2017).1.1.3 Common MethodsCanopy turbulence has been described using high frequency wind and temperature measurements (e.g. Chris-ten et al., 2007; Launiainen et al., 2007; Miller et al., 2017), theoretical considerations (e.g. Wilson and Shaw,1977; Finnigan, 2000; Finnigan and Belcher, 2004), wind tunnels and flume measurements (e.g. Shaw et al.,1995; Poggi et al., 2004; Böhm et al., 2013), and numerically using large eddy simulations (e.g. Finniganet al., 2009; Bailey and Stoll, 2013, 2016). As the present study deals with data collected in the field, focusis given to similar studies, including methods of field data collection and analysis.In most of the studies on CSL turbulence, at least one 3D sonic anemometer is set up to capture highfrequency wind and temperature measurements of the flow (e.g. Launiainen et al., 2007). Often, the set-upincludes instruments mounted vertically to capture the mean and turbulent profiles of wind and scalars. In afew studies, set-up of instrumentation has been on a horizontal transect, but the focus of these studies havebeen on the description of advection of CO2, and occasionally the advection of heat and momentum (e.g.Thomas, 2011), rather than on the spatial nature of turbulence in the CSL. Commonly, averaging periodsfor CSL turbulence studies are the classical 30-minute periods (Christen et al., 2007; Launiainen et al., 2007;Miller et al., 2017). However, Dupont and Patton (2012) utilise a 5-minute averaging period for stable casesin their study of turbulence within an orchard, with the assumption that this period is small enough to avoidlarger-scale trends and large enough to capture the largest scale turbulent fluctuations in the flow.Time-series of scalar fields reveals the ramps associated with the predominant mode of sweeping and ejectingmotions in the flow (Gao et al., 1989; Paw U et al., 1992). Conditional sampling such as the use of a quad-rant analysis (Antonia, 1981) has elucidated the dominant modes, efficiency, and intermittency of turbulenttransfer in teh RSL (Raupach, 1981; Christen et al., 2007; Launiainen et al., 2007; Poggi and Katul, 2007).The same information on turbulent transfer can be alternatively obtained using an analysis on the third andfourth order statistical moments (Launiainen et al., 2007; Poggi and Katul, 2007).4Integral statistics have allowed for the identification of characteristic turbulent scales. Integral methodstypically involve the integration of time lagged single-point correlations to derive a dominant time scalefor coherent structures (e.g. Shaw et al., 1995; Christen et al., 2007), and then the application of Taylor’sfrozen eddy hypothesis and an estimated convection velocity (uc = 1.8u) to formulate a single-point dom-inant length scale (e.g. Shaw et al., 1995; Christen et al., 2007; Launiainen et al., 2007). In the case ofspatially separated sensors, a two-point length scale can be calculated using distance-lagged correlations(Shaw et al., 1995). Finally, the lagged correlations, as functions of lagged time or distance, can be usedas a visualisation method for the coherent structures in the flow (e.g. Shaw et al., 1995; Christen et al., 2007).For revealing the variety of turbulent scales, spectral analysis can be employed (e.g. Finnigan, 2000; Milleret al., 2017). However, as the Fourier transform is not localised in space/time, a more robust method fordescribing the variety of interacting turbulent scales is the use of a wavelet based analysis. Because waveletsretain the spatial/temporal information in the frequency spectrum, they can be used to locate structuresand derive eddy spacing and frequency (e.g. Collineau and Brunet, 1993; Thomas and Foken, 2007b).1.2 Drainage WindUnder weak synoptic pressure gradients and relatively clear night skies over complex terrain, surface coolinginduces negative buoyancy over a slope leading to the development of a down-slope (drainage) wind. Drainagewind is a common occurrence that influences local and regional climate (e.g. Sturman et al., 1999) and holdsimportant implications for the transport of pollutants (e.g. Moroni et al., 2014; Chemel and Burns, 2015),the formation of cold air pools (e.g. Burns and Chemel, 2015; Geiss and Mahrt, 2015), CO2 budgets (e.g.Aubinet et al., 2003), the formation and dissipation of fogs and low clouds, and the distribution of surfaceair temperatures which holds implications for frost damage in vineyards and orchards (Zardi and Whiteman,2013). However, despite their importance in a variety of processes, drainage winds are often unresolvedin current numerical weather prediction models and standard measurements (e.g. Grisogono et al., 2015).Further complicating this is the paucity of information on drainage winds over varying canopies, such as avineyard canopy. In the following section, a brief overview of the theory and characteristics of drainage windis provided and common observational techniques are reviewed.51.2.1 Brief Theory and Characteristics of Drainage FlowDrainage wind is a (generally) nighttime occurrence that develops over a slope due to the cooling of the slopeatmosphere (e.g. Whiteman, 2000). This cooling occurs via a loss of radiative heat from the slope surfaceand a transfer of sensible heat from the near-slope air to the ground (e.g. Whiteman, 2000). As the slopeair cools, a horizontal temperature gradient develops between the air just above the slope surface and thatover the valley, leading to negative buoyancy along the slope which then drives the air to flow down-slopeunder the influence of gravity (e.g. Ball, 1956; Haiden and Whiteman, 2005; Poulos and Zhong, 2008; Mo,2013; Zardi and Whiteman, 2013). Typically, the drainage flow is associated with temperature inversionsthat start at the slope surface, there is a near surface wind speed maximum, and a near-surface peak in theTKE (Figure 1.1).Figure 1.1: Schematic of typical temperature, wind, and turbulent kinetic energy (TKE) vertical profilesfor the nighttime drainage wind, modified from the image provided in Zardi and Whiteman (2013).Inversion depth defines the depth of the drainage layer, which can be on the order of 1 - 200 m (e.g.Amanatidis et al., 1992; Zardi and Whiteman, 2013). Ideally, the jet maximum occurs around 30-60% ofthe inversion depth, and decreases to zero at the top of the inversion layer (e.g. Zardi and Whiteman, 2013).Estimates for the depth of the inversion layer can be made using vertical drop distance from the ridge (e.g.Horst and Doran, 1986; Amanatidis et al., 1992), but different estimation techniques, which have been basedon field data, yield different values for the location of the jet maximum. Theoretically, a return flow existsabove the inversion layer, but, this is a rarely observed phenomenon in the field (e.g. Zardi and Whiteman,2013; Burns and Chemel, 2015).61.2.2 Typical Drainage Onset ConditionsThe development of strong, locally generated, drainage flow is associated with outgoing long-wave radiationamounts of at least 30 W m−2, while weaker flow can still develop for amounts as low as 15 W m−2(Gudiksen et al., 1992). Synoptic activity must be weak, with larger-scale winds typically not exceeding 5m s−1 (Gudiksen et al., 1992). This larger scale flow threshold is apparently variable, with other thresholdsobserved in association with drainage flow in the literature (2-3 m s−1 for Zardi and Whiteman (2013) and6 m s−1 for Papadopoulos et al. (1997)). Naturally, there arises a seasonal dependence in many locationsfor drainage flow, requiring times when nighttime skies are relatively clear, synoptic pressure gradients areweak, and the atmospheric and soil moisture are relatively low (Devito and Miller, 1983; Gudiksen et al.,1992; Banta and Gannon, 1995; Komatsu et al., 2003; Zardi and Whiteman, 2013).1.2.3 Observational TechniquesHistorically, drainage winds have been observed and characterised using data collected through a verticaltransect of the atmosphere either with tower mounted anemometers at various height levels (e.g. Papadopou-los et al., 1997; Aubinet et al., 2003; Froelich and Schmid, 2006; Rebman et al., 2010; Oldroyd et al., 2014)which provide a snapshot of the vertical structure with time, or with a single anemometer that is movedthrough the vertical in time, i.e. a tethered-balloon sounding (e.g. Manins and Sawford, 1979; Devito andMiller, 1983) which is a resource saving alternative, but is only appropriate if the wind can be assumedstationary. The use of fog machines has helped to visualise drainage flow dynamics (e.g Pypker et al., 2007).Most studies using tower data have looked at point measurements (e.g. Oldroyd et al., 2014), with a fewmore recent studies deploying multiple tower point measurements around a sloped region for a more completepicture of the flow (e.g. Staebler and Fitzjarrald, 2005). However, drainage flow is not stationary (e.g. Mahrt,2010), is highly sensitive to a variety of parameters that are typically not constant along or across a slope,and normally contains other sub-meso motions and gravity waves within the wind structure as well (e.g.Mahrt, 2014). This makes sparse point measurements aimed at characterising the structure of a drainageflow problematic.In recent years, field investigations have begun to deploy instrumentation capable of the high spatial andtemporal resolution needed to completely characterise drainage flow, like the 2D distribution of high reso-lution fibre-optic temperature sensors used by Thomas et al. (2012), and the thermal infrared screen andcamera methods devised by Grudzielanek and Cermak (2015). While these new techniques present an op-7portunity to greatly further complete understanding on the dynamics of drainage wind, they have to dateonly been applied over grassy slopes.1.3 Study ObjectivesWhile numerous studies have characterised CSL turbulence for various canopies, most of the studies havefocused on turbulence under near-neutral conditions. The few studies that have considered stability havedone so for more homogeneous canopies - like tall forests (either dense or sparse) (e.g. Thomas and Foken,2007a). While attention is beginning to turn to row-gap organised agricultural canopies, such as vineyards(Francone et al., 2012; Chahine et al., 2014; Miller et al., 2017), to our knowledge, the consequence of night-time drainage within a vineyard has not been examined.As the major wine-producing region of British Columbia, most of the vineyards in the Okanagan Valley aresituated on or near complex terrain. To date, topographically forced drainage has not been resolved withinand above canopies, let alone how the presence of drainage affects CSL turbulence and the communicationbetween the atmosphere and the canopy. To understand the local affects of drainage and the advection ofscalars and momentum, which hold potential implications to both vineyard and human health, the turbulentfield within a vineyard under drainage conditions needs to be understood.To this end, the goals of this study are to 1) characterise nighttime drainage flow within the vineyardCSL, and 2) quantitatively and qualitatively describe the turbulent exchange of heat and momentum withinthe vineyard CSL during the drainage events. Fulfilling these two objectives allows for a more robustunderstanding of the implications of nighttime drainage within an organised canopy with consequence tonighttime advection and dispersion of scalars, including heat and disease/pollutants, and to the canopy-atmosphere exchange of heat and momentum.82 Methods2.1 Field Site DescriptionFigure 2.1: Topographic map of the southern Okanagan Valley. Map of British Columbia was obtained fromESRICanadaED (https://www.arcgis.com/home/item.html?id=dcbcdf86939548af81efbd 2d732336db). Mapprojection is BC Albers 1984. Scale provided is for the coloured topographic map.The field campaign took place on a west-facing ∼7◦ vineyard slope on Burrowing Owl Estate Vineyard(BOV) property in Oliver, British Columbia, Canada. The particular plot was populated with Chardonnaygrapevines, and was irrigated using a drip-method. This site is located within the Black Sage - Osoyoosviticulture region, which is dominated by sandy, rapidly draining soil with very low moisture holding ca-pacity (Bowen et al., 2005). BOV property in Oliver is located approximately 3 km up-valley (north) fromthe northern tip of Osoyoos Lake, with the specific field site slope approximately 1 km down-slope (west) ofthe foot of steeper mountain terrain leading into the Inkadeep territory. A topographic map of the region9surrounding the study site, as well elevation profiles extending east (Figure 2.2(a) and north (Figure 2.2(b))2 km from the ultrasonic tower location (Mast A, Figure 2.3) is provided by Figure 2.1. The slope transectprovided in Figure 2.1 correspond with the elevation transect provided in Figure 2.2. The slope of the chosensite was measured using an inclinometer iPhone application, to an assumed accuracy of ±1◦, see Section5 for an analysis and discussion on the implication of an inaccurate slope measurement on measured windcomponents and reported fluxes. The vineyard canopy was maintained at a height, hc, of on average 2.3m above ground level (AGL), with a fruit line at 0.65 m AGL; there were approximately four vine trunksper 6 m, and a row spacing of 3 m (Figure 2.3). Regular maintenance of the vineyard ensures that the rowspacing is consistent. Throughout the campaign, vines deviating from the row were clipped back to ensurecontinuity. Vines were watered in the morning, to our knowledge, using a drip-watering system.Table 2.1 summarises the time line of the set-up procedure, and all instrumentation related issues encoun-tered during campaign. Most issues were related to thunderstorm activity in the region.Figure 2.2: Elevation (m above sea level) transects between the ultrasonic tower and 2 km (a) east and (b)north.10Date(dd/mm/yy)Site Visit Details04/07/16 Arrive at field site early afternoon; Choice of exactfield site slope made.05/07/16 Set up of instrumented tower, including placementof CR3000 and CR1000 logger boxes, and AM25Tboxes (2).06/07/16 Installment of along-slope thermocouple masts.Thermocouples begin collecting data in earlyevening.07/07/16 All thermocouples at below z/h = 2 removed due toapproaching evening thunderstorm. Time of removalbegan around 12:30 LST.09/07/16 Thermocouples replaced on masts by 14:30 LST.10/07/16 CR3000 fuse breaks around 02:00 LST. Fuse is re-placed at 12:00 LST. Thermocouple H3 replaced dueto solder joint failure. Logger clocks were unaffectedby main fuse break.11/07/16 Battery accidentally connected at 10:45 LST brieflyduring regular site maintenance.12/07/16 Lateral thermocouple masts installed between 10:30and 11:40 LST.15/07/16 All thermocouples at below z/h = 2 removed due toapproaching evening thunderstorm. Time of removalbegan around 20:30 LST.16/07/16 Thermocouples replaced on masts by 14:00 LST.20/07/16 Thermocouples AR2, C1, C4, and F3 are replaced.AR thermocouple mast turned 90◦ at some pointduring measurements, and returned to original loca-tion during site visit.22/07/16 All instrumentation removed from field site and re-turned to UBC.Table 2.1: Time line of field campaign in the southern Okanagan Valley in July 2016.2.2 InstrumentationFive ultrasonic anemometers (CSAT-3D, Campbell Scientific Inc., Logan, Utah, USA) were co-mounted withfive Type-E 0.001" thermocouples (TC, OMEGA Engineering, Laval, Quebec, CA) on a 4.73-m tall pumpup tower (Figure 2.4) at vertical heights above ground level (AGL) of 0.45, 0.9, 1.49, 2.34, and 4.73 m.TCs were constructed by hand, except for the 0.001" bare Chr-Con junctions, which were factory-welded byOMEGA Engineering. Details on the construction of the fine-wire TCs can be found in Figure 2.5. Three11Figure 2.3: Schematic of field site set-up. Bird’s eye view provides to-scale spacing of thermocouple (TC)masts and the ultrasonic tower. The side-view provides a to-scale visual of the vertical alignment of CSAT-3D’s on the pump-up tower and the TCs on respective masts.12Figure 2.4: Photos of the field site. (a) is a panorama view from east (90◦) over south to west (270◦) of thevineyard plot where the study slope is located, position of thermocouple (TC) masts and ultrasonic towerare labelled (see also Figure 2.3). (b) is a close-up view looking up-slope (east) of the ultrasonic tower, withlabelled vertical positions of the individual CSAT-3D’s normalised by the canopy height hc = 2.3 m AGL.(c) provides a close-up of TC mast set-up, the position of some of the TCs and the infrared thermometers(IRTs) that were mounted on the tower. Credit: A. Christen.13infrared thermal (IRT, Apogee Instruments Inc., Logan, Utah, USA) sensors were mounted on the tower,one directed at the ground below the ultrasonic array, one at the vegetation to the north of the tower, andone at the vegetation to the south of the tower. Seven TC masts (A - H) were placed up slope of theultrasonic tower at distances of 0.5, 1.0, 2.0, 4.0, 8.0, 16.0, and 32.0 m to the east of the ultrasonic tower,on which five TCs each were mounted at heights AGL of 0.45, 0.9, 1.49, 2.34, and 4.73 m. Two additionalTC masts were placed near the vegetation to the north and the south of the TC mast located at 1.0 mfrom the tower (Figure 2.3), with TCs placed at heights AGL of 0.45, 0.9, 1.49, and 2.34 m. All fine-wireTCs were multiplexed by two Campbell Scientific AM25T multiplexers; TCs on Masts A - C (including CNand CS, Figure 2.3) were multiplexed by AM25T1 (multiplexer closest to the ultrasonic tower), and TCs onMasts D - H were multiplexed on AM25T2 (multiplexer furthest from ultrasonic tower). The tower and theTC masts were secured in place throughout the campaign by guy wires extending into adjacent rows. AllCSAT-3Ds, TCs and IRTs were logged by a Campbell Scientific CR3000 data logger. CSAT-3Ds were run at60 Hz with a 20 Hz sampling frequency; TCs and TIRs were sampled at 2 Hz. An NR Lite2 Net radiometerwas mounted facing west at 4.8 m AGL on the pump-up tower, set to sample and integrate at the slow, or60-Hz rejection integration; samples were further averaged into 1-minute values and logged by a CampbellScientific CR1000 data logger. Six extension-grade type-E TCs were placed in a vertical array in the soilspaced at 1 cm (Figure 2.6(a)). The soil thermocouple array was located near the centre of the adjacentrow to the north of the site, and were sampled and logged at 1-minute intervals by the CR1000 data logger.Volumetric soil water content was sampled once a day during data download at the tower location (0 m) andat TC mast H (32 m up-slope) using a Campbell Scientific HydroSense Soil Water Measurement sensor.Figure 2.5: Schematic of fine-wire thermocouple (TC) deployed on slope for air temperature measurements.A: Polyvinyl shielded Chromel-Constantan (Chr-Con) extension grade wire (EXPP-E-24S-SLE) is connectedto B: female connector which connects to C: male connector which connects to 30-gauge Chr-Con wire whichfeeds into D: a small brass protection tube of length 15.24 cm. E: the 30-gauge wire is then soldered toF-G: the 0.001" factory-welded bare Chr-Con TC junction. F represents the Chr-Con 0.001" wires, and Grepresents the factory-welded junction.14Figure 2.6: (a) Soil thermocouple (TC) array, located in the centre between the N-vegetation row and theadjacent row the the N of the study site. Six TCs constructed from polyvinyl shielded Chromel-Constantan(Chr-Con) extension-grade wire are spaced at 1 cm, with the topmost measurement at 1 cm below the soilsurface. Note that photo was taken during installation; soil was filled in afterwards. (b) Diagram of soilTC. A: Extension-grade Chr-Con wires; B: Polyvinyl-shielded extension-grade Chr-Con wire. Soil TCs areconstructed by twisting the ends of the Chr-Con wires to create a ’junction’. Chromel wires are colouredpurple, and are the positive legs; Constantan wires are coloured red, and are the negative legs.2.3 Measurement Uncertainties2.3.1 Campbell Scientific 3D Sonic AnemometerAll of the ultrasonic anemometers employed in this study were part of an inter-comparison campaign in 2009(Liss et al., 2009). Following the methodology of Emmel (2014), the calculated standard deviations from theinter-comparison campaign are used as the instrument related uncertainties. The uncertainties calculatedfor CSAT-3D 1341, which was the CSAT-3D positioned at the canopy top, are used in the present study asthe instrument uncertainties for mean wind components, wind speed and temperature, Reynold’s stressesand heat flux, turbulent kinetic energy (TKE), and velocity and temperature skewness (Table 2.2). As theuncertainty in u′v′ was not given, it is calculated as the average between the uncertainty in u′u′ and v′v′.15Quantity Uncertaintyu 0.05274 m s−1v 0.03627 m s−1w 0.01335 m s−1T 0.05286 KU 0.05674 m s−1u′u′ 0.02229 m2 s−2u′w′ 0.00517 m2 s−2v′v′ 0.01863 m2 s−2v′w′ 0.00921 m2 s−2w′w′ 0.00777 m2 s−2w′T ′ 0.00463 m K s−1u′v′ 0.03226 m2 s−2Sku 0.08460 m s−1Skv 0.12312 m s−1Skw 0.07910 m s−1SkT 0.39635 KTable 2.2: Table of CSAT-3D instrument uncertainty, as calculated from reported standard deviations inLiss et al. (2009)Uncertainty in the vertical gradients of above-mentioned quantities is calculated using:Uadz =Uadz(2.3.1)where Uadz is the uncertainty in the vertical gradient and Ua is the uncertainty in the measurement. Forthe velocity gradients, a cubic spline was used to determine gradients at the measurement points using alayer of thickness = 0.04 m. The error in the velocity gradient is calculated as in equation (2.3.1), withthe knowledge that the use of the natural cubic spline may affect the reported errors. Because the gradientused is so small, the error in the reported velocity gradients is large, despite the fact that with increasingmeasurement distance, the error in determining a gradient between the two sensors is reduced. The amountof curvature is assumed to be reduced through applying the natural cubic spline interpolation only on the5-minute averaged data points.162.4 Post-Processing2.4.1 CSAT-3D RotationsCoordinate rotation is an important step in the use of turbulence data. While there are a variety of methodsavailable for coordinate rotation of CSAT-3D components (Lee et al., 2005), we employ a two-step rotationsimilar to the planar fit method in that we rotate the system into a plane parallel to the slope surface. Thefirst rotation aligns the x-axis with the mean wind direction (using traditional meteorological wind directiondefinitions) using the rotation matrix R1:R1 =−cos(α) −sin(α) 0−sin(α) −cos(α) 00 0 0 (2.4.1)where α is the 30-minute averaged wind direction at z/hc = 2.05, also referred to as the pitch angle. Therotation is set up such that +x = 90◦ is flow directed down slope (i.e., wind comes from the east). Thechoice of using the averaged wind direction at z/hc = 2.05 has the possible consequence of non-zero meancross-slope wind at the lower measurement heights. For this reason, Reynolds stresses cannot be simplified,and when possible, all terms are calculated and reported.The second rotation aligns the z-axis with the local slope via a rotation about the y-axis using rotationmatrix R2:R2 =cos(βsin(α)) 0 −sin(βsin(α))0 0 0sin(βsin(α)) 0 cos(βsin(α)) (2.4.2)Where β is the slope, or yaw, angle. Directionally dependent yaw rotations have been applied in other studieson flow measurements within a sub-canopy environment (e.g. Mahrt and Lee, 2005; Francone et al., 2012;Miller et al., 2017), and our use of a sine function is justified by observed sinusoidal behaviour of streamlineswith varying wind direction at the site (Figure A1, Appendix 5). This rotation assumes that the slope isplanar and oriented E-W, which is generally true, but could be modified due to the highly variable terrainin the region. However, rotation into one plane allows for the calculation of vertical gradients in a straight-forward manner. Sub-canopy momentum fluxes are sensitive to the choice of rotation method (e.g. Mahrt17et al., 2000; Mahrt, 2010; Francone et al., 2012), thus it is necessary to consider the overall implications ofthe current choice of methods.While both the pitch and yaw rotations merely redistribute fluxes, vertical fluxes are highly sensitive to thechoice of yaw rotation method (if employed at all). In the case of a sloped environment, a slope rotationshould be employed, but, it is recognised here that the errors in the slope angle measurement may holdimplications for the sign of reported fluxes. Over-rotation would be especially problematic in the currentstudy given the implied (and interpolated) location of a jet maximum within the measurement domain (seeFigure 3.8(a) in Section 3.2). Analysis on the effect of rotation errors with relation to potential momentumflux sign changes reveals little to no effect on the total fluxes presented here (see Appendix 5 for details).Appendix 5 additionally provides the mean absolute error (MAE) in the calculated fluxes associated with a±1◦ measured slope angle uncertainty.The uncertainty in the measured slope angle will be most critical to the octant and associated analyses.Given that the largest (potential) errors are concentrated during low-flux times, use of a hyperbolic hole inall octant and associated analyses circumvents the issue of potential uncertainty induced momentum fluxsign changes. Therefore, a hole size of H = 3 for vertical stresses and a hole size of H = 1 for horizontalstresses is applied for all octant related analyses (see Section 5 for details).2.4.2 CSAT-3D Wind ComponentsTheoretically, under zero-wind conditions, the ultrasonic anemometers should measure zero for all wind com-ponents. However, this is not the case in reality, and while factory specific offsets are provided by CampbellScientific Inc (2015), instrument specific offsets are calculated in the present study.18Figure 2.7: Photos of CSAT-zeroing set-up.To test the ability of the ultrasonic anemometers deployed during the 2016 Okanagan field campaign to reachzero (i.e., during no-wind conditions), a radius of approximately 6 cm of protective foam was removed fromthe ultrasonic anemometers storage containers where the ’head’ of the sensor normally rests. The ultrasonicanemometers were sealed (using duct tape) in their cases, with additional foam added to the exit site of theSDM connection cable for the sensor as damage protection (see Figure 2.7). The ultrasonic anemometerswere then connected to the data logger and run for at least 24 hours in a temperature controlled lab. The labis occasionally frequented during the day, and empty and locked during the night. Because it is recognisedthat small thermal gradients could potentially develop around the sensor, particularly during the night, avariety of case rotations were conducted to investigate the effect on the mean measured components as theycycled through representing the vertical wind. Each case rotation was tested for the same diurnal cycle.Vertical thermal gradients and diurnal changes in temperature did not affect the wind components andquality of zero-tests, thus were not accounted for in the final offset calculations. Table 2.3 provides the finaloffset values applied to the ultrasonic anemometer data as a first step in post-processing.19Ultrasonic Anemometer (CSAT-3D)z/hcWind ComponentsSerial Number x y z0428 2.05 -0.0388 m s−1 0.0221 m s−1 -0.0064 m s−11341 1.01 -0.0909 m s−1 0.0377 m s−1 -0.0051 m s−11389 0.647 0.0028 m s−1 0.0354 m s−1 -0.0365 m s−11393 0.391 0.1047 m s−1 -0.1159 m s−1 0.0554 m s−11396 0.195 0.0744 m s−1 0.0138 m s−1 0.0056 m s−1Table 2.3: Corrections obtained through ultrasonic anemometer zero-wind calibration tests. ultrasonicanemometers are identified by serial number, and their vertical placement on the flux tower indicated (z/hc;z = height AGL, hc = height of canopy). Corrections for x- y- and z- were subtracted from all CSAT-3Dmeasurements.All of the corrections are on the order of 1 cm s−1, except for CSAT-3D 1393 (z/hc = 0.391) yieldedcorrections values of ∼10 cm s−1. Running under the assumption that the applied zeroing methods wereadequate (it is argued that the method deployed is superior to common bag methods deployed), this indicatesa potential issue with CSAT-3D 1393. However, it seems as though the application of the corrections makesvertical gradients more physically reasonable (Figure 2.8), and confidence is still held in all of the ultrasonicanemometers deployed during the campaign.Figure 2.8: Vertical profiles of mean wind speed for case study on the night of 06/07/2017. Ui =1N∑Nt=1√x¯i(t)2 + y¯i(t)2, where N = number of 30-minute records in case study night (18), x¯i(t) is the30-minute mean of component x for record t, and index i indicates the CSAT-3D at which the average iscalculated.2.4.3 CSAT-3D Acoustic TemperaturesIt is well known that the mean acoustic temperatures measured by the CSAT-3D ultrasonic anemometerstend to drift, due to sensitivity to humidity and other quantities that affect the speed of sound, thus yielding20unreliable mean temperatures. To correct for any drift, five minute averaged acoustic temperatures arecompared with five minute averaged tower co-mounted TC temperatures (Mast A) for all of the selected casestudies. Using this select grouping of data ensures that the corrections not only avoid daytime radiationerrors, but also ensures that the comparison is made during times when both the ultrasonic array and the TCarray were operating properly. Figure 2.9(a) and Table 2.4 summarise the acoustic temperature offsets. Themean difference between CSAT-3D measurements and TC measurements of temperature were subtractedfrom the acoustic temperatures prior to further investigation. Figure 2.9(b) shows improved agreementbetween two temperature measurements post correction.z/hc Correction (K)2.06 1.3341.02 1.6160.647 0.1340.391 2.4240.195 0.948Table 2.4: Calculated mean difference between CSAT-3D acoustic temperature and the mean thermocoupletemperature.Figure 2.9: Comparison between the CSAT-3D acoustic temperatures and the thermocouple (TC) temper-atures before (a) and after (b) applied acoustic temperature corrections.212.4.4 Thermocouple TemperaturesDuring the nighttime cases, an unexplained warm bias is observed for the five TC masts (D - H) multiplexedby AM25T2 (located ∼16 m up-slope from AM25T1) at all heights. The bias could be due to either in-strumentation failure or some real phenomenon. Post-campaign testing reveals no apparent issue with TCinstrumentation, but at present, we are unable to physically explain the bias. To remove the potential effectsof this bias from analysis, the five minute average vertical temperature gradient at z/hc = 2.05 betweenMasts A (0 m up-slope) and H (32 m up-slope) was used to calculate ’reference’ five-minute average tem-peratures at z/hc = 2.05 for the other six masts along the slope. The difference between the ’reference’ fiveminute average temperatures and that of the actual five minute average temperatures at z/hc = 2.05 wasthen subtracted from the five minute blocks of 2 Hz data for each mast. An example of this calculation isprovided in Appendix 5.In the case that the observed bias is indeed physically based, this adjustment was not necessary. However,as this method corrects temperatures on an average tower basis, there are no implications for the quantitiesof interest in the present study, like turbulence statistics (i.e., two point length scales) or vertical gradients.The only implication in the present study is that presented absolute TC temperatures are in reference tothe ’background’ stratification, and only the absolute mean temperatures at Masts A and H are the actualmeasured temperatures. For this reason, all presentation of first statistics for TC temperatures are for MastsA and H only (and are further specified when reported).2.5 Case Study SelectionFor the selection of case studies, five-minute block averages are analysed. Nighttime is here defined as between21:30 local standard time (LST) and 06:30 LST. This selection of nighttime includes evening and morningtransitions during and right after sunset and sunrise, respectively. The issue of transition is addressed instep 2 of the case study selection process (using a net radiation threshold). A three-step pseudo-objectivemethod was used to select the case studies in the current analysis. In the first step, the evolution of relevantvariables (i.e., net radiation (Q∗), temperature stratification (Γlocal), wind direction (WD), and turbulentkinetic energy (TKE)) was analysed to subjectively determine whether or not the night had the potentialfor drainage flow. In the case of strong synoptic activity, lack of winds from the drainage range, and/orno apparent temperature stratification anywhere in the measurement domain, the night was discarded fromfurther analysis. During this first step, drainage events were identified, and the general characteristics ofthe events were noted (see Table 2.5 and used to inform clustering in step 2). In the second step, the block-22averages are clustered into two groups using a k-means clustering routine, and in the third step, individualcluster identities are redefined to make more physical sense for the drainage cases.2.5.1 Time Series InvestigationFive nights were excluded from analysis due to stormy conditions and a broken fuse on one of the nights(see Table 2.1). Initial visual inspection of gradient Richardson numbers (Ri) at canopy top, wind directionat canopy top and topmost CSAT-3D, buoyancy frequency (N2), and local thermal stratification revealtwo dominant regimes. The first is the anticipated drainage flow due to temperature stratification and thelocal sloping terrain (DF); the second is an either presumably stronger valley flow or drainage flow fromterrain complexities to the northwest of the site. Figures 2.10 and 2.11 provide the most ideal and stationaryexamples of a stable DF night and a more neutral VOF night, respectively. Under both regimes, Q∗ andN2 suggest a general stable environment. However, strong local stratification is achieved only during theDF cases. There are two possible explanations for why similar larger scale atmospheric stability can corre-spond to two different regimes. Either 1) larger scale stability allows for strong valley drainage (which isperpendicular to the vineyard rows) which acts to increase shear generated turbulence in the local vineyardenvironment, thus mixing out thermal gradients in the vineyard canopy environment and preventing thegeneration of local drainage; or 2) strong synoptic activity under clear sky conditions prevents the gener-ation of local drainage in the same way that a strong valley flow, or drainage from nearby mountains tothe northwest, would. Current data does not allow us to resolve whether or not this is stronger larger scaledrainage, or synoptic activity at play, but the direction of the prevailing wind under these locally neutralnighttime cases suggests larger scale drainage.23Figure 2.10: Example of a drainage flow night (DF). Five minute averages of variables are plotted for thenight of 07 July 2016.24Figure 2.11: Example of a valley drainage or other flow type (VOF). Five minute averages of variables areplotted for the night of 07 July 2016.Case study nights were selected on the basis of six criteria, four of which differ based on whether or notthe period was to be classified as local slope drainage or drainage either down-valley or from other terraincomplexities to the northwest of the site. Selection was based on the behaviour of net radiation (Q∗), thebuoyancy frequency (N2), wind direction (WD), local thermal stability (either strong temperature gradientapparent or week/nonexistent), gradient Richardson number (Ri), and the turbulent kinetic energy (TKE,either low/very low or moderate, with relative regards to typical TKE values during the night at field site).Selection criteria are summarised in Table 2.5 below. This method is subjective, and is only carried forwardin step 2, during which clustering variables are chosen and thresholds for clusters are defined.25Slope Drainage Valley/Other DrainageNet Radiation Q∗ < −30 Wm−2Buoyancy Frequency N2 < 0 s−2Wind Direction 45◦ < WD < 135◦0◦ < WD < 45◦or 315◦ < WD < 360◦Local Stability Strong Weak or NeutralGradient Richardson number Rf i > 1 − 13 < Ri < 13Turbulent Kinetic Energy Low HighTable 2.5: Summary of selection criteria during initial visually based clustering methods.2.5.2 K-Means ClusteringAs evidenced from time series analysis, drainage events at the site are associated with low TKE and highRi, whereas the valley flow (or otherwise) events are associated with higher TKE and lower Ri. Usingthis knowledge, a k-means clustering routine was performed using the five minute bock averaged TKE andRi at z/hc = 2.05 and z/hc = 1.01 as a more objective separation of cases. The clustering routine wasperformed on nighttime cases with Q∗ < −30 W m−2, leaving a total of 639 five minute block averages to beevaluated. The routine was performed for the identification of two clusters, one which contains the drainageevents (DS cluster), and the other which contains unrelated events (valley drainage or ’other’ flow (VOF)cluster). In the present study, we only focus on drainage events and an exploration of the suspected largerscale valley-drainage events are reserved for a later study.Further refinement of cluster identification was employed to ’correct’ classifications. Cases classified in theDS cluster with block averaged wind directions at z/hc = 1.01 outside of the down-slope domain were re-classified into the VOF cluster. This step redistributed 17 five minute blocks into the VOF cluster. Thisout-of-range issue is possible during very weak wind conditions outside of the domain, so that despite anenhancement of shear and mixing due to the angle of attack of the wind at the top of the vineyard, TKE isstill relatively low. Additionally, cases classified in the VOF cluster with block averaged wind directions atz/hc = 1.01 within the down-slope domain and block averaged temperature gradients (between z/hc = 0.2and z/hc = 2.05) greater than 1 K m−1 were reclassified into the DS cluster. This step redistributed 81 fiveminute blocks into the DS cluster. All redistribution occurred on the boundary between the two clusters,and in effect adds pertinent directional and stability information to the classifications in the present study.Figure 2.12 provides an example of the separated clusters, following the additional corrections. The reclas-26sification step is justified as it increases the temporal stability of cluster identity and coerces the clusteringtowards the classifications described in Section 2.5.1. Following the reclassification, drainage events occurredduring 25.25 hours of the campaign (∼17.5% of all nights).Figure 2.12: Five-minute block aver-aged turbulent kinetic energy (TKE)versus five-minute block averaged gra-dient Richardson number (Ri) for allnighttime cases with outgoing net ra-diation (Q∗) < −30 W m−2 at z/hc =1.01 and z/hc = 2.05. (a) caseswith a five-minute averaged wind di-rection at z/hc = 1.02 outside of thedown-slope domain (between 45◦ and135◦; (b) cases with a five-minute av-eraged wind direction at z/hc = 1.02within the down-slope domain. Val-ley or other flow (VOF) clusters arecoloured red; Drainage flow (DS) clus-ters are coloured blue. TKE and Riat z/hc = 2.06 are denoted by aster-isks, and that at z/hc = 1.02 by opencircles.As the reclassification did not completely ameliorate stationarity issues, a further test is applied to isolatedrainage events. Only drainage conditions that persist for at least 25 minutes are considered drainage events.Furthermore, of these drainage events, only the middle 15 minutes is used in further analysis to avoid any’leakage’ from non-drainage events into the analysis (i.e. leakage into the five minute block averages). Fur-thermore, cases are excluded when the identification switches between regimes more than two times withina 45 minute time period. This conservative time padding allows for further confidence in the selected datafor further analysis.After the time padding, 211 five minute data chunks, or 17.6 hours of the campaign, are classified as drainageevents for further analysis, summarised by Table 2.5.2. Occasional TC failure (see Table 2.1) does not affectthe selected case studies, however, there are only six hours of side-wall temperature data (Masts CS and CN,see Figure 2.3 available within the selected case studies due to the delay in the set-up of the TCs, and theside-wall TCs breaking easily and often (not reflected in the Table 2.1).27Night Time Range (LST)06 - 07 July 201621:35 – 00:0000:20 – 5:2512 - 13 July 201600:30 – 00:5501:20 – 01:4002:20 – 5:2518 - 19 July 201603:05 – 03:5004:10 – 04:3004:50 – 05:2520 - 21 July 201622:45 – 23:2003:15 – 06:30Table 2.6: Summary of selected drainage events.2.6 AnalysisAveraging ProcedureThe five-minute average of a variable, a is denoted as a, while the ensemble averaged of multiple five-minuteaverages is denoted, 〈a〉. A five minute averaging period, as opposed to the classical 30-minute period, ischosen to avoid including lower frequency motions in the analysis, and is used in other CSL studies understable conditions (e.g. Dupont and Patton, 2012).Spatial averages of the five-minute mean, which can be calculated for the TC array, are denoted withcurly brackets, {a}.Turbulent Flux CalculationsThe turbulent portion of a variable, a, is defined as the deviation from the five-minute mean:a′(t) = a(t)− a (2.6.1)where t is a time step in the five-minute interval. The variable a stands for the 3 wind components, u, v,and w, and measured temperature, T , and calculated potential temperature, θ.Turbulent fluxes, or correlations, are then defined as the five-minute average of the product of two turbulentquantities:28a′b′ =1Nt=N∑t=1a′b′ (2.6.2)where N is the number of time steps within the five-minute block, and b is a second dummy variablerepresenting the same parameters as a. The nine possible correlations between the three velocity componentsmake up the Reynolds Stress, τij :τij =u′u′ u′v′ u′w′v′u′ v′v′ v′w′w′u′ w′v′ w′w′ (2.6.3)where i and j are indices equal to either 1, 2, or 3, which represent the wind components, u, v, and w,respectively.Potential Temperature and StabilityPotential temperature, θ is calculated as:θ = Tz + Γz (2.6.4)where Γ = 0.00981 ◦C m−1 is the dry adiabatic lapse rate and z is the height in m above ground level. Aspressure is not measured during the campaign, we substitute the ground surface for the 1000 mb height.Canopy top stability is characterised using the Obukhov length:Lo =u3∗θkgw′T ′(2.6.5)where k = 0.4 is the von Karman constant, w′T ′ is the kinematic heat flux (m ◦C s−1, and u∗ is the frictionvelocity (m s−1), calculated as:u∗ = (u′w′2+ v′w′2)1/4 (2.6.6)where both u′w′ and v′w′ are used because cross-stream velocities are non negligible. Friction velocities andstability parameters are calculated for the five-minute intervals, and are only calculated at the top of thearray where surface layer physics are most likely to still hold.The Brunt-Väisälä frequency was calculated using the TC array as:29N2 = − gθA5θH5 − θA5dsin(α)(2.6.7)where g is the acceleration due to gravity, θA5 and θH5 are the potential temperatures at z = 4.73 m forMasts A and H, d = 32 m is the distance between Masts A and H, and α = 7◦ is the slope angle.Ground Heat Flux and Temperature GradientsGround heat flux is calculated using:G = −kdTdz(2.6.8)where k = 0.68 W m−1 K−1 is the approximate thermal conductivity for a sandy soil, calculated as thelinearly interpolated value at 6% (the average volumetric soil water content for the site at 12 cm depth)between a volumetric water content of 0% and 10% for a mineral soil. Negative G is defined as heat enteringthe subsurface, whereas positive G is defined as heat leaving the subsurface. The soil thermal gradient iscalculated as:dTdz=TIRT − TTC6cm0− 0.06 (2.6.9)Wind Direction DifferenceFollowing the methods of Miller et al. (2017), the difference between the wind direction as the top of thecanopy (z/hc = 1.02) and the direction of the vineyard row (90◦), δ, is calculated as:δ = |90◦ −WD| (2.6.10)Turbulence IntensityTurbulence intensity can be quantified by the turbulent kinetic energy, TKE:TKE =12(u′2 + v′2 + w′2) (2.6.11)Gradient Richardson NumberThe gradient Richardson number, Ri, is calculated as:30Ri =gT∂θ∂z(∂u∂z )2 + (∂v∂z )2(2.6.12)Flux Richardson NumberThe flux Richardson number, Rf , is calculated as:Rf =gT w′θ′u′w′ ∂u∂z + v′w′ ∂v∂z(2.6.13)Conditional SamplingFluxes are conditionally sampled (e.g. Antonia, 1981) to analyse the contribution of along-gradient andcross-gradient fluxes in the flow. An octant analysis is applied with the along slope velocity fluctuations, u′,the temperature fluctuations, T ′, and the vertical velocity fluctuations, w′, to evaluate gradient heat transferby the along-slope momentum stress (u′w′; Figure 2.13). Octants are simplified into quadrants for a moregeneral analysis of the momentum flux (see Table 2.7, and general quadrants are analysed for the sensibleheat flux.Figure 2.13: Diagram of octants. The numbers identify the octants.31Description u′w′ w′T ′Quadrant 1 (Outward Interaction) O1 & O5 O1 & O2Quadrant 2 (Ejection) O2 & O6 O5 & O6Quadrant 3 (Inward Interaction) O3 & O7 O7 & O8Quadrant 4 (Sweep) O4 & O8 O3 & O4Table 2.7: Octants necessary for the calculation of quadrant stress fractions for common quadrant analysisfor both the stream-wise vertical momentum flux (u′w′) and the cross-stream vertical momentum flux (w′T ′).Given the potential for a change in sign of the various momentum fluxes (which then affects the quadrantanalysis), a hyperbolic hole is used to not only investigate the importance of short-lived, large magnitude,events to the bulk transfer of momentum and heat (e.g. Shaw et al., 1983), but to also constrain the analysisto those events that are not associated with the uncertainty in the slope angle measurement (see Appendix5). The size of the hole, H is defined as:H =|u′w′||u′w′| (2.6.14)where the point (u′,w′) lies on the hyperbola bounding the hole region. This hole size changes with every 5minute block. The hole size necessary to avoid most of the error related to slope angle uncertainties (exceptfor the already very small flux situations, as discussed in Appendix5) is H = 3 for the stream-wise andcross-stream vertical stresses, and a hole size H = 1 for the horizontal stress (see Figure A2).Stress fractions, Si,H , for both the quadrants and the octants, are defined as:Si,H =〈a′w′〉a′w′(2.6.15)Where the angle brackets (〈 〉) denote a conditional average in this case (not a time ensemble average asotherwise defined), a′ is either u′, v′, or T ′, i is the octant (or quadrant), and H is the hole size - unlessotherwise stated, H = 3. The conditional average is the average stress within the quadrant.To avoid averaging fractions, ensemble averages of the stress fractions are calculated by taking the averageof total conditional stresses (TSi,H) and the total stresses (a′w′total) and then computing stress fractions,where the total conditional stress and the total stress is defined by:32TSi,H =t=T∑t=0a′w′i,H(t) (2.6.16)a′w′total =t=T∑t=0a′w′(t) (2.6.17)Where T is 5 minutes, and a′ again represents either u′, v′, or T ′. Time fractions, TFi,H are computed inthe same way as the stress fractions, except they represent the fraction of time during the five-minute blockinterval that the stresses reside in a certain octant/quadrant.Exchange EfficiencyAs a measure of the efficiency of momentum transport, the exuberance, e, of the flow is calculated, which isthe ratio of the counter-gradient stress to that of the along-gradient stress (Shaw et al., 1983):e =S1,H + S3,HS2,H + S4,H(2.6.18)Where S2,H and S4,H are the traditional ejections and sweeps characteristic of gradient transport and S1,Hand S4,H are the traditional outward and inward interactions characteristic of counter-gradient transport.When e = 1, the transport of high momentum fluid downwards is equally balanced by the transport of highmomentum upwards. For −1 < e < 0, transport of high momentum fluid downwards dominates.Measurements of Sweep/Ejection Cycle ImbalanceThe skewness in the 3D velocity components, Sku, Skv, and Skw, and acoustic temperatures, SkT , are usedto elucidate any imbalances in the sweep/ejection cycle. For example, Sku = 0 and Skw = 0 would implicatea balance between the contribution of sweeps and ejections to the transfer of momentum.While Shaw et al. (1983) report ratios of sweeps (traditionally Q4) to ejections (traditionally Q2), we reportthe ratio of ejections to sweeps as a means of direct comparison with Miller et al. (2017).Integral ScalesTo characterise the length and time scales of the larger turbulent coherent structures, integral length andtime scales are calculated (e.g. Shaw et al., 1995). These integral scales represent the largest eddies which areassumed responsible for the bulk of turbulent transfer. Integral scales are calculated by integrating the either33time lagged (for time scale) or distance ’lagged’ (for length scale) Eulerian correlation tensor. Correlationsfor increasing time (τ) or distance (horizontal = r, vertical = d) lags are calculated as:Ra(x, z, t, r,d, τ) =a′(x, t)a′(x+ r, z + d, t+ τ)(a′2(x, z, , t) a′2(x+ r, z + d, t+ τ))1/2(2.6.19)Where (x, z) is the distance origin, and t is the time origin of the correlation. For time scales, r and d = 0,and for length scales, τ = 0. Correlations are fit with an exponential decay function, and then the functionis numerically integrated with a distance/time steps of 0.01 m / 0.25 s, respectively. As time and lengthcorrelations may not reach zero within the five-minute and 32 m constraints, integration is performed fromRa = 1 to Ra = 1e . In the case that the correlation does not reach the e− folding distance or time, a scaleis not calculated.The time scales (T˙ ) are known as one-point scales as information from only one sensor is needed, while thelength scales (L¨) are two-point as information from two separated sensors is needed. Integral time and lengthscales are calculated at each TC. Horizontal and vertical length scales are calculated individually, while thecombination of horizontal and vertical separation correlations are used to visualise the approximate shapeand size of coherent structures in the flow. An average convection velocity, uc, can then be calculated using:uc =L¨T˙(2.6.20)343 Results3.1 Graphical DefinitionsFor the following results section, box plots represent the ensemble of five-minute averaged measurementsor calculations. The notches in the box plots provide the 95% confidence interval for the median, the solidblack lines within the boxes represent the median, the outer boundaries of the boxes represent the 25th and75th percentiles (inter-quartile range), the lower whiskers represent either the minimum of the data or the25th percentile −1.5 ∗ IQR (whichever is the largest of the two values), and the upper whisker representseither the maximum of the data or the 75th percentile +1.5 ∗ IQR (whichever is the smallest of the twovalues) (see Figure 3.1). Ensemble averages are represented by solid red lines in the box plots, and asterisksrepresent the outliers. The translucent green shading in each profile plot represents the approximate locationof the ’crown-space’ for the vineyard. The translucent grey shading represents the associated measurementerror for the represented quantity. All above-ground heights are normalised by the height of the canopy,hc = 2.3m.Figure 3.1: Diagram describing the statistics represented by the box plots presented in this study. Q1represents the 25th percentile, Q2 is the median, Q3 is the 75th percentile, and the IQR is the Inter-QuartileRange, defined as Q3 - Q1. The notches in the box plots represent the 95% confidence interval for thecalculated median, and a represents the parameter described by the box plot.353.2 General Case OverviewThermalFigure 3.2: Measured and calculated components of the energy balance for the drainage layer as a functionof time after sunset (Sunset is approximately 21:05 LST)Five-minute averaged net radiation, shown in blue, is negative and fairly constant throughout the night. Thesoil heat flux at the surface, shown in red, is positive, with a slight decrease in magnitude throughout thenight. Assuming that the measured net radiation at the top of the domain and the ground heat flux at thebottom of the domain are representative of the whole volume in which measurements are made, |G| > |Q∗|implies an overall positive input of available energy into the measurement domain (in black) through thenight, which slightly decreases in magnitude with time (Figure 3.2).36Day%Water Content0 m (Tower) 32 m (up-slope)12 cm 20 cm 12 cm 20 cm09-07-16 8 4 9 410-07-16 7 3 7 311-07-16 7 4 6 312-07-16 6 2 6 313-07-16 8 4 6 214-07-16 8 4 6 215-07-16 6 3 4 117-07-16 5 2 6 218-07-16 7 3 4 119-07-16 6 3 6 220-07-16 6 3 4 121-07-16 6 3 5 222-07-16 6 3 6 2Average 6.6 3.2 5.8 2.2Table 3.1: Measured soil volumetric water content at the tower and at 32 m up-slope from the tower (nearMast H).37Figure 3.3: Relationship between volumetric water content and the soil thermal conductivity for a mineralsoil. Red star indicates value used for soil in study.Overall, the volumetric water content (VWC) of the soil was consistent throughout the campaign, with thedown-slope location being slightly wetter than the up-slope location. The soil closer to the surface is wetterthan that deeper in the surface (Table 3.1). Thermal conductivity of the soil, k, is estimated to be around0.68 W m−1 K−1. This estimate is based off of a linear interpolation between the known conductivity at aVWC at 0% and that at 10% (Figure 3.3).38Figure 3.4: Ensemble average of nighttime case study soil temperature with depth. Surface temperatureis measured by the IRT (red dot), whereas soil temperatures are measured by extension-grade TCs (blackdots).The soil warms with depth, implicating a movement of heat upwards towards the surface (Figure 3.4). Theaverage soil heat flux, is -87 W m2, where the negative sign indicates a movement of heat away from thesub-surface and into the atmosphere.Figure 3.5: Box plots of the 211 five-minuteaveraged potential temperature profiles as mea-sured by fine-wire TCs (dark-gray) and infraredthermal sensor (light-gray; labelled IRT). Forbox plot statistics definitions, see Figure 3.1 atthe beginning of Section 2.6. The translucentgreen shading provides approximate location ofthe vegetated portion of the vineyard canopy atthe site; hc denotes the approximate top of thecanopy; hb denotes the approximate bottom ofthe vegetated portion of the vineyard canopy.Ensemble average is given by red line.39Figure 3.6: Profiles of side wall temperature (north (a) and south (b)) and the average horizontal gradientbetween the centre of the gap and the vineyard rows (c). Box plot statistical definitions are provided byFigure 3.1 at the beginning of Section 2.6.An inversion is observed within the ’crown-space’ (between z/hc = 0.39 and z/hc = 1.02) of the canopy,whereas a lapse is present in the ’trunk-space’ (between z/hc = 0 and z/hc = 0.39; Figure 3.5). The inver-sion strength between z/hc = 0.39 and z/hc = 2.06 is on average 0.73 K m−1, that between z/hc = 0.39and z/hc = 2.06 is on average 0.52 K m−1, that between z/hc = 0 and z/hc = 2.06 is 0.059 K m−1, andthat between z/hc = 0 and z/hc = 0.9 is -2.77 K m−1, where a positive value indicates an inversion and anegative value indicates a lapse.Very mild temperature inversions are observed near the vegetation to the north and south of the tower(Masts CN and CS, respectively), but the gradients on each side act in opposite direction. For example,between z/hc = 0.39 and z/hc = 0.65, the near-vegetation air to the north (CN) of the tower is lapsed, whilethat to the south (CS) is inverted (Figure 3.6(a - b)). These opposing temperature profiles yield unclearhorizontal temperature gradients between the vegetation and the gap centre. Figure 3.6(c) provides theaverage difference between the two vegetation side walls and the centre of the gap. Only near the centre ofthe canopy (z/hc = 0.65) does the average horizontal temperature gradient indicate a favourable horizontalgradient for heat loss from the canopy.40MechanicalFigure 3.7: Boxplots of the 211 five-minute averaged profiles of turbulent kinetic energy (a), normalised windspeed (b), and wind direction (c). (a) Turbulent kinetic energy (TKE), ensemble average is given by redline; (b) wind speed (ms−1) measured by CSAT-3D’s normalised by the wind speed at hc, ensemble averageis given by red line; (c) Wind direction (WD ◦) measured by CSAT-3D’s, wind coming from the east (90◦;down-slope) is given by dark green line. Box plot statistical definitions are provided by Figure 3.1 at thebeginning of Section 2.6TKE is smaller within the canopy than in the above-canopy environment. The vertical gradient of TKEis also relatively small and unchanging between the ground and the centre of the canopy, but steepens nearthe top of the canopy and in the above-canopy environment (Figure 3.7(a)).Wind speed increases with height, with an apparent inflection point in the profile near the canopy top (Figure3.7(b)). The steepest gradients in wind speed are on average between the retarded wind near the surface(z/hc = 0.19) and that at the crown-space bottom (z/hc = 0.39), and between the centre of the crown-space(z/hc = 0.65) and the top of the canopy (z/hc = 1.02). There is no significant gradient in wind speedbetween z/hc = 0.39 and z/hc = 0.65.The canopy acts as a channel to the drainage layer. While wind directions aloft have a wider range (note: onlyWD1.02 was constrained in the analysis), wind flow is more-or-less parallel to the vineyard rows, especially41deeper within the canopy at z/hc = 0.65 and z/hc = 0.39. Near the surface, the wind directions slightlyturn north again out of the canopy alignment (Figure 3.7(c)).3.3 FluxesDuring 50.7% of the cases, u∗ at the canopy top is less that the commonly used threshold of 0.08 m2 s−2,implicating a low-flux situation for the chosen drainage cases, which is not entirely unexpected given theselection criteria described in section 2.5.2. During the case studies, the median Ri and Rf at the top of thecanopy was 0.0402 and 0.1334, respectively, indicating that shear is an important driver in the generation ofturbulence, despite the low-flux stably stratified situations.Figure 3.8: Vertical profiles of (a) stream-wise vertical, (b) cross-stream vertical, and (c) cross-vine mo-mentum fluxes. Box plot statistical definitions are provided by Figure 3.1 at the beginning of Section 2.6.Asterisk at z/hc = 1.65 in (a) gives location of interpolated jet-height.The stream-wise momentum flux (u′w′) is greater in magnitude than that of the cross-stream momentumflux (v′w′), except for near the ground where both fluxes are completely within the uncertainty range for theultrasonic anemometers (Figure 3.8(a - b)). The cross-vine flux (u′v′) is larger than the vertical momentumfluxes by about an order of magnitude, and is generally negative within the canopy and positive above thecanopy (Figure 3.8(c)). While others have briefly considered cross-vine fluxes (Miller et al., 2017), it hasbeen reported to be generally noisy and thus focus is given to the stream-wise momentum flux here.42The maximum flux in the stream-wise momentum is located at the top of the canopy, with the secondarymaximum at the top of the measurement domain (Figure 3.8(a)). The stream-wise momentum flux changessign between the canopy top and the top of the measurement domain, indicating the presence of a jetmaximum. With linear interpolation (Grachev et al., 2015), the location is on average at approximately 3.79m, or z/hc = 1.65, indicated by an asterisk in Figure 3.8(a).Figure 3.9: Kinematic sensible heat flux withheight. Box plot statistical definitions are pro-vided by Figure 3.1 at the beginning of Section2.6Heat flux within the inter-quartile range of the five-minute averaged data is everywhere negative (towardssurface), with the strongest flux at the top of the canopy (Figure 3.9). Flux in the inter-quartile rangeat z/hc = 0.19 and z/hc = 0.39 is within the instrument uncertainty bounds for the heat flux, with someoutliers indicating both positive and negative heat fluxes during some of the five-minute cases. The locationof the maximum heat flux is at the canopy top, which is the same for the along slope momentum flux.433.3.1 The Flux-Gradient RelationshipFigure 3.10: Relationship between the vertical gradient in u-momentum and the vertical flux u′w′.44Figure 3.11: Relationship between the vertical gradient in v-momentum and the vertical flux v′w′.Figure 3.12: Relationship between the vertical gradient in T and the vertical heat flux w′T ′.45Figures 3.10 - 3.12 provide the relationship between the vertical gradient in u, v, and T , and the verticalfluxes u′w′, v′w′, and w′T ′, respectively. Quadrants 1 and 3 (upper right-hand corner and lower left-handcorner, respectively) represent gradient fluxes, whereas Quadrants 2 and 4 (upper left-hand corner and lowerright-hand corner, respectively) represent counter-gradient fluxes. For the most part, there is no strongrelationship between the vertical gradient and the vertical flux for any of the quantities. There does notseem to be any relationship between stability and the correlation between turbulent flux and vertical meangradient.3.4 Characterising Exchange3.4.1 Profile of Third MomentsFigure 3.13: Vertical profiles of ensemble averaged skewness in the 5 minute data blocks for all three velocitycomponents and for temperature during the selected case study nights. Error bars represent the standarddeviation of the skewness data, and the grey shading represents the uncertainty due to instrumentationerrors.Skewness in the combined horizontal velocity components and temperature, u, v and T , and the verticalcomponents, w, reveals the offset from a joint Gaussian distribution, which is an indication of an unequalcontribution of either sweeps or ejections (depending on the sign of the skewness) to the gradient transportof momentum. Within the canopy, u is skewed towards positive values, except for at the top of the arraywhere the average skewness is within the uncertainty bounds (Figure 3.13(a)). Skewness in the cross-streamcomponent, v is very small and within the uncertainty bounds at the top three heights (z/hc = 2.06, 1.02, and0.65), and is then skewed negatively near the ground (Figure 3.13(b)). Skewness in the vertical component isnear zero near at the top of the measurement domain, positive at the canopy top, and then negative within46the canopy (Figure 3.13(c)). Temperature skewness is positive within the canopy and negative at the top ofthe measurement domain (Figure 3.13(d)).3.4.2 Connectivity between Heat and MomentumFigure 3.14: (a) Octant heat flux stress fractions. Blue colours are associated with −T ′ and red colourswith +T ′. Solid lines represent gradient transport of stream-wise momentum, and dashed line representcounter-gradient transport of stream-wise momentum. (b) Separation of the stream-wise momentum fluxexuberance into instances of gradient (red) and counter-gradient (black) sensible heat flux.Figure 3.14(a) provides the ensemble averaged flux fraction for the heat flux as a function of height for eachoctant. The colouring represents whether or not the octant represents a cooler (blues) parcel or a warmer(reds) parcel. The solid lines represent octants for gradient transport of stream-wise momentum, and thedashed lines represent the counter-gradient transport of stream-wise momentum. Octants 3, 4, 5, and 6represent gradient transport of heat (warmer air downwards/colder air upwards), and octants 1, 2, 7, and 8represent counter-gradient transport of heat. At all heights, the gradient transport of heat contributes pos-itively to the heat flux, whereas counter gradient transport contributes negatively, as is expected given thesign of the heat flux at all levels (Figure 3.14(a)). Octants 4 and 6 contribute the most to the flux fraction,which are associated with gradient transport of momentum. Further, octant 4 contributes the most withinthe canopy to the heat flux, which is associated with sweeps of high momentum and higher temperature47(Figure 3.14(a)).Figure 3.14(b) provides a breakdown of the stream-wise momentum flux exuberance as a function of heattransport either along the gradient (black) or against the gradient (red). During times of gradient sensibleheat transport, the momentum flux is exuberant, and follows closely the overall trend for the total (Figure3.16(b)). For the instances of counter-gradient sensible heat transport, the momentum flux is not exuberant,indicating that neither sweeps nor ejections dominate the counter-gradient transport of sensible heat (Figure3.14(b)). In particular, inward and outward interactions (counter-gradient momentum transfer) becomemore important to the counter-gradient transport of sensible heat near the centre of the canopy, whereasnear the canopy-top and the surface, there is no discernible preference towards gradient or counter-gradientmomentum transport and the counter-gradient transport of sensible heat (Figure 3.14(b)).3.4.3 Event Size and Transfer MechanismsFigure 3.15: 〈u′w′〉 quadrant stress fractions (a) and time fractions (b) as a function of hole size, H3.15(a) describes the decline in flux contribution as a function of the magnitude of the stream-wise fluxevent. Quadrants 1 and 3 (upper right and lower left, respectively) represent the contribution due to out-ward/inward interactions, respectively, and quadrants 2 and 4 (upper left and lower right, respectively)represent the contribution due to ejections and sweeps, respectively. Figure 3.15(b) provides information onthe amount of time that the events of a certain size spend contributing to the flux. For example, if a verylarge event contributed to 20% of the five-minute total flux, but an event of this size or larger only occurredonce during the time period, then the time fraction for the event would be 16000 , where the denominator48represents the number of measurements made within a five-minute period, and the numerator represents thenumber of times the flux magnitude is detected within the time period.As hole size increases, the fraction of stream-wise momentum flux remaining at or above the threshold holesize slowly decays (Figure 3.15(a)). The decay is the slowest for the stream-wise momentum flux near thesurface (z/hc = 0.19 and z/hc = 0.39), and quickest at the top of the canopy (Figure 3.15(a)). Instantaneousflux is most frequently small (Figure 3.15(b)), evidenced by the quick decay in the time fractions withincreasing hole size. This is particularly true for the momentum flux at the top of the canopy, which isdominated by smaller (relative to the ensemble averaged of the flux at the canopy top) more frequent events.The time fraction decays the slowest for the near-surface measurements (Figure 3.15(b)).Figure 3.16: (a) 〈u′w′〉 quadrant stress fractions as a function of normalised height for a hole size, H = 3;(b) Ensemble averaged exuberance of the u′w′ flux; (c) the ejection sweep ratio for the u′w′ fluxFigure 3.16(a) provides the ensemble averaged heat flux fraction for each of the quadrants. Gradient trans-port is represented by a positive flux fraction, whereas counter gradient transport if represented by a negativeflux fraction. There is an apparent regime change between the exchange of momentum within the canopyand that at the top of the measurement domain. Stress fractions for the vertical momentum fluxes aregenerally smallest in magnitude at the canopy top. Within the canopy, quadrants 2 and 4 contribute the49most to the stream-wise momentum flux, with quadrant 4, which is associated with sweeps, dominating atand below z/hc = 0.65 (Figures 3.16(a).Figure 3.16(b) provides the exuberance, e as a function of height. Exuberance is used to describe the effi-ciency of the transfer of high momentum fluid to the surface (Shaw et al., 1983). However, in the presentcase we adopt a flexible definition of e so that it represents the efficiency of the transport of high momentumfluid downwards below the jet, and high momentum fluid upwards above the jet. When e = −1, the transferof high momentum fluid downwards below the jet (upwards above the jet) is equal to the transfer of lowmomentum fluid downwards (upwards). When −1 < e < 0, the transport of high momentum fluid down-wards (upwards) exceeds that of the transport of low momentum fluid downwards (upwards). Exchangeof stream-wise momentum is most efficient at the top of the canopy. At and below z/hc = 0.65 and atz/hc = 2.06, the exchange is still efficient, but only slightly (Figure 3.16(b)).Figure 3.16(c) provides the ratio of ejections to sweeps as a function of height. When this ratio is lessthan one, sweeps dominate, and vice versa for when it is greater than one. This is inverse to what is givenby Shaw et al. (1983). Sweeps are most dominant near the centre of the crown-space (z/hc = 0.65), andremain slightly dominant within and above the canopy (Figure 3.16(c)). The profile of the ejection/sweepratio found here follows closely that reported by Shaw et al. (1983) for a corn canopy under near-neutralconditions. Miller et al. (2017) found sweeps to dominate over ejections within a vineyard up to z/hc = 2.4where the ejection/sweep ratio equals 1, which is consistent with our results.50Figure 3.17: Flux fractions (a) and exuberance (b) for the heat flux as a function of height.Figure 3.17(a - b) is the same as Figure 3.16(a - b), except for the heat flux. There is no change in regimefor the heat flux - quadrants 2 and 4 are consistently contributing to the flux across the entire domain(Figure 3.17(a)). Within the canopy, quadrant 4, which is associated with sweeps, contributes the most tothe transport of heat. At the canopy top, the contribution of sweeps and ejections is almost exactly the same(Figure 3.17(a)). The flow is most exuberant within the top portion of the canopy (between z/hc = 0.65and z/hc = 1.02; Figure 3.17(b)).3.5 Characteristic Turbulent Scales51Figure 3.18: Normalised two point length scales (a), time scales (b) and normalised, ensemble averaged, wind speed and convection velocity (c) withheight.52Figure 3.19: Dependence of two point, L¨ and shear, Ls, length scales on the incident wind angle at canopytop. WD = 90◦ corresponds with row-parallel flow.One-point time scales (T˙ ) are shortest within the canopy, with the longest T˙ occurring at the top of themeasurement array (Figure 3.18(a)). Two-point length scales (L¨) follow the time scale pattern closely. L¨scales well with canopy height within the canopy, particularly in the centre of the canopy (Figure 3.18(b)).The behaviour of L¨ and T˙ across the entire domain results in quicker convection velocities at the canopy topand within the canopy, and slower convection velocities at the top of the measurement domain and near thesurface (Figure 3.18(c)).53Figure 3.20: Median convection velocity for parallel wind (a; 12 five minute cases) and oblique wind (b; 5five minute cases) normalised by average canopy top wind speedWhen five-minute cases are isolated into strictly parallel cases (88.5◦ < WD < 92.5◦; 12 total cases) andoblique cases (WD < 47.5◦ or WD > 132.5◦; five total cases), new patterns in the convection velocitiesarise (Figure 3.20). During the oblique cases, convection velocity (〈ucobl〉) behaviour with height is verysimilar to the all-direction case given in Figure 3.18(c). 〈ucobl〉 is greatest at the top of the canopy, andless than the Eulerian velocity at the canopy top under oblique wind conditions (〈uobl〉) at z/hc = 2.06 andz/hc = 0.39. During the parallel cases, the convection velocities (〈ucpar〉) increase as a function of height,except for within the crown-space of the canopy, where 〈ucpar〉 is more or less constant with height (Figure3.20(a). The Eulerian velocity as a function of height for the strictly parallel cases reveals a weaker inflectionpoint at the canopy top as compared to that for the strictly oblique cases (Figure 3.20(b)).Figures 3.21 - 3.23 are ensemble averaged contour plots of the spatial temperature correlations for all 211cases (Figure 3.21), the 12 parallel wind cases (Figure 3.22), and the 5 oblique wind cases (Figure 3.23).Positive distances in the plots indicate a correlation in which the ’stationary’ TC is down-slope (x-direction)of, or vertically (z-direction) below, the ’roving sensor’. Therefore, the correlations at Up-slope Distances of54-32 m are between masts A and H, where H contains stationary sensors and A contains the roving sensors.The stationary sensor is located at the (x, z) point (0,0) in the plots. To ensure a common correlationscale, following the ensemble averaging procedure and prior to contour plotting, all negative correlations arere-coded as zero-correlations. This exaggerates the extent of ’no correlation’ at the edges of the plottingdomains, but allows for inter-comparison between the five different heights.There is agreement between calculated longitudinal length scales and the size of the eddies in Figure 3.21,whereby the largest structures are located at the top of the measurement domain and the smaller structuresare located within the crown-space. According to Figure 3.21, eddies are more circular near the top of thecanopy, whereas within the canopy space, the structures are flatter, and near the centre of the crown-space(z/hc = 0.65), are tilted upwards from the surface facing down-slope. During conditions when the windangle at z/hc = 1.02 is between 90◦ ± 2.5◦, structures are more elongated, particularly near the canopytop, and the structures within the canopy are slightly more tilted from slope-parallel (Figure 3.22). Duringconditions when the wind angle at z/hc = 1.02 is less than 47.5◦ or greater than 132.5◦, structures withinthe canopy are less elongated, and more correlated in the vertical (Figure 3.23).55Figure 3.21: (Time) ensemble averaged two-point correlations between all possible TC distance combinations. Correlations made up-slope are positivex−distances, and correlations made upwards are positive z−distances.56Figure 3.22: (Time) ensemble averaged two-point correlations between all possible TC distance combinations for cases during which the five-minuteaveraged wind direction was within 90◦ ± 2.5◦. Distance definitions are provided in Figure 3.2157Figure 3.23: (Time) ensemble averaged two-point correlations between all possible TC distance combinations for cases during which the five-minuteaveraged wind direction was less than 47.5◦ or greater than 132.5◦. Distance definitions are provided in Figure 3.21584 Discussion4.1 Drainage Flow Characteristics within the Vineyard4.1.1 Thermal AspectsContrary to typical drainage flow over non-vegetated slopes where an inversion is found from the ground up(see Section 1.2.1), the characteristic temperature inversion - which forces the drainage flow - does not startuntil around z/hc = 0.39 (Figure 3.5). An elevated inversion such as observed here has been observed in othercanopies under stable conditions (Jacobs et al., 1994; Dupont and Patton, 2012). However, these canopieswere all denser than the present case (i.e., orchard and forest canopies), whereas for more ’open’ canopies,strong inversions have been observed in the trunk-space under stable conditions (Launiainen et al., 2007).For the denser canopy cases, a lapse is not entirely surprising in the near-surface region during the nighttimegiven that the vegetation at the ’crown’ can act to prevent out-going long-wave radiation from the surfaceescaping to the above-canopy environment. Furthermore, it could be expected that under the denser canopyconditions, a fair amount of heat is redirected to the surface from the crown-space of the canopy given thatthe canopy elements cool throughout the night as well. However, in the present case, the canopy is open (atleast in comparison with a forest canopy), the soil is dry, and the skies mostly clear, so it would be expectedthat cooling from the surface would overcome any small heating due to long-wave radiation from the canopyelements, and that the canopy elements would not act to trap the outgoing long-wave radiation, particularlyin the gap region, allowing for an inversion to develop from the ground surface upwards. While the outgoinglong-wave radiation is considerable, and great enough to force a drainage flow (e.g. Gudiksen et al., 1992),this loss is overcome by the heat input from the surface (Figure 3.2). Assuming that heat is only exchangedin the vertical, and that our measurements at the top and bottom of the domain are representative for theentire vertical domain, this imbalance would indicate a gradual heating of the air layer around the ultrasonictower during the nighttime, which is not the case (Figure 3.5). Therefore, it is likely, especially given thepresence of drainage (Thomas, 2011), that a non-negligible amount of heat, on the order of ∼52 W m−2, isadvected out of the domain in the horizontal. While advection is difficult to estimate in canopies (Thomas,2011), given the flow direction, it is likely that some of this heat is transported down-slope with the drainagelayer.59Figure 4.1: Measure surface temperature of vegetation to the north and south sides of the instrumentedtower as a function of time since sunsetGiven the lapse, it is highly unlikely that the drainage layer itself has been formed locally due to surface cool-ing. Further, the average temperature profiles near the north and south vegetation sidewalls (masts CN andCS, Figure 2.3) in comparison with those at the centre of the gap (mast C) do not demonstrate favourablehorizontal gradients for cooling at the side walls, except for near z/hc = 0.65 (Figure 3.6). However, vegeta-tion surface temperatures do cool throughout the night (Figure 4.1, indicating that, in combination with thehorizontal temperature gradients near canopy centre, the canopy could possibly play a role in the formationand sustainment of the nighttime drainage layer. It is likely, given the proximity of the site to steeper slopesto the east and north-east, that the drainage layer is fed both locally and non-locally within the measurementdomain. This non-local influence is evidenced further by the predominance of above-canopy flow from thenorth/north-east (Figure 3.7(c)), suggesting a forcing from the steeper slopes upwind of these directions (seeFigures 2.1 and 2.2).4.1.2 Mechanical AspectsIt is clear, given the weak inflection point near hc (see Figure 3.7(b)) and the interpolated near-surface jetwithin the measurement domain (see Figure 3.8(a)), that both dynamics related to drainage and typicalCSL flows are present during the case studies. The weak inflection point implies a region of hydrodynamicinstability that could lead to the generation of the larger coherent structures known to be responsible for a60large fraction of momentum transfer in canopies (e.g. Finnigan, 2000). At the same time, the presence ofthe jet acts as a near-surface source of high momentum fluid to feed turbulence within the CSL, despite thestable stratification within the region. How the presence of the inflection point and the near-surface jet inconcert influences the character of nighttime exchange is an important question not yet addressed in paststudies, and is explored more in the following sections, particularly Section 4.2.Further complicating the nature of mechanically generated turbulence in the present case is the orientationof the above-canopy wind vectors with respect to the orientation of the canopy, which under favourableconditions (i.e., when δ > 0, Miller et al. (2017)) leads to smaller L¨ (see Figure 4.2). From Figure 3.7(c), itis apparent that shear is added in the presence of drainage within the study site, given that the winds fromaloft are consistently forced to flow along the vineyard rows, particularly near z/hc = 0.65. This type offorced turning of the wind vectors was also observed by Miller et al. (2017), who also found that under stableconditions, this effect is increased. This added shear is evidenced by the apparent relationship between anincreasing δ and decreasing shear and two-point length scales (Ls and L¨, respectively). The modulation ofthe turbulent field by δ is explored in more detail in Section 4.3.Figure 4.2: Relationship between length scales - shear, Ls, and integral, L¨ - and δ614.2 Fluxes, Gradients, and their Relationship4.2.1 Flux-Gradient RelationshipGiven that the transfer of both heat and momentum is dominated by larger events, it is unsurprising thatK-theory fails to represent the relationship between turbulent correlations and the mean gradients (Figures3.10-3.12). This failure of gradient transport theory is not unlike other canopies under neutral conditions(Denmead and Bradley, 1987; Finnigan, 2000) due to the predominance of larger structures controlling muchof the turbulent flux.Further, the sensible heat flux, especially near the surface, is dominated by counter-gradient flux, which isnot unlike other canopies (Finnigan, 2000). This result, while not new to CSL studies, does hold new impli-cations for future drainage flow models within vineyards, which would be advantageous from a managementperspective. Higher-order closure is needed within the canopy (e.g. Wilson and Shaw, 1977), particularlyunder stable conditions when the likelihood for exchange deeper in the canopy to be dominated by verylarge, coherent, structures is even higher. This conclusion, of course, must not be taken as absolute. Sim-ilarly to Emmel (2014), low-flux situations in the nighttime are related to counter-gradient flux within thecanopy, particularly near the surface. While there doesn’t seem to be any strong relationship at any heightbetween the the vertical flux and the mean vertical gradients in heat and momentum, the results presentedare for the most part within the uncertainty range of the instruments, and could be under-representationsof the total flux. Further, because the measured flux is for the most part within the uncertainty rangeof the instrument, final conclusions on the validity of the flux-gradient relationship within the vineyardcanopy under drainage cannot at present be made. Because our ability to measure finer scale structures islimited, our analysis is missing the contribution of flux due to the canopy element-scale (i.e., leaf and stemscale) wake production of turbulence (e.g. Cava and Katul, 2008; Böhm et al., 2013), as well as any dispersiveflux (e.g. Poggi and Katul, 2008), and turbulent longitudinal and lateral flux (due to instrumentation set-up).For the following discussion on the momentum and heat fluxes, the terms ’gradient’ and ’counter-gradient’transport are still used to describe the behaviour of the local fluxes, despite the apparent failure of gradient-transport theory. For the most part, the break-down of the fluxes via the quadrant and higher-order statisticalmoment analyses indicate a slight preference towards gradient transport. Further, these terms are used todescribe the ’general’ or expected gradients. For example, the transfer of warm air downwards, even in thelapsed near-surface region, is classified as gradient transport. This is because this transfer near the surfaceis likely due to canopy-top activity, where a negative heat flux is indeed along the gradient. This is done62to make clear the non-local nature of transport, especially near the surface. Additionally, while the terms’sweeps’ and ’ejections’ are not classically used to describe modes of heat transport, they are used here forease of explanation.4.2.2 Momentum FluxThe change in the sign of the momentum flux between the top of the canopy and the top of the measure-ment domain indicates the presence of a low-level jet between z/hc = 1.02 and z/hc = 2.06 (e.g. Grachevet al., 2015). The presence of this jet is particularly important to the way that the total exchange betweenthe surface and the outer environment behaves. While high momentum is transferred downwards towardsthe surface below the jet, high momentum is also transferred upwards away from the jet and the canopy.The transport of the high momentum fluid away from the jet is more efficient below the jet than aboveit, likely due to canopy acting as a strong momentum sink compared to the above-jet environment whichlacks roughness elements to impose drag (Figure 3.16(b)). Because the jet is located above the canopy, andnot within it, the classical dominance of sweeps to the transfer of momentum should, and does hold. Thispredominance of sweeps within the canopy is supported both by the quadrant analysis (Figure 3.16(a andc) and by the sign of Sku and Skw (Figure 3.13(a and c)). Sku > 0 and Skw < 0 indicates a preferencetowards higher momentum transported downwards. A notable difference between this canopy and othersis that the skewness in u- and w−components is less than that typically found in canopies under neutralstability (Raupach et al., 1996), indicating that the sweeps occurring are either weaker, and/or not as dom-inant in comparison. Further, the location of the most negative Skw, which has been observed near thecanopy top in other studies (Dupont and Patton, 2012; Miller et al., 2017), is here observed near the centreof the canopy. This is supported by the ejection sweep ratio for the momentum flux within the canopy,which reaches a minimum at z/hc = 0.65, indicating that sweeps are the most dominant mode of transferin this region, compared to the other measured regions in the domain. This is not wholly surprising, and isan indication that the structures generated in the shear-instability region are penetrating downwards intothe canopy, despite the inversion, but only to a certain extent perhaps due in part to the inversion. Thispenetration of turbulence into the canopy decreases as a function of distance from hc towards the surface,as evidenced by the increase in the ejection-sweep ratio past z/hc = 0.65 (Figure 3.16(c)). The ejection tosweep ratios within the canopy during stable conditions are comparable to those found during near-neutralconditions by Miller et al. (2017) for the row-parallel momentum flux. The average ejection to sweep ratiohere is ∼0.8, whereas in the neutral case, the average was found to be ∼0.7, likely suggesting that duringthe stable cases, the strength of the mixing layer at canopy top is slightly weaker than that during the nearneutral situations, which makes sense given flux magnitudes and velocity inflection strength.63While the stream-wise momentum flux is greatest in magnitude near the canopy top (Figure 3.8(a)), fluxin this region is dominated by more frequent, (locally) relatively smaller events (Figures 3.15(a - b)). This,however, does not mean that the events near the top of the canopy are smaller than the ones within thecanopy - when hole sizes are calculated, they are based upon a local vertical flux threshold, meaning thata hole size, H = 4, at z/hc = 1.02 could be the same size as that of H = 6 at z/hc = 0.65. Therefore, theflux at the top of the canopy is dominated by ’smaller’, more frequent events, which then penetrate into thecanopy and are perceived as much larger events relative to the local average vertical flux.Indicative of the amount of turning necessary to force the drainage wind along the vineyard rows, cross-stream fluxes (v′w′) are greatest in magnitude near the centre and bottom of the canopy (z/hc = 0.65 andz/hc = 0.39; Figure 3.8). Interestingly, the average cross-stream flux is negative near the centre of the ’crownspace’, whereas the cross-stream flux is on average positive at the bottom of the vineyard ’crown space’.Given that these fluxes are calculated under the same rotation, this change in sign indicates that the windnear the surface turns again out of the canopy. Whether this turning near the surface is due to drainageis not a resolvable question, in spite of the wind direction, as the presence of the lapse would suggest thepotential for anabatic (or up-slope) flow (e.g. Whiteman, 2000) if the flow situations are topographicallyinfluenced as assumed here.Vexing questions that remain include how the jet affects the communication of canopy sub-layer air with theabove-canopy environment, and how the presence of the jet adjusts our definitions of the roughness sub-layer,which is normally defined as at least twice the height of the canopy (Raupach et al., 1996; Finnigan, 2000). Bytraditional definition, the roughness sub-layer would extend at least up to 4.68 m, which is about 1 m abovethe interpolated jet height. Under classical drainage wind theory, the above jet and below jet environmentsare somewhat decoupled, with MOST applying well in the above-jet environment (Horst and Doran, 1988;Grachev et al., 2015), and unknown scaling applying in the below-jet near-surface environment. Both theabove-jet and below-jet environments are contained within the present CSL (note that the jet location stillcalls into question whether or not the CSL truly extends past the jet). Given the additional thermal profileof the current case, the communication between the very near-surface environment, canopy ’crown-space’environment, and the above-canopy environment is complicated. Due to the importance of sweep/ejectionmotion to the transport of momentum, decoupling is not entirely likely.644.2.3 Sensible Heat FluxOf particular interest is the behaviour of the sensible heat flux near the surface. Despite the lapse near thesurface, the turbulent heat flux is negative, indicating that heat is still being transported towards the grounddespite how warm the ground surface is. The downwards transport of heat is typical for a drainage layer,and is the mechanism by which the near-surface air loses heat. While the near surface air does cool throughthe night, the lapse persists (Figure 4.3). There are a variety of reasons why the heat flux measurement inthe near surface reason could be compromised, however. For one, the measured flux is small and within theuncertainty range of the instrument. Further, spectral flux corrections are not applied, despite being so nearto the surface, so it is very likely that flux is in general under-estimated (note that this would not, however,impact the sign of the flux). The eddies that are resolved by the ultrasonic anemometers are fairly large,but there are likely a wide variety of smaller sizes impacting the transport of heat and momentum. Withthe prospect of large dispersive fluxes (e.g. Poggi and Katul, 2008) and spectral short circuiting limiting themedium-range eddy sizes (e.g. Cava and Katul, 2008), the small eddies unresolved by the anemometers couldbe contributing largely to the flux, especially near the surface.Despite the possibility for the flux to be under sampled, and inconclusive in the region, the persistence ofthe lapse and the cooling throughout the nighttime at a similar rate as the measurement locations withinthe inversion region (Figure 4.3), makes the lapse further perplexing. As the surface is comparatively warm,and because the soil heat flux is negative (i.e., the surface is losing heat to the air), it would make moresense for the near surface air to be warming - or as discussed earlier, for there to be a significant advectiveheat flux. The considered advective heat flux in Section 4.1.1 only accounts for the vertical imbalance inthe radiative heat loss at the top of the domain and the heat input at the bottom of the domain, and notentirely the additional cooling throughout the night. This additional cooling is indicative of heat loss withinthe layer near the surface, which could mean either an advective loss larger than the original estimate, couldexplain in part the negative turbulent kinetic heat flux in the region, and/or could be related directly tothe dispersive flux that current anemometry is unable to resolve, but has been shown to be large in sparsecanopies (Poggi and Katul, 2008). While there are uncertainties in the ability of the TCs to capture meantemperatures, the uncertainty is very small, and would not change the fact that the air near the surface iscooling throughout the night.Assuming that the measurements near the surface are at the very least correct in terms of the sign, thedownwards turbulent flux near the surface is likely due to a combination of the presence of the drainage65Figure 4.3: Hourly averaged potential temperature profiles through night of 07-06 - 07-07, 2016. Timesare displayed in LST for each profile. Over bars in the present plot indicate hourly averages as opposed tofive-minute averages.66layer and CSL turbulent dynamics. Consistent with other canopies under near-neutral stability, sweeps andejections are the most dominant modes of transport for heat in the vineyard (Figure 3.14(a)) (e.g. Finnigan,2000). Further, sweeps dominate within the canopy, with increasing dominance as the surface is approached3.14(a)), consistent with behaviour over rough surfaces (Raupach, 1981). The fact that sweeps dominatewithin the canopy and that the canopy is cooling, further validates the assumption that the negative heatfluxes within the canopy (despite the lapse) are not erroneous measurements (Cava et al., 2006). Further,it is apparent that the gradient transport of heat (i.e., associated with sweeps and ejections, rather thaninteractions, and along the ’general’ inversion gradient) is connected to the gradient transport of momentum(Figure 3.14(b)). This could indicate that the structures sweeping into and out of the canopy retain tosome extent their ’original’ temperature - where original here does not necessarily mean an absolute origin.Therefore, it is likely that as higher momentum fluid is swept into the canopy, so too is warmer air. Ifthe penetration of structures is deep enough, this warmer air can reach the near-surface region. Despitethe near-surface lapse, the average temperatures are still lower than those above the canopy - and evenwith in the canopy (Figure 3.5) - which would mean a measured negative turbulent heat flux in the region.Interestingly, at the canopy top, the movement of colder air upwards slightly overtakes the movement ofwarmer air downwards (O5+O6O3+O4 = 1.06; Figure 3.14(a)), which further implies the coupling of the movementof heat and momentum in the present case. While the imbalance is very slight, it is in contrast to thewithin-canopy case where the movement of warm air downwards dominates the heat flux. The fact thatejections overtake sweeps at the top of the domain calls into further question the definition of the CSL whendrainage is present.4.3 Turbulent Scales and Coherent StructuresIt is apparent that the movement of coherent structures though the flow is a very important mode of transportwithin the canopy. Therefore, characterising these structures is a first step towards further understandingthe major mechanism behind transport under stably stratified conditions over a vegetated slope. In charac-terising the scales for coherent structures, it is of important note that our results depend on the quantitieswe measure. As aptly observed by Finnigan (2000), "coherent structures in canopy flows... are complexpatterns of pressure, velocity, and translating air particles and that their presence is manifested in differentways depending upon which variables we choose to measure". Data here allows us to characterise single-pointtime (T˙ ) and two-point length (L¨) scales using correlations in temperature fluctuations for a 2D transectalong the slope, whereas the ultrasonic anemometer tower allows us to investigate time scales. An advantageto the TC array is the circumvention of applying Taylor’s frozen hypothesis, which is thought to fail within67canopies (e.g. Thomas, 2011), to describe the structures.L¨ and T˙ are smallest near the canopy top (Figure 3.18), which is in agreement with the apparent inflectionpoint near the top of the canopy. As is the case in the urban environment, where flow channelling andcanopy-top shear is important, L¨ increases towards the surface from hc, and also increases upwards from hc(Christen et al., 2007). This is a direct effect of the differences in shear intensity as a function of height. L¨seems to scale well with hc, but there is a z−-dependence that is otherwise not present in ’typical’ canopyflows (Finnigan, 2000). The increase of L¨ into the canopy is likely a result of the flow channelling present inthe trellised environment. L¨ scales well with the height of the canopy, and T˙ profiles follow the same trendas those for L¨.Of particular interest is the speed at which the structures move through the flow. While median wind speedsreach a maximum outside of the canopy, the convection velocity (uc) - which is the speed at which thecoherent structures move - reaches a maximum at the canopy top. This follows along the line of thoughtthat smaller eddies will transverse more quickly through the flow. Contrary to reports from other roughnessand canopy sub-layer studies, the ratio of uc to the Eulerian velocity at the height of the canopy (uc) is notexactly 1.8, rather is almost twice that at the top of the canopy (uc 2.85 m s−1). The ratio at the top of themeasurement domain agrees with other studies, but does not agree within the canopy. The speed at whichthe structures move through the flow changes with height in the canopy, more-so than U , which is in contrastto other findings (Finnigan, 2000). The lack of consistency in uc within the canopy could be a consequenceof the stability, drainage layer, and structure of the canopy, all of which influence the turbulence in the flow.4.3.1 Coherent Structure FormThe dual influence of a drainage flow layer and that of the canopy becomes more apparent when investigatingthe shape of the structures in relation to vertical location. Structures within the canopy are inclined at anangle as would be expected (Shaw et al., 1995), while those at the top of the domain do not seem (visually)to be inclined, and are more elongated in the row-parallel direction (Figure 3.21). Determination of specificinclination angles of the structures is outside of the scope of the study, but is worth further investigation inthe future. The elongation along the drainage path is a result of the drainage layer and the lack of roughnesselements acting to break up the larger structures - especially in the centre of the gap. The effect of drainageto elongate the structures in the row-parallel direction is more apparent when comparing the structure shapesand sizes between more obliquely-oriented wind directions (45◦ < WD < 47.5◦ or 132.5◦ < WD < 135◦;Figure 3.23) and row parallel wind directions (88.5◦ < WD < 92.5◦; Figure 3.22). When the wind is angled68obliquely to the vine rows, coherent structures are smaller, and more circular - the correlation with heightand along-slope distance is more similar. Whereas when the wind at the top of the canopy is directed alongthe vine rows, the structures are flatter and more elongated (i.e., x > z), as well as more inclined, especiallynear the centre of the canopy. In consequence, it is likely that under more parallel drainage (i.e., drainagedirected along the rows), the turbulence is more non-local in a horizontal distance sense (turbulence withinthe canopy is still swept in from at canopy top, and therefore non-local in a vertical sense near the surface),and during more oblique drainage (i.e., drainage from mountains to north-east of site), the turbulence withinthe canopy is more locally generated in a horizontal sense. While correlations are only made along the row-parallel transect, is can be easily assumed that the structure sizes, at least within the canopy, along thecross-vine direction, are constrained by the vine gap distance (∼3 m).4.3.2 Structure Scale and Behaviour Dependence on Wind DirectionThe canopy orientation is perhaps one of the more important factors in determining the turbulent nature ofthe flow under drainage conditions. When the wind angle is obliquely oriented in relation to the vineyardcanopy, shear and two-point length scales decrease (Figure 4.2), indicating an increase in turbulent activity.The importance of the incident wind angle on CSL turbulence has been explored by Miller et al. (2017),but only for neutral and unstable cases. Even under the stably stratified situations, the canopy architec-ture is important, and slight deviations from row-parallel flow introduces more turbulence into the canopy.Interestingly, when the wind angle is parallel to the vineyard rows, the median convection velocities withinthe canopy are very similar to the canopy-top velocity (Figure 3.20), meaning that structures moving withinthe canopy may be controlled by the Eulerian velocities at canopy top during these situations. If uc withinthe canopy is determined by the Eulerian wind speed at the location of the core of the generated structures(Bailey and Stoll, 2016), then during these row-parallel cases, it can be expected that unstable mode in theflow is indeed near z/hc = 1.02. Under more oblique cases, uc within the canopy is much larger than theactual velocity within the canopy (Figure 3.20), which is likely reflecting the fact that during the obliquecases, canopy air is sheltered a bit more from the mean flow, thus yielding lower wind velocities within thecanopy (Figure 3.20). During these more oblique wind direction cases, shear is higher, thus the structuresare smaller and move quicker along the canopy gap. As the restrictions placed on the wind direction limitsoblique cases to 25 minutes of data and the parallel cases to only an hour of data, these results need to bechecked against more robust data sets.694.3.3 Similarity to Plane Mixing Layer TheoryAlthough it is mentioned throughout earlier discussion, it is worth summarising the similarities between theobserved flow through the vineyard, and the plane mixing layer. It is well known that canopy velocity profilesmirror those of plane mixing layers, and that this fact is the reason why coherent structures play such alarge role in RSL turbulence (Raupach et al., 1996; Finnigan, 2000). As in the plane mixing layer, velocityprofiles for the drainage flow through the vineyard display mild inflection points near the canopy top. Thiscanopy top region is thus also the location of maximum (observed) stream-wise shear stress. While Sku doesnot entirely follow that of a plane mixing layer (where it would be expected that the skew would be zero atthe interface between the two fluid layers), Skw does follow a trend very similar to that of the plane mixinglayer. While the data presented here is of the first to explore drainage through a vineyard canopy in such away, it is apparent that such flows are a complex combination of the dynamics characteristic of plane mixinglayers and that of cold-air drainage.Perhaps a consequence of this dual canopy mixing-layer and canopy drainage situation is an alteration tothe form of the coherent structures, and the way in which they move through the canopy space. For ahomogeneous canopy, like a wheat field, coherent rollers develop perpendicular to the stream-wise directiondue to Kelvin-Helmholtz instabilities (e.g. Finnigan, 2000; Finnigan et al., 2009). These instabilities arisedue to shear at the canopy top, but in the case of a wheat field, the direction from which the wind aloftoriginates does not affect the generation of these rollers. In the case of the vineyard, ’classical’ rollers atthe canopy top may be inhibited under certain wind directions. For example, due to drainage, structuresare elongated in the stream-wise direction, rather than the cross-stream direction, and are (at least withinthe canopy) restricted in size along the cross-stream axis, due to the inflexible canopy organisation. Whilethere is still an inflection point visible in the Eulerian velocity profile under vine-parallel conditions (Figure3.20(b)), the behaviour of the structures is apparently different from typical CSL structures under neutralconditions, and is worth further investigation with methods that are able to resolve structure size in morethan just one direction (i.e., large eddy simulations) as is the case here.705 Conclusions and OutlookHigh frequency wind and spatially distributed high frequency temperature measurements were made withina vineyard in the interior of British Columbia to assess turbulent exchange under drainage conditions overand within a vineyard canopy on a slope. Drainage was observed for approximately 17.6 hours during thethree-week campaign in July 2016. Typical drainage in the vineyard is associated with a persistent tem-perature inversion starting around the bottom of the vineyard ’crown-space’ (around z/hc = 0.39, wherehc = 2.3 m is the canopy height), and a persistent lapse in the near-surface environment. While the near-surface lapse indicates that the drainage flow is not locally generated, there is still the possibility that theflow is buoyantly fed by cooling of the vineyard canopy. The character of the drainage flow is similar tothat of both the canopy-plane mixing layer and a drainage layer. A weak inflection point is identified in thevelocity profile near the top of the canopy, while a near-surface jet is identified around z/hc = 1.65 usinglinear interpolation between the stream-wise momentum flux at z/hc = 1.02 and z/hc = 2.06. The dualityof the situation influences the transfer of heat and momentum both within and above the canopy.Turbulence is found to be most intense near the top of the canopy, where the the location of the hydrody-namic instability in the velocity profile is located and where higher momentum fluid swept downwards fromthe jet interacts with the row-oriented roughness elements. This interaction between the jet and the canopytop is further influenced by the angle of attack of the stream-wise momentum - when canopy-top wind isdirected at a more oblique angle to the rows, turbulence length scales decrease. The structures created atthe top of the canopy then penetrate into the canopy, increasing the transfer of heat and momentum betweenthe within and above-canopy environments. Turbulent kinetic energy decreases with distance from the topof the canopy as the canopy elements absorb the momentum of the structures generated at the top of thecanopy, but perhaps not to the same extent as in a denser, more homogeneous canopy. This is apparentin the vertical flux profiles within and above the canopy. Unique to drainage cases within vegetation, highmomentum is additionally transported upwards away from the canopy due to the jet, calling into questionthe extent of canopy influence on the above-canopy environment during drainage conditions, in addition toapplication of traditional definitions of the CSL.It is found that while the turbulent exchange of heat and momentum do not follow basic K-theory, pre-cluding the estimation of a turbulent Prandtl number, both heat and momentum appear to be transportedtogether during the larger coherent events responsible for the failure of K-theory. These larger events occurinfrequently, but contribute to most of the transfer of momentum. As is expected for canopy flow, the71transfer of the stream-wise momentum is exuberant, with the most efficient transfer occurring at the canopytop. Sweeps dominate everywhere, but are particularly important at the centre of the canopy, likely due toproximity to the top of the canopy where the coherent structures are generated. Another unique feature ofthe drainage layer is the change in definition of the classical quadrants, necessitating careful considerationof transfer mechanisms during drainage conditions within the canopy.Coherent structure visualisation via 2D temperature correlations indicate that the structures dominating thetransfer of heat are elongated in the stream-wise direction. In particular, the structures are most elongatedunder row-parallel conditions, corresponding with more local drainage, when the flow at the centre of thegaps interacts the least with the vegetated side-walls. During the parallel wind-angle attacks, when drainageis assumed to be more locally feds, horizontal transfer of turbulence is more non-local. During the obliquewind-angle attacks, when drainage is assumed to be more non-locally fed, the structures generated are morevertically coherent, and more circular. During this non-local drainage, the transport of turbulence is morehorizontally local.Current data does not allow for absolute conclusions to be made for over 50% of the time due to inadequateu∗ values (less than the typical threshold of 0.08 m2 s−2). Furthermore, most of the measured and calculatedvalues from ultrasonic anemometer data is within the instrument uncertainty limits. Because the situationsinvestigated here are during expected (and observed) low-flux and weak turbulent activity, this instrumen-tation issue is unavoidable at present. The characterization of the cases as ’low-flux’ situations is madebased on what is observable by the ultrasonic anemometers. It is recognised that the current anemometryis unable to capture the very small scale turbulent wakes produced by the canopy elements, and that withinthe canopy, the conversion from lower frequency turbulence to frequencies outside the detection range of theultrasonic anemometers, deemed spectral short-circuiting, is likely occurring (e.g. Finnigan, 2000; Cava andKatul, 2008), thus further lending to an underestimation of the total flux. To fully resolve the stably strat-ified drainage canopy situation within the vineyard, instruments with the ability to capture much smallerscale fluxes are necessary. We are also at present unable to resolve the origin of the drainage layer.It is worth noting that the quadrant analysis employed here tends to underestimate the contributions dueto ejections. It is well known that sweeps in the canopy tend to be larger, more infrequent events, whereasejections tend to be smaller, more frequent events (e.g. Thomas and Foken, 2007a). Due to the use of thehyperbolic hole method, we are knowingly excluding a number of smaller ejection events. However, as thesefluxes are very small, and do not lend an incredible amount to the total flux, conclusions made on total flux72contributions are not affected. Further, the quadrant analysis does not represent the spatial or temporalscales of the transporting eddies, making it difficult to conclusively link the transport of heat and momentumwith the passing of the coherent structures with the described scales. To do this, a wavelet based conditionalsampling method, like that described in Thomas and Foken (2007a) could be employed.Despite the instrumentation limitations, future work can still be done on the current data set. A thor-ough investigating into the advective heat flux is possible, given the TC array, and would help to resolveunanswered questions about the abnormal near-surface thermal character of the flow. The use of a waveletbased analysis to characterise the turbulent length and time scales would be advantageous - particularly indetermining the validity of the use of integral scales to describe eddy length and time scales. Wavelet basedmethods have been used successfully in other canopy studies as objective event detection methods (Brunetand Irvine, 2000; Salmond et al., 2005; Christen et al., 2007), which would allow for the additional calculationof event frequency and stream-wise eddy separation, and would allow for a more detailed investigation onthe fluxes associated with particular coherent events. Calculation of the spectra would allow for additionalidentification of dominant scales within the flow, but would not be necessary if a wavelet based approachwere to be taken.Knowledge on the mean and turbulent character of drainage conditions within the sloped vineyard envi-ronment is important not only to current efforts to completely understand nighttime surface fluxes, butalso to the furtherance of viticulture. For example, in the present vineyard, heat is advected down-slope,which is of importance to not only the health of the BOV vines, but also to the vineyards at the bottom ofthe slope within the Okanagan Valley which may depend on the advected energy to prevent frost damage.Furthermore, in the case of heat advection, there is the possibility that energy is wasted while running theinversion-preventing wind mill devices found in the Okanagan.73ReferencesAmanatidis, G., Papadopoulos, K., Bartzis, J. and Helmis, C. (1992), ‘Evidence of katabatic flows deducedfrom a 84 m meteorological tower in Athens, Greece’, Boundary-Layer Meteor. 58, 117–132.Antonia, R. A. (1981), ‘Conditional sampling in turbulence measurement’, Annu. Rev. Fluid Mech. 13, 131–156.Aubinet, M. (2008), ‘Eddy covariance co2 flux measurements in nocturnal conditions: An analysis of theproblem’, Ecological Appl. 18(6), 1368–1378.Aubinet, M., Heinesch, B. and Yernaux, M. 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P.(2005), ‘Modeling and measuring the nocturnal drainage flow in a high-elevation, subalpine forest withcomplex terrain’, J. Geophys. Res. 110.Zardi, D. and Whiteman, C. D. (2013), Mountain Weather Research and Forecasting: Recent Progress andCurrent Challenges, Springer Netherlands, Dordrecht, chapter Diurnal Mountain Wind Systems, pp. 35–119.80AppendicesAppendix A: CSAT-3D Rotation Sensitivity and Error AnalysisChoice of slope rotation was partially informed by the slope measurement in the field, and the inclinationangle of the streamlines at a 90◦ wind direction at all of the heights (Figure A1). It is expected that airwill flow most parallel to the local terrain slope at the lowest point of measurement and at the top of thevegetation, where the vineyard rows mimic the sloping ground. Inclined wind angles at these locations(z/hc = 0.19 and z/hc = 1.02) agree well with the measured slope angle, and thus a value of 7◦ is used asthe final rotation angle for the second rotation into the plane (see Section 2.4.1).Figure A1: Inclination angles with varying wind direction with height.81The mean absolute error (MAE) in the case study fluxes associated with an error of ±1◦ in the slopeangle rotation are are given by Table A1. MAE is calculated using Equation 5.MAE =1nn∑n=1|yi − xi| (A1)where yi is the predicted value - or that when a slope angle of 7◦ is used in the rotation, and xi is theobserved - or that when either a slope angle of 6◦ or 8◦ is used, and n is the number of samples. In this way,the MAE is representing the potential amount of flux that is incorrect in our reported values.z/h uw vw wT2.06 0.0013 0.0008 0.00171.02 0.0008 0.0004 0.00110.647 0.0004 0.0002 0.00050.391 0.0003 0.0001 0.00030.195 0.0002 0.0001 0.0003Table A1: Mean absolute error (MAE) for vertical momentum and heat fluxes associated with ±1◦ slopeangle measurement errors. MAE is calculated from 211 5-minute case study time series.z/h 6◦ 8◦uw vw uv uw vw uv2.06 0.42 % 0.06 % 0 % 0.4 % 0.04 % 0 %1.02 0.12 0.76 0 0.12 0.75 00.647 0.34 0.08 0 0.33 0.07 00.391 0.58 0.11 0 0.58 0.1 00.195 0.88 0.36 0 0.84 0.32 0Table A2: Percent contribution of fluxes (potentially) affected by over or under rotation (6◦ or 8◦, respec-tively) to the total calculated flux.The change in magnitude and the fact that there are incidences of a change in sign of the momentum fluxesbased upon a difference of 1◦ in the measured slope angle affects the quadrant, and associated, analyses.Given, however, that when the slope angle uncertainty implicates a change in the sign of the momentumfluxes, the flux itself is very small (on the order of at most 0.5% of the mean flux), the use of a hyperbolichole in all quadrant and associated analyses for momentum circumvents the issue of potential uncertainty in-duced momentum flux sign changes. As small fluxes will already be minimally represented in statistical firstmoments, such as the mean, they are not excluded. Figure A2 provides an analysis on where the majority ofthe instantaneous flux associated with a potential change in sign with slope angle uncertainty is contained.The figure shows that for increasing hole size, the amount of flux contributed by the potentially erroneous82flux decreases. It is of note that the y-axis gives the number of instances that the flux exceeds the hole size,and therefore, H = 0 in the plot provides the total number of potentially erroneous flux instances. Evidently,the use of a hole size, H = 3 for the vertical stresses and a hole size of H = 1 for the horizontal stressessufficiently avoids the potential changes in sign being associated with the octant and quadrant analyses formomentum.For the u′w′, the hole size is larger at z/hc = 0.64 because the mean flux at this location is very small; thesame issue occurs at z/hc = 1.02 for the v′w′ flux. Despite this, the reported hole size of 3 for the verticalfluxes is still used - even at this hole size, a large amount of the possible flux error is avoided.Figure A2: Density plot of contribution of flux associated with a sign change to the total flux. solid linesrepresents the contribution associated with an over rotation, and dashed lines represent the contributionassociated with an under rotation. When the lines reach zero, there is no longer any contribution of the fluxto the mean.On average, correlations in any octant at or larger than H = 3 occur around 50% of the time, while thosefor H = 1 occur around 70% of the time (Table A3)83Hole Size z/hc0.19 0.39 0.65 1.02 2.063 55.5% 56.1% 51.9% 27.4% 43.3%1 77.3% 77.7% 75.0% 55.3% 69.2%Table A3: Percentage of time that the flux is above the threshold hole size of 3 or 184Appendix B: Thermocouple Corrections - Sample CalculationFigure A3: Sketch of problem set-up and variables used in example calculation of the temperature correctionsfor Mast F.First, the background stratification is calculated using the average 5-minute temperature at z = 4.73 m forMasts A (at tower) and H (32 m up-slope):Γref =TH5 − TA5∆zH(A2)Next, the correction to be applied to the averages of the TC on Mast F (8 m up-slope) is calculated:TF,correct = TF5 − (TA5 − Γref ∗ 8 ∗ sin(α)) (A3)The corrected mean temperature at the top of the Mast F array is only a function of the 5-minute calculatedbackground stratification and the vertical distance, ∆zFTF5,new = TA5 − Γref ∗ 8 ∗ sin(α) (A4)While the mean temperatures are the other 4 locations below the top TC are calculated by removing thecorrection, TF,correct from their respective time series:TFj,new = TF4 − TF,correct (A5)where j here represents indices 1− 4 (TC measurements at heights 0.45, 0.9, 1.49, and 2.34 m, respective).85

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