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Turbulent transfer and radiation distribution within and above a straw mulch Chen, Wenjun 1997

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TURBULENT TRANSFER AND RADIATION DISTRIBUTION WITHIN AND ABOVE A STRAW MULCH by Wenjun Chen B. Sc. (Meteorology), Nanjing Institute of Meteorology, China, 1983 M.Sc. (Agrometeorology), Nanjing Institute of Meteorology, China, 1988 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF SOIL SCIENCE We accept this thesis as conforming to the required.standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1996 ©Wenjun Chen, 1996 Authorization In presenting this thesis in partial fulfillment of the requirement for an advanced degree at the University of British Columbia, I agree that the library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his/her representatives. It is understood that the copying or publication of this thesis for financial gain shall not be allowed without my written permission. Wenjun Chen Department of Soil Science The University of British Columbia i i ABSTRACT Mulching can be both beneficial, promoting soil and water conservation, and detrimental, slowing soil warming in spring and delaying seed germination. However, the processes which govern the exchanges of energy and mass within the soil-mulch-atmosphere system are not well understood. While researchers have successfully measured and modeled the exchange processes within the soil and atmosphere, progress within mulch canopies has been limited by technical difficulties in measuring turbulence and radiative fluxes with current micrometeorological techniques, such as eddy correlation. In searching for alternatives, we developed and tested an improved tension-plate system for measuring first-stage evaporation or condensation rates under a mulch to an accuracy of 5 W m"2 (Chapter 2), a renewal model which calculates sensible heat flux within and above canopies from the statistics of measured temperature fluctuations and the friction velocity (Chapter 3 and 4), and a radiation distribution model that determines short and long-wave radiation components at all levels (Chapter 5). Chapter 6 and 7 report turbulence statistics, turbulent fluxes of sensible and latent heat, and energy balance within 2, 5, 10, and 15 t ha"1 straw mulches. The renewal model is calibrated and tested with data measured above and within a Douglas-fir forest, and above a straw mulch and bare soil. We show that the renewal model describes half-hour variations of sensible heat flux very well both within and above the canopy for stable and unstable atmospheric conditions. The radiation model, which uses a measured clumping index and temperature differences between upper and lower Ill surface of the mulch elements, agrees well with measurements for net radiation at the top of and total downwelling radiation beneath 2, 5, 10, and 15 t ha'1 mulches. The air flow measured within mulch canopies was highly turbulent, with its longitudinal turbulence intensity varying from 0.64 to 0.91. At an occurrence frequency of about 1 Hz (determined from analyzing air temperature and wind speed time series), large-scale coherent eddies dominated the canopy flow. The dominance of these coherent eddy structures was also evidenced by the large values of skewness and kurtosis of the velocity components. The strong day-time thermal stratification within the mulch had no effect on the canopy flow, but under nocturnal low-wind conditions the thermal instability may have caused the observed nearly steady within-canopy convective air flow. Evaporation from non-wetted mulch elements was relatively small except during early morning hours when the elements were wet from dew fall and soil evaporation at night. At night, soil water evaporation under the mulch remained considerable and nearly constant. It decreased to near or below zero in the early morning, and increased to a peak in the afternoon. Condensation was observed throughout the daytime under a mulch wetted completely by sprinkle irrigation. In the daytime, the net radiation flux attenuated quickly through the top of the mulch canopy, and then decreased slowly with the height in the middle and bottom layers of the mulch. The strong clumping of elements in the middle and lower layers resulted in a relatively large fraction of net radiation arriving at the soil surface. A similar pattern was observed for sensible heat flux using the renewal model, i.e., its main source strength was near the mulch top. Counter-gradient sensible heat flux was measured during daytime at iv the middle of the canopy, while air temperature reached a maximum at about 2/3 of the mulch canopy height. Energy budget closure was reasonably good at all heights within and above the mulch. Turbulence enhanced the water vapour conductance within straw mulches by typically 2 to 7 times the molecular value for wind speeds in the range 0.5-3 m s"1, computed from the measured soil evaporation rate and the vapour pressure profile when the water content of the mulch canopy was steady. V Table of contents page Abstract ii Table of contents v List of tables x List of figures xiii List of symbols xxviii Acknowledgements xxxvi Chapter 1. Introduction 1 Chapter 2. An improved tension-plate system for measuring first-stage evaporation under straw mulch 3 2.1. Introduction 3 2.2. Development of the improved tension-plate system 5 2.2.1. Mass-flow analysis of the Arkin et al. (1974) system -normal operation 5 2.2.2. Mass-flow analysis of the Arkin et al. (1974) system -ma constant 11 2.2.3. Improved tension-plate system 16 2.2.4. Measurement errors in the improved tension-plate system 19 2.3. Field tests 21 2.3.1. Bare soil 21 2.3.2. Non-wetted straw mulch 25 2.3.3. Artificially wetted straw mulch 30 2.4. Evaporation under and above a non-wetted mulch 33 2.5. Summary and C oncluding Remarks 35 2.6. References 37 Chapter 3. Coherent eddies and temperature structures functions for three contrasting surfaces. Part I: Ramp model with finite microfront time 39 3.1. Introduction 39 3.2. VA theory and temperature ramp model 40 3.3. Ramp model with finite microfront time 46 3.4. Comparison with ramp detection by wavelet transform 56 3.5. Summary and concluding remarks 66 3.6. References 68 Chapter 4. Coherent eddies and temperature structure functions for three contrasting surfaces. Part II: Renewal model for sensible heat flux 71 4.1. Introduction 71 4.2. Model derivation 73 4.3. Field experiments 76 4.3.1. Douglas-fir forest 76 4.3.2 Straw mulch and bare soil 79 4.4. Model calibration 84 4.4.1. Determination of (3. 84 4.4.2. Determination of a. 86 4.4.3. Combined coefficient apmy. 90 4.5. Model tests 90 4.6. Sensible heat flux profiles within the mulch and a bare opening in the mulch 95 4.7. Summary and concluding remarks 99 4.8 References 100 Chapter 5. Simulating radiation distribution within a straw mulch 105 5.1. Introduction 105 5.2. Materials and methods 107 5.2.1. Clumping index 107 5.2.2. Mulch radiation model 113 5.2.3. Experiment 118 5.3. Results and discussions 121 5.3.1. Comparison with field measurements 121 5.3.2. Model sensitivity analysis 127 5.3.3. Model application examples 129 5.4. Conclusions 133 5.5. References 134 Chapter 6. Turbulent exchange processes within and above a straw mulch. Part I: Statistics of the flow field 137 viii 6.1. Introduction 137 6.2. Methods 139 6.2.1. Experimental site and mulch properties 139 6.2.2. Measurement of mean horizontal "cup" wind speed 140 6.2.3. Measurement of high-frequency wind components 141 6.2.4. Determination of turbulence statistics 142 6.3. Results 144 6.3.1. Diurnal patterns of mean horizontal cup wind speed 144 6.3.1.1. Daytime high-wind conditions 147 6.3.1.2. Nocturnal low-wind conditions 150 6.3.2. Vertical profile of mean horizontal cup wind speed 154 6.3.3. Turbulence statistics 157 6.3.3.1. Friction velocity and higher-order moments 157 6.3.3.2. Frequency distributions of wind speeds 160 6.4. Conclusions and discussions 164 6.5. References 166 Chapter 7. Turbulent exchange processes within and above a straw mulch. Part II: Sensible and latent heat flux densities 171 7.1. Introduction 171 7.2. Methods 172 7.2.1. Calculation of sensible heat flux densities 172 7.2.2. Measurement of latent heat flux densities 173 7.2.3. Determination of other energy components 174 7.3. Results 176 7.3.1. Profiles of sensible heat flux and temperatures for a non-wetted mulch 176 7.3.2. Profiles of latent heat flux and water vapour pressure for a non-wetted mulch 184 7.3.3. Turbulent diffusivity and conductance for water vapour.. 188 7.3.4. Energy budget closure for a non-wetted mulch 192 7.3.5. Turbulent fluxes and energy balance for a wetted mulch 196 7.4. Conclusions 203 7.5. References 206 Chapter 8. Conclusion remarks 209 Appendix. Mulch Characteristics 213 X List of tables page 3.1. Ratios ofM, % and Mix determined with VA's linearized cubic structure function theory to those determined using the ramp model with finite microfront time above the Douglas-fir forest, straw mulch, and bare soil. Five extreme outliers for tcalculated with VA's method were not included in the averages because they were 1-2 orders of magnitude larger than the rest and would have distorted the ratios 55 3.2. Comparison between tf, M, and T determined from the ramp model with finite microfront time for the indicated time periods and Tf measured directly on 10 well-defined ramps in each time period. Normalized T{ is calculated by multiplying tt from the 10 ramps by the ratio of M from the finite microfront model to M from the 10 ramps 66 4.1. Air renewal model calibration (J3 and a) and testing statistics for the Douglas-fir forest, straw mulch, and bare soil. All linear regressions were forced through zero. The n indicates the number of measurement periods (half-hour except for /? for the mulch and bare surfaces, which were 10 min) 78 4.2. Average coefficients a, /?, and y (from Chapter 3) and the combined coefficient aR2ny for the Douglas-fir forest, straw mulch, and bare soil 86 xi 5.1. Transmittances (to, uncorrected; TCI, corrected for the influence of underlying acrylic film and the frame; % further corrected for the mulch layer back-reflection of the ground reflection) of a fresh straw mulch at various application rates. Also included is the clumping index calculated from Eq. (5.2) 110 5.2. Mulch composition (barley straw or a mixture of barley, alfalfa, and weeds), canopy height (/?), average diameter of the mulch element (de\), reflectance of the mulch element (rei) and soil (rs) for various application rates in the 1993 experimental season 116 5.3. Linear regression (intercept = 0) statistics describing the agreement between measured and simulated net radiation fluxes (R„) at top of, and global downward radiation fluxes (Sf+L1) at z = 0.6 cm within a mulch of application rates 2, 5, 10, and 15 t ha"1 124 5.4. Fractional sensitivity ofRn to variables So, 7u-7tl, e^, parameters r d , rg, and Q as defined in Eq. (5.22) 128 6.1. Mean cup wind speeds, s, at z = 9.6 cm measured with a triple hot-film constant-temperature anemometer (CTA) and a hot-wire anemometer (HW), and surface friction velocities, w*, at z = 7.6 and 9.6 cm above a 10 t ha"1 straw mulch measured using the CTA comparing those calculated from vertical wind profiles measured with HW's 156 6.2. Average values of wind speed (J), turbulent intensity (/s, zw), skewness (Sks), and kurtosis (Krs) at heights within and above a 10 t ha"1 straw mulch during indicated time periods Mean duration of an event, T, (i.e., from the beginning of a gust to the beginning of the next gust) for different threshold speeds at heights within and above a 10 t ha"1 mulch canopy during indicated time periods. Also listed is the mean duration of a gust (T g) Daylight mean net irradiance (Rn), latent and sensible heat flux densities (LE and H), and heat storage in mulch and soil layers («SH) as well as the ratio (Go+Sn+LE+H)/Rn for a non-wetted mulch (August 20, 1994) and a wetted 10 t ha'1 mulch (August 29-September 1, 1994) at various heights. The values of Rn and (G0+Stf+LE+H)/Rn for the wetted mulch were calculated at first by using R of fresh straw, and then corrected by increasing R by 75% and assuming linear distribution with no increase at the canopy top (values in bracket) xiii page 2.1. Schematic diagram of the Arkin et al. (1974) tension-plate system (upper right) and our modification to it (lower left) 5 2.2. Detailed diagram of the Arkin et al. (1974) tension-plate system showing symbols used in the mass-flow analysis 6 2.3. A sample time trace of (negative) gauge pressure of the air in the water column measured on September 30, 1992, at a sampling rate of 1 Hz by the pressure transducer from (a) 11:00-11:20 PST and (b) a one minute subsample, showing variations associated with air bubble entry 7 2.4. Rate of change of water column air mass calculated with the mass-flow analysis of the Arkin et al. (1974) tension-plate system for August 25, 1994, using the measured data in Fig. 2.5 10 2.5. Latent heat flux density under a 10 t ha"1 straw mulch (a) and water column air temperature (b) measured using the improved tension-plate system on August 25, 1994. The break in LE(t) occurred when manually refilling the water column 11 2.6. Water storage rate for one of our two tension plates as a function of water tension at the plate surface, including fitted empirical function (a) and measured steady-state flow rate to this plate as a function of height difference between plate surface and air inlet in the water column, xiv including fitted straight line (b) 13 2.7. Apparent values of latent heat flux density calculated with Eq. (2.10) (from the pressure transducer) and Eq. (2.19) (from height of water) in the mass-flow analysis of the Arkin et al. (1974) tension-plate system compared with measurements using the improved tension-plate system for August 25, 1994 15 2.8. Cumulative evaporation measured by Arkin et al. (1974) using tension plates in a bare soil and under 1, 4, and 10 t ha"1 straw mulches on August 17, 1973. Incoming solar is expressed as equivalent cumulative evaporation 16 2.9. Rate of change of water column air mass calculated with the mass-flow analysis of the Arkin et al. (1974) tension-plate system modified to include a parallel flow line for August 25, 1994. Measured data in Fig. 2.5 were used with PAt) = 100 kPa and LEs(t) = 102 W m'2 Also shown is the critical value of dmjdt 17 2.10. Latent heat flux density measured with two improved tension-plate systems and four micro-lysimeters in a bare soil on July 20, 1994. The breaks in tension-plate data occurred when manually refilling the water columns 22 2.11. Latent heat flux density measured with an improved tension-plate system and the Bowen ratio/energy balance method (a) and vapour pressure gradient between 1 and 5 cm heights measured with capacitance-type humidity sensors (b) for a bare soil on October 16-18, 1993. The breaks in tension-plate data occurred when manually refilling the water column 2.12. Latent heat flux density measured with an improved tension-plate system and four micro-lysimeters under a non-wetted 10 t ha*1 straw mulch on September 17, 1992. The break in tension-plate data occurred when manually refilling the water column 2.13. Comparison between daytime (7:00-17:00 PST; unfilled symbols) and nighttime ( 17:00-7:00 PST; filled symbols) average latent heat flux density under non-wetted 2, 5, and 10 t ha"1 straw mulches measured with an improved tension-plate system and with micro-lysimeters (average of four replicates). Measurement dates were September 20-22, 1992 (2 t ha"1 mulch), September 12-15, 1992 (5 t ha"1 mulch), and September 16-18, 1992, and August 29-September 1, 1994 (101 ha"1 mulch) 2.14. Latent heat flux density measured with an improved tension-plate system under a non-wetted 10 t ha"1 straw mulch and vapour pressure gradient between 0 and 1.5 cm heights within the mulch measured as described in the text on August 25, 1994. The break in LE(t) occurred when manually refilling the water column 2.15. Latent heat flux density measured with an improved tension-plate system and two micro-lysimeters under an artificially wetted 10 t ha"1 straw mulch from August 29-September 1, 1994. Unfilled symbols are daytime values and filled symbols are nighttime values. The breaks in tension-plate data XVI occurred when manually refilling the water column 32 2.16. Latent heat flux density measured with an improved tension-plate system under an artificially wetted 10 t ha"1 straw mulch and vapour pressure gradient between 0 and 1.5 cm heights within the mulch measured as described in the text from August 29-September 1, 1994. The breaks in LE(t) occurred when manually refilling the water column 33 2.17. Latent heat flux density measured with improved tension-plate systems in a bare soil and under a non-wetted 10 t ha"1 straw mulch on August 29, 1993. Also shown is LE(t) above the mulch calculated from mulch weight loss as described in the text. The breaks in LE(f) occurred when manually refilling the water columns 34 3.1. Temperature ramp model of VA showing definitions ofM, ts, tr, and rand 7C(0 and A7'c(/), for 0 < At < ts 4 2 3.2. Typical plots of measured -(ATf versus At for above the Douglas-fir forest, straw mulch, and bare soil. Also shown is the VA linearized ramp model (dashed lines with unit slope) and his full model (solid lines) calculated as described in the text 4 4 3.3. Typical plots of measured -(AT)31 At versus At for above the Douglas-fir forest, straw mulch, and bare soil (same data as in Fig. 3.2). Also shown is the VA linearized ramp model (dashed horizontal lines) and his full model (solid lines) calculated as described in the text ^ 3.4. Temperature ramp model with finite microfront time showing the definition of tf and rc(0 and ATc(t) for 0 < At < tf, tt<At< r-tf, and t-t{<At<t. 5. Schematic diagram of the vertical cross-section of air temperature and wind vectors at one height for a single ramp structure during daytime. Contour lines are temperature and arrows are typical wind vectors near the top of the canopy. The tilted narrow region with dense contours is the microfront (after Gao et al., 1989) 6. Typical air temperature ramp structures for above the Douglas-fir forest, straw mulch, and bare soil from the data sets in Fig. 3.2 (after subtraction of average temperature, T). The time interval between successive data points is 0.101 s for the forest and 0.0125 s for the mulch and bare surfaces 7. Typical plots of measured -(AT)31 At versus At for above the Douglas-fir forest, straw mulch, and bare soil (same data as in Fig. 3.3). Also shown is the fitted ramp model with finite microfront time (solid lines) and the fiill VA ramp model with the sameMand rand 4 = 0.25T(dashed lines) 8. Typical plots of normalized measured -(AT)31 At versus normalized At for above the Douglas-fir forest, straw mulch, and bare soil (same data as in Fig. 3.7). The ocean data of VA is included (z = 3.81 m). Also shown is the fitted normalized ramp model with finite microfront time (various lines) 9. Correction factor /= (MliB)l[-(Kff I At]m at At = Atm versus Atjzfor above the Douglas-fir forest (z = 23 m, calibration days only, see Chapter xviii 4), straw mulch (z = 9.6 cm), and bare soil (z = 3 cm) 55 3.10. Determination of optimum a - am at the maximum of MHAT W(a), illustrated for the straw mulch 57 3.11. Typical segments of air temperature time series (after subtraction of T) and MHAT F(am,b) from the data sets in Fig. 3.2 for above the Douglas-fir forest, straw mulch, and bare soil. Every zero-crossing with a negative slope for F(am,b) signifies a ramp event 58 3.12. Probability distributions of t determined with the MHAT wavelet transform above the Douglas-fir forest, straw mulch, and bare soil. Average rfor each surface is also indicated 59 3.13. Plot of 1/T determined with the MHAT wavelet transform versus uh/h above the Douglas-fir forest and straw mulch. The solid line is the prediction of linear stability theory according to Raupach et al. (1989) 61 3.14. Comparison between average T determined with the MHAT wavelet transform within and above the Douglas-fir forest The measurements within and above were made simultaneously. The range in which values differ by less than a factor of 2 is indicated 62 3.15. Comparison between average T determined with the MHAT wavelet transform and T determined by fitting the ramp model with finite microfront time to the 3rd-order temperature structure function for above the Douglas-fir forest, straw mulch, and bare soil. The range in which xix values differ by less than a factor of 2 is indicated 63 3.16. Same as Fig. 3.15 but for within the Douglas-fir forest. The data point surrounded by a square for z = 7 m is considered in Fig. 3.17 64 3.17. Variation of measured -(AT7)3 / At with At within the Douglas-fir forest for a time period for which ramp model and MHAT r are in poor agreement (Fig. 3.16). Also shown is the fitted ramp model with finite microfront time 65 4.1. Calibration of /J according to modified Eqs. (4.3) as described in the text for the Douglas-fir forest, straw mulch, and bare soil. Also shown are fitted straight lines 85 4.2. Calculated a (calibration) versus zlh (Douglas-fir forest and straw mulch) or versus z (bare soil). Vertical lines are the average values for each surface 87 4.3. Measured (symbols) and modelled (lines) half-hour H versus t for the Douglas-fir forest on the calibration days. Model uses average a in Fig. 4.2. Also shown is measured Rn-Go (filled triangles) 88 4.4. Measured (open circles) and modelled (lines) half-hour H versus t for the straw mulch and bare soil on the calibration days. Model uses average values of a shown in Fig. 4.2. Also shown is measured R„-G0 (filled triangles) 89 4.5. Difference of 0between z = 7 m and indicated height above it versus M at 7 XX m calculated by fitting the ramp model with finite microfront time to the cubic temperature structure function for the Douglas-fir forest on July 27 and 28, 1990. Only data such that TWm > r7m > TA.6m and H > 0 are shown 91 4.6. Measured (symbols) and modelled (lines) half-hour H versus t for the Douglas-fir forest on the test days (one day not shown). Model uses average afi2,3y in Table II for the forest. Also shown is measured R„-Go (filled triangles) 92 4.7. Measured (symbols) and modelled (lines) half-hour H versus t for the straw mulch on four successive test days (11:00, August 29 to 18:00, September, 1, 1994) following overnight sprinkler irrigation of the mulch. Model uses average a/3my in Table 4.2 for the straw mulch. Also shown is measured Ra-G0 (filled triangles) 93 4.8. Same as Fig. 4.7 but for the bare soil 94 4.9. Daytime vertical profiles of predicted air renewal (dashed line), molecular diffusion (dotted line), and total (solid line) H within the straw mulch as described in the text. Also shown is the concurrent vertical profile of measured T. 96 4.10. Same as Fig. 4.9 but for nighttime 97 4.11. Same as Fig. 4.9 but for the centre of an 18 cm diameter circular bare opening in the straw mulch. The corresponding measured (energy balance method) H above the surrounding mulch was 280 W m"2 98 xxi 5.1. Clumping index, i2, as a function of residue area index, R, for a horizontal straw mulch 5.2. Solar radiation transmittance, % as a function of residue area index, R. Lines are calculated from Eq. (5.2) using different Q values: Q = 1 (random distribution) and i2from Eq. (5.9) (i.e., measured) 113 5.3. Schematic representing fluxes of radiation in a soil-mulch-atmosphere system. The net radiation flux at rth layer, R^i, then is defined as S*-S» + l}-/« 114 5.4. Difference between lower- (or upper-) surface temperature and air temperature, -Ta (or T* - Ta), plotted against the net radiation flux (Rn) at top of a 10 t ha1 straw mulch. Td - 7/a (or r - TJ was measured during 0:00, August 18 to 24:00, August 22, 1994 (or 8:00, August, 28 to 24:00, August 31, 1993) 121 5.5. Diurnal variation of hourly net radiation flux, Rn, at the top of a mulch. Lines are calculation and symbols are measurement 122 5.6. Comparison of measured and calculated hourly net radiation flux, Rn, at the top of a mulch. Statistics for the figure are listed in Table 5.3 124 5.7. Diurnal variation of hourly global downward radiation flux, Sf+lJ, at z = 0.6 cm within a mulch. Lines are calculation and symbols are measurement. Note the difference in scale 125 5.8. Comparison of measured and calculated hourly global downward radiation flux, Si+L\ atz = 0.6 cm within a mulch (see statistics in Table 5.3) 126 5.9. An example of simulated downward short- and long-wave (S* and L\ upward short- and long-wave (S1 and Lu), and net radiation flux (Rn = F*-F^+L^-U) within a 10 t ha"1 straw mulch during 12:00-13:00 PST, August 29, 1993 130 5.10. An example of simulated downward long-wave (Z,d), upward long-wave (Z,u), and net radiation flux (R„ = Ld - Lu) within a 10 t ha"1 straw mulch during 0:00-1:00 PST, August 29, 1993 131 5.11. Variations of net short-wave radiation flux (S* -S°) profiles corresponding to different clumping degrees of mulch elements within a 10 t ha"1 straw mulch during 12:00-13:00 PST, August 29, 1993 132 6.1. 10-min mean horizontal cup wind speed, s, measured using cup anemometers at z = 24 and 57 cm, and using hot-wire anemometers at four other heights within and above a 10 t ha"1 mulch from August 23-25, 1994. 144 6.2. Wind speeds at various heights plotted against those at z = 57 cm for the same data set as Fig. 6.1. The numbers in bracket are r2 from linear regression between J values at the indicated height and at 57 cm 146 6.3. The ratio of wind speed within-canopy (z = 1.1 or 3.3 cm) to above-canopy (z = 9.6 cm) plotted against wind speed at z = 57 cm for the same data as in Fig. 6.1. The value s51 = 0.6 or = 1.1 cm s"1 is chosen as an approximate criterion to categorize low and high-wind speed conditions 147 6.4. The ratio of wind speed within-canopy (z = 1.1 or 3.3 cm) to above-canopy (z = 9.6 cm) versus air temperature gradient between z = 1.1 and 4.4 cm. xxiii Data sets are the same as in Fig. 6.1 except for cases where ATJAz between 1.1 and 4.4 cm > 0 148 6.5. Depth of penetration (/p = c 7 W 0 U t / A7", where N is the Brunt-Vaisala frequency) into a 10 t ha"1 mulch canopy for the fractional data in Fig. 6.1 when ATJAz between 1.1 and 4.4 cm > 0. Five / p > 30 cm points are excluded in this figure 150 6.6. 10-min mean horizontal cup wind speeds at 1.1 or 3.3 cm versus (a) at 57 and, and (b) at 6.6 cm (mulch top). Data sets are the same as in Fig. 6.1 except for low-wind conditions (s57cm < 60 cm s"1). Numbers in brackets are regression coefficients r 2 151 6.7. The Rayleigh number, Ra, in a 10 t ha"1 mulch canopy for the fractional data in Figure 1 that meets the nocturnal low-wind-speed criterion (i.e., y 5 7 c m < 60 cm s'1 and 19:00-7:00 PST). Also included is the critical Ra number (Rac =1706) 152 6.8. The ratio of wind speed within-canopy (z = 1.1 or 3.3 cm) to above-canopy (z = 9.6 cm) versus the within-canopy Richardson number Rii„ for the same data as Fig. 6.1. Triangles are for daytime and circles for nighttime 154 6.9. Vertical profile of mean horizontal cup wind speed, s, normalized by surface friction velocity, within and above a 10 t ha"1 straw mulch. Measured wind speeds are average values for all available data (see the detailed description in the text) 155 xxiv 6.10. Variation of aju^ (circles) and (Jju* (squares) with normalized height z/h. The lines are given by equations (6.10.a) and (6.10.b) 158 6.11. An example of a longitudinal velocity component (w) time series at z = 1.1 cm within a 10 t ha"1 straw mulch, measured using the triple hot-film constant-temperature anemometer (CTA) 161 6.12. Fraction of time occupied by gusts (s exceeds s by various amounts) at different heights within and above a 10 t ha"1 straw mulch. The line is a prediction based on the Gumbel extreme distribution (Eq. 6.3) 162 7.1. Measured vertical profiles of sensible heat flux density (H) and its two components due to molecular diffusion (Hm) or air renewal by coherent structures (Hc), and measured air temperature within and above a non-wetted 10 t ha"1 straw mulch from 11:30-12:00 PST, August 23, 1994 177 7.2. Diurnal variation of measured 30-min sensible heat flux density (H) at various heights within and above a non-wetted 10 t ha"1 straw mulch on August 20, 1994 179 .7.3. Diurnal variation of (a) measured sensible heat flux density (H) as well as its two components due to molecular diffusion (Hm) or air renewal by coherent structures (HT) at z = 3.3 cm, and (b) air temperature at z = 2.2, 3.3, and 4.4 cm within a non-wetted 10 t ha"1 straw mulch on August 20, 1994. Counter-gradient H occurred from 9:00-14:00 PST 180 7.4. Vertical profiles of measured air and soil temperatures above, within, and below a non-wetted 10 t ha"1 straw mulch at various times on August 20, X X V 1994 181 7.5. Measured and calculated (Eq. 7.3) temperature differences between the mulch element upper-surface (Tu) and air (Ta) at the top of a non-wetted 10 t ha"1 straw mulch (z = 6.6 cm) for four consecutive days (7:30, August 28 to 24:00, August 31, 1993) 182 7.6. Diurnal pattern of measured mulch element upper-surface temperatures, Tu, within a non-wetted 10 t ha"1 straw mulch on August 30, 1993. For clarity, Tu values at z = 2.2 and 3.3 cm (which conveniently fall between those of underlying and overlying levels) were omitted in this figure 184 7.7. Vertical profiles of measured latent heat flux density (LE) and water vapour pressure (e) within and above a non-wetted 10 t ha"1 straw mulch from 11:30-12:00 PST, August 23, 1994 185 7.8. Diurnal variation of measured latent heat flux density (LE) and water vapour pressure (e) at heights within a non-wetted 10 t ha"1 straw mulch on August 20, 1994. For clarity, LE values at z = 2.2, 4.4 and 5.5 cm (which lie between those of underlying and overlying levels) were omitted in this figure 187 7.9: Measured water content (dry-weight basis, <9ml) of a 1.1 cm straw mulch layer at various heights within a non-wetted 10 t ha"1 straw mulch, averaged over four days (see text for details). For clarity, 0ml values at z = 1.1-2.2, and 3.3-4.4 cm (which fall between those of underlying and overlying levels) were omitted in this figure jgg XXVI 7.10. Vertical profile of turbulent diffusivity for water vapour within and above a 10 t ha"1 straw mulch from 16:00-16:30 PST, August 20, 1994. During this period, the mulch water content decreased to < 1% and the mulch contributed to the total evaporation by < 10% 190 7.11. Ratios of mulch conductance to conductance in still air for water vapour through a 10 t ha-1 straw mulch, plotted against wind speed at z = 57 cm for all available 52 half-hour periods during August 28-September 1, 1993, and August 10-25, 1994. In each of these half hour periods, the mulch water content changed by < 1% and the mulch contributed to the total evaporation by < 10% 191 7.12. Profiles of net irradiance (R„ measured above canopy and simulated within canopy) as well as combinations of sensible heat flux (H), latent heat flux (LE), soil heat flux Go, and heat storage in mulch elements (Su) within and above the non-wetted 10 t ha"1 straw mulch from 11:30-12:00 PST, August 23, 1994 193 7.13. Comparison between net irradiance RN (lines) and GO+SE+LE+H (symbols) at z = 0, 1.1, 3.3, and 6.6 cm for a non-wetted 10 t ha"1 straw mulch on August 20, 1994. Note the difference in scale. 194 7.14. Measured water content (6mX) of a 1.1-cm layer at various heights within a wetted 10 t ha"1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The mulch was wetted completely by sprinkle irrigation during the night of August 28. For clarity, 8ml values at z = 1.1-2.2, and 3.3-4.4 xxvii cm (which lie between those of underlying and overlying levels) were omitted in this figure. 197 7.15. Measured latent heat flux density (LE) and water vapour pressure (e) within and above a wetted 10 t ha"1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The first four hourly LE values lie beyond the figure scale which has a maximum reaching 230 W m"2. The mulch was wetted completely by sprinkle irrigation throughout the night of August 28. For clarity, LE values at z = 2.2, 4.4, and 5.5 cm (which lie between those of underlying and overlying levels) were omitted in this figure 198 7.16. Measured sensible heat flux density (H) and air temperature (TA) within and above a wetted 10 t ha"1 straw mulch 11:00, August 29 to 18:00, September 1, 1994. The mulch was wetted completely by sprinkle irrigation throughout the night of August 28 200 7.17. Comparison between net irradiance RN (lines) and GO+SH+LE+H (symbols) at z = 0, 1.1, 3.3, and 6.6 cm for a wetted 10 t ha"1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The mulch was wetted completely by sprinkle irrigation during the night of August 28. Note the difference in scale 201 7.18 Same as Fig 17 except that RN values are corrected by assuming the residue area index (R) increases by 75% and is distributed linearly with no increase at the mulch top 203 xxviii List of symbols Roman symbols unit Ac cross-section area of the water column m2 Am cross-section area of a perforated acrylic container used m2 for measuring evaporation rate from mulch layers am W{a) reaches a maximum at a - am s Am\ cross-section area of micro-lysimeter m2 Ap surface area of the evaporation plate m2 b coefficient indicating the degree of turbulence dimensionless C mean fraction of cloud cover dimensionless Cmi heat capacity of mulch elements J m"3 °C"1 cp specific heat of air J kg"1 °C~l cw heat capacity of water J m"3 "C"1 d displacement height m d' adjusted displacement height m dei characteristic dimension of the straw m Dv turbulent diffusivity for water vapour m2 s"1 7_)T molecular diffusivity fro sensible heat m2 s"1 D™° molecular diffusivity fro water vapour m2 s"1 / view factor (Chapter 5) or dimensionless gust occurrence frequency (Chapter 6) s"1 xx i x F(a,b) wavelet transform dimensionless f(s) time fraction of s exceeds a preset threshold wind speed dimensionless j{Tp) water storage rate d^p/d ,^) kg Pa"1 F(z) source density at height z W m"3 fp fractional sensitivity dimensionless tortuosity factor for the mulch dimensionless g acceleration of gravity m s"2 g(a,b,p,f) wavelet function, where a is the scale dilation parameter, dimensionless b is the translation parameter, p is a power coefficient Go soil heat flux density at the surface W m"2 h height of the water in the water column (Chapter 2) or m canopy height (elsewhere) m H length of the water column (Chapter 2) cm or sensible heat flux density (elsewhere) W m"2 Hc sensible heat flux density due to air renewal W m"2 Hm sensible heat flux density due to molecular diffusion W m"2 hp height of the evaporation plate above the base of the m water column zs turbulence intensity of horizontal wind speed dimensionless zw turbulence intensity of vertical wind speed dimensionless k van Karman's constant dimensionless kmi mulch conductance for water vapour m s"1 XXX still air mulch conductance for water vapour m s Krs L Ld LE LEC LEm LES h Ln r M N hydraulic conductance of the flow path from the water W m"2 Pa"1 column to the evaporation plate kurtosis of horizontal wind speed latent heat of water vaporization downwelling longwave radiation flux density latent heat flux density equivalent latent heat flux density for the flow out of the W m'2 water column latent heat flux density from mulch layer W m"2 equivalent latent heat flux density for the flow in the W m"2 second line dimensionless Jkg"1 Wm"2 Wm"2 Monin-Obukhov length penetration depth longwave net radiation flux density upward longwave radiation flux density average ramp temperature change or amplitude mass of air at the top of the water column total data points in a measurement period (Chapter 3) total number of mulch "elemental" layers (Chapter 5) Brunt-Vaisala frequency (Chapter 6) pressure in the air at the top of the water column m m Wm"2 Wm"2 Kor °C kg dimensionless dimensionless s"1 Pa xxxi PJt) atmospheric pressure Pa Ph pressure at the bottom of the water column Pa Pi shelter factor dimensionless p\ pressure at the air inlet of the water column Pa pp pressure in the water at the evaporation plate surface Pa Ra gas constant of air J kg"1 K"1 Ra Rayleigh number dimensionless Rac critical Rayleigh number (= 1706) dimensionless R residue area index dimensionless re\ reflectance of mulch elements dimensionless rg reflectance of the ground dimensionless Rg solar radiation reflected from ground up to mulch layer W m"2 r H boundary resistance to heat transfer s m"1 Ri i n within-canopy bulk Richardson number dimensionless r m reflectance of a mulch layer dimensionless Rn net radiation flux density W m"2 Sn short-wave net radiation flux density W m"2 £ 0 incident solar radiation at the mulch canopy top W m"2 S* downward short-wave radiation flux density W m"2 Sks skewness of horizontal wind speed dimensionless Sp water storage at the evaporation plate kg Su heat storage in mulch layers W m"2 XXX11 5" upward short-wave radiation flux density W m"2 s mean horizontal "cup" wind speed m s"1 s~r mean horizontal "cup" wind speed at the reference height m s"1 3^  ratio of within-canopy wind speed to that above the dimensionless 5 o u t canopy t time d, min, or s T temperature K or °C 71 air temperature °C Tc coherent part of temperature K or °C temperature on the lower surface of elements °C ti microfront time s r K a temperature of air at the top of the water column K Tr random part of temperature K or °C 4 ramp duration (Van Atta's (1977) ramp model) s 4 quiescent period between two ramps (Van Atta's (1977) s ramp model) Ts soil surface temperature °C V temperature on the upper surface of elements °C u longitudinal wind speed m s"1 Wh longitudinal wind speed at canopy height m s"1 friction velocity (m s"1) m s"1 -u'w' kinematic Reynolds stress m2 s"2 XXX111 v lateral wind speed m s" Pa volume of air at the top of the water column m3 F w volume of water in the water column m3 Vy,o initial value of Vw m3 W weight of a micro-lysimeter or a mulch layer kg w vertical wind speed m s"1 W(a) wavelet variance K 2 we effective vertical exchange velocity m s"1 z height above ground cm or m z0 roughness length m zT reference height m Greek symbols a X AR At coefficient accounting for the air renewal ratio scaling factor between u^l z and 1/r (Chapter 4) or between uh/h and lit (Chapter 7) dimensionless dimensionless dimensionless ratio of daily solar radiation flux to total hemispheric solar dimensionless radiation incident on a horizontal surface at the outer edge of the earth's atmosphere residue area index of an "elemental" mulch layer time lag dimensionless xxxiv A/„ (AT)3/At reaches a maximum at At = Atn ATm temperature difference between two moments of time lag °C (AT)" 7 r e P At, wth order temperature structure function pressure difference (= Pa(i)-pi) atmospheric emissivity for clear sky conditions atmospheric emissivity for cloudy sky conditions (°C)n Pa dimensionless dimensionless factor accounting for the underestimation of MI^B by dimensionless [-(ATJ /Atm]'\ i.e., y= [-(ATJIAtmf l(Mli13) adiabatic lapse rate potential air temperature water content of a mulch layer on mass basis volumetric water content of a mulch layer density of air density of mulch layer density of water standard deviation of horizontal wind speed standard deviation of vertical wind speed "Cm"1 Kor°C dimensionless dimensionless kgm"3 kgm"3 kgm"3 m s"1 m s"1 ratio of within-canopy standard deviation of vertical wind dimensionless speed to that above the canopy XXXV z average ramp duration (Chapter 3 and 4) s transmittance of radiation flux (Chapter 5) dimensionless mean duration of gust events (Chapter 6) s r c l solar transmittance after correcting for the influence of dimensionless the acrylic film and frame Tg mean duration of gusts s tp water tension at the evaporation plate surface Pa ta uncorrected solar transmittance dimensionless v kinematic viscosity m2 s"1 Q clumping index dimensionless Wm diabatic profile correction factor for momentum dimensionless £ index of atmospheric stability (= zl LMO) dimensionless xxxvi Acknowledgements The study was supported by a grand from the National Science and Engineering Research Council of Canada. I was personally supported by the University Graduate Fellowships of BC, St. John's Fellowship, and research and teaching assistantships in the Department of Soil Science, UBC. I am grateful to the faculty, staff, and students of the Department of Soil Science fro their help and friendship during my years of study at UBC. In particular,we wish to extent my sincere thanks to Dr. M.D. Novak, my supervisor, for his constructive advice and participation in the field experiments and preparation of the manuscript, and to his family for their kindness in many ways, we also wish to thanks Dr. T.A. Black for his interest and advice in my study over the years. Appreciation is also due to Drs. M.C. Fortin and D.G. Steyn for being in my supervisory committee; staff of UBC Plant Science Station for preparing the study site for several times; Mr. R. Ketler, Dr. A. Orchansky and Mr. Z. Nezic for assisting with instrumentation, monitoring and computing; P. Young, A.S. Wu, P. Blanken, U. Gramann, and Drs. J.M. Chen, X. Lee and B. Hermawan for their friendship and assistance. Finally, I express my gratitude to my wife Hongying Hu and daughter Joan for their patience and love. My wife's sacrifice of taking time out of her career to take care of our daughter is very much appreciated. Chapter 1. Introduction 1 Chapter 1 Introduction Mulching, which maintains the surface of soils covered with plant residues between successive crops, or when the plant canopy cover is incomplete, has been widely adopted in agriculture, forestry and horticulture. Mulching can be both beneficial, promoting soil and water conservation, and detrimental, slowing soil warming in spring and delaying seed germination. To maximize the benefits of mulching and to reduce its disadvantages, a better understanding of the thermal and moisture regimes in a soil-mulch-atmosphere system is essential. These regimes are primarily determined by the interactions between mulch attributes and the radiation distribution and turbulent exchange processes in a soil-mulch-atmosphere system. While researchers have successfully measured and modeled exchange processes within the soil and atmosphere, progress within mulch layers has been limited by technical difficulties in measuring turbulent and radiative fluxes using current micrometeorological techniques such as eddy correlation. Therefore, a main goal of this thesis was to develop new methods which measure or estimate turbulent and radiative fluxes within a mulch canopy. The second goal was to characterize the regimes of turbulent and radiative fluxes within the mulch canopy. This thesis consists of six papers. The first paper (Chapter 2) reports the development and testing of an improved tension-plate system for measuring first-stage evaporation and condensation rate under a mulch to an accuracy of 5 W m"2. To estimate Chapter 1. Introduction 2 sensible heat flux, a new air renewal model was developed and tested, based on the fact that most turbulent transfer within and above canopies is associated with large-scale coherent eddies. This is described in the second and third papers (Chapter 3 and 4). The new model calculates sensible heat fluxes, using measured temperature fluctuations and friction velocities, at all levels within and above a canopy under both stable and unstable atmospheric conditions. The fourth paper (Chapter 5) describes a new mulch radiation model, which incorporates specific features of a mulch canopy, such as the degree of clumping. The new model can be used to determine short and long-wave radiation components at all levels within a mulch canopy. While the first four papers are devoted to the first goal of the thesis, the remaining two (Chapter 6 and 7) are concerned with the second goal. Wind and turbulence regimes, sensible and latent heat fluxes, and the energy balance within and above a straw mulch canopy are characterized in these two chapters. Chapter 2. Improved tension-plate system 3 Chapter 2 An improved tension-plate system for measuring first-stage evaporation under straw mulch 2.1. Introduction Mulching, in which crop residues are spread or left on the soil surface between successive crops or when crop cover is not complete, has been widely used in tropical and temperate areas because it reduces soil erosion by wind and rain, limits water loss by evaporation, and reduces soil temperature variations (Stigter, 1984). Many researchers have studied the effects of mulching on runoff, erosion, and soil thermal and moisture regimes (Russel, 1939; Adams, 1966; Bristow et al., 1986; Hares and Novak, 1992) and on crop yield (Aiyelaagbe and Fawusi, 1986). However, as Bussiere and Cellier (1994) noted, a major problem in modeling these effects is the uncertainty of describing turbulent transfer within mulches, which is poorly understood and has not been studied in detail. Therefore, we have undertaken a series of field experiments to measure energy balance components, vapour and heat transfer rates, and profiles of vapour pressure, temperature, and wind speed in straw mulches of varying thickness applied to bare soil. Measuring evaporation rate accurately under mulches is an important component of these experiments. This rate is often very low and may even be negative when Chapter 2. Improved tension-plate system 4 condensation occurs below the mulch (Hares and Novak, 1992). This makes its continuous measurement challenging. One option is to use micro- or mini-lysimeters (Boast and Robertson, 1982; Dugas and Bland, 1989; Grimmond et al., 1992). However, manual weighing is inconvenient, time consuming, and as will be shown later, inaccurate under mulches because of errors incurred when disturbing the mulch and exposing the micro-lysimeter to above mulch conditions, however briefly. Placing a micro-lysimeter on a buried accurate digital balance and recording the weight continuously avoids these problems, but is expensive and subject to noise caused by wind. The accuracy of the weighing lysimeter described by Grimmond et al. (1992) was about 30 W m"2, which is too large by an order of magnitude for measuring under mulches. A second option is the tension-plate technique, originally described by Arkin et al. (1974), and used by Tanner and Shen (1990) to measure first-stage (energy-limited) evaporation rates beneath a mulch (Fig. 2.1). However, we were unable to properly measure evaporation rates under thick straw mulches using their system. In this paper, we analyze the flow of air and water in the Arkin et al. (1974) system, demonstrate why it does not function properly when evaporation rate is low, and describe a modification that circumvents this problem. We then test the improved system by comparing latent heat flux density measured with it against micro-lysimeter and Bo wen ratio/energy balance measurements for bare soil and micro-lysimeter measurements under non-wetted and artificially wetted straw mulches. Chapter 2. Improved tension-plate system To Atmosphere • To Data Logger- ¥Cb 7 Pressure Transducer O Stevenson Screen ,Water Column Tension Plate Control Valves •Salt Solution NDrop Counter Fig. 2.1. Schematic diagram of the Arkin et al. (1974) tension-plate system (upper right) and our modification to it (lower left). 2.2. Development of the improved tension-plate system 2.2.1. Mass-flow analysis of the Arkin et al. (1974) system - normal operation Many of the symbols used in the mass-flow analysis of the tension-plate system are shown in Fig. 2.2. In normal operation, air flows in at the height h\ of the water column to replace the volume of water flowing out at the bottom of the column to the evaporation plate. Air entry at h is controlled using either a hypodermic needle inserted through the side wall of the column or a vertical tube inserted through the top of the column. After Chapter 2. Improved tension-plate system 6 H h Y Y l O ! .Water Column (A) •Air (pa, F a, w a, T K a) •Water(Kw) Tension Plate (A , p) » j = ^a(0-Pi / — Air Flow I Water Flow Fig. 2.2. Detailed diagram of the Arkin et al. (1974) tension-plate system showing symbols used in the mass-flow analysis. averaging out the regular fluctuations of pressure associated with entry of the air as a series of bubbles (Fig. 2.3), the pressure at the air inlet, pt, is given by P=PXt)-Sp„ (2-1) where Pa(t) is atmospheric pressure, which may be changing with time, /, and is a constant offset, of order 0.1% of PJt), which is a function of needle or inlet tube diameter. Neglecting pressure loss due to outflow of water, the pressure in the air at the top of the column, pa, is given by the hydrostatic equation P*=Pb-pwgh, (2-2) Chapter 2. Improved tension-plate system 1 0 200 400 600 800 1000 1200 920 1 1 1 1 1 1 0 10 20 30 40 50 60 f(s) Fig. 2.3. A sample time trace of (negative) gauge pressure of the air in the water column measured on September 30, 1992, at a sampling rate of 1 Hz by the pressure transducer from (a) 11:00-11:20 PST and (b) a one minute subsample, showing variations associated with air bubble entry. where p\ = 1000 kg m"3 is the density of water, g - 9.8 m s"2 is the acceleration of gravity, h is the height of water in the column, and pb, the pressure at the bottom of the column, is given by the hydrostatic equation as Pb=Pi+P*gth- (2-3) The pressure p& is related to the volume of air at the top of the column, Va, by the ideal gas law P*K=™ATKM (2-4) Chapter 2. Improved tension-plate system 8 where m3 is the mass of air, Ra = 287.0 J kg"1 K"1 is the gas constant for air, and Tyjf) is the absolute temperature of the air, which may be changing with time. By geometry, the total volume of water in the tube, ¥„, is related to h by r .=4A (2-5) where Ac is the column cross-sectional area. The volume Va is similarly given by K=Ac(H-h), (2.6) where H is the length of the column. If the latent heat flux density at the evaporation plate is LE(t), and if storage changes at the tension-plate surface are negligible, then a water balance of the column yields (2.7) where Av is the area of the evaporation plate and L = 2.45 x 106 J kg"1 is the latent heat of vaporization of water. Integrating Eq. (2.7) with respect to time yields Vw = V^-^j'LE&W>, (2-8) where V*o is the initial value of Vw. Combining Eqs. (2.1), (2.2), (2.3), (2.5), and (2.8) yields A -W) = +P.gfh ~^f[Ko-^fwiW- (29) A pressure transducer measures the quantity Pa(t)-pa, which as shown by Eq. (2.9) is independent of any variations of P a and 7^ with t. Differentiating Eq. (2.9) with respect to t then gives LE(t) as follows: Chapter 2. Improved tension-plate system 9 LE(t) = -LAC d ( P . ( Q - A ) H dt (2.10) The air mass ma can be written in terms of LE(i) by combining Eqs. (2.4), (2.6), (2.8), and (9) as follows: For the system to operate properly, ma must be an increasing function of time since there is no provision for air to be released from the water column, i.e., the air inflow rate, dmjdt > 0. Eq. (2.11) shows that if Pa(t) decreases fast enough or TYJJ) increases fast enough then ma could decrease with time. This is illustrated in Fig. 2.4, which shows dmjdt calculated by differentiating Eq. (2.11) with respect to t and using LE(t) and Tka(t) measured on August 25, 1994 (Fig. 2.5), a relatively clear day. Air pressure Pa(t) was not measured and was assumed to be constant at 100 kPa. The latent heat flux density LE(f) was measured under a 10 t ha"1 straw mulch with the improved tension-plate system (described later); missing data was interpolated. Characteristically, LE(t) decreased dramatically, even becoming slightly negative, after sunrise, an effect associated with dew that had accumulated on the mulch during nighttime. The column air temperature 7ka(0 was measured with a chromel/constantan thermocouple glued to the outside wall of the water column, which was within a Stevenson screen, as indicated in Fig. 2.1. Also shown in Fig. 2.4 is dmjdt calculated with 7ka(r) = 289.4 K, the average value measured on August 25 and Pa(t) = 100 kPa, and with 7k»(0 = 289.4 K and Pa(t) decreasing from 100 (2.11) Chapter 2. Improved tension-plate system 10 kPa at 0:00 PST at a constant rate of 5 kPa d"1, which is an extreme rate of decline. Other parameters and initial conditions estimated for August 25 were: 6p; = 290 Pa (needle), hi = 0.03 m, Ac = 1.13 x 10"3 m2, Ap = 0.09 m2, H = 0.762 m, and = 5.0 x 10"4 m3. The results show that the Arkin et al. (1974) system is more sensitive to variations of 7ka(0 than of PJJ) and that no measurements would be possible with their system between 6:00-12:30 PST on this day. As we shall see next, the system would fail to function for several hours beyond 12:30 PST because of excess water stored at the tension plate. 1 1 1 1 1 1 J K a Measured, Pa(0 =100 kPa TK = 289.4 K, P.(0 = 100 kPa 2 — ",a a _ JK a= 289.4 K, dPa(r)/dr =-5 kPa d"1 I i i i i i I 0 4 8 12 16 20 24 /(h PST) Fig. 2.4. Rate of change of water column air mass calculated with the mass-flow analysis of the Arkin et al. (1974) tension-plate system for August 25, 1994, using the measured data in Fig. 2.5. Chapter 2. Improved tension-plate system 11 Fig. 2.5. Latent heat flux density under a 10 t ha"1 straw mulch (a) and water column air temperature (b) measured using the improved tension-plate system on August 25, 1994. The break in LE(t) occurred when manually refilling the water column. 2.2.2. Mass-flow analysis of the Arkin et al. (1974) system - ma constant Since air cannot be released from the water column, what actually happens when dmjdt becomes negative is that dmjdt = 0 and ma remains constant. Then according to Eq. (2.4), d ^ d ^ d ^ o o Pa K W) ' In this case the outflow rate from the water column differs from the evaporation rate at the tension plate, so that water storage at the plate must be accounted for, i.e., Chapter 2. Improved tension-plate system 12 Mp=pJK -j-^, (2.13) where dSp is the change in water stored at the plate (kg) in time interval dt. This storage is related to water tension (suction) at the plate surface, tp = PJt) - P p , where P p is the pressure in the water at the tension-plate surface, such that dS, - B - = /M. (2.14) The water storage rate_/(2p) measured for one of our tension plates is shown in Fig. 2.6. Also shown are measurements of steady-state flow rate to this plate as a function of height difference between plate surface and air inlet in the water column, from which we determined hydraulic conductance between column and plate. Details of our tension-plate construction and these measurements are discussed later. As will be seen, hydraulic conductance of our plates is very large so that pressure varies nearly hydrostatically, i.e., Ph=PP+Pwg»P, (2.15) where hp is the height of the tension plate above the base of the water column. Combining Eqs. (2.2), (2.6), (2.13), (2.14), and (2.15) with the fact that dpp = dPa(r) - dz;, yields 4P. = — — }pwdVa + ^L E ^ d t + dP(t). (2.16) Ac f(rp)r Lf(r) Solving Eqs. (2.12) and (2.16) for dVa yields dV = r p ^ - A ^ - d P M r i \ + p v , g A , A V ^ a A / ( T p ) , (2.17) and d/?a is given by Eq. (2.12) with dVa from Eq. (2.17). Note that from Eqs. (2.1), (2.3), and (2.15) Chapter 2. Improved tension-plate system 13 *=^.(0+A£(4-^)- />p. (2-18) which shows that dpi is not constant when pp varies because of storage changes at the tension plate. Eqs. (2.12) and (2.17) were solved approximately in finite-difference form using measured LE(t), 7ka(0> and parameters for August 25, 1994, as before with Pa(r) assumed constant and with/Tp) in Fig. 2.6. Eqs. (2.12) and (2.17) began to apply at 6:00 PST rp(Pa) 0 200 400 600 800 hrhp (Pa) Fig. 2.6. Water storage rate for one of our two tension plates as a function of water tension at the plate surface, including fitted empirical function (a) and measured steady-state flow rate to this plate as a function of height difference between plate surface and air inlet in the water column, including fitted straight line (b). Chapter 2. Improved tension-plate system 14 when dmjdt became negative; before this time the equations for normal operation applied. Initial values of Va and pa were those calculated at 6:00 PST. The height hp was such that xp = 490 Pa at 6:00 PST. Fig. 2.7 shows apparent values of LE(t) deduced from either Eq. (2.10) or from the following relation: ^ ( ^ . M ^ . (2.19) Ap dt The values using Eq. (2.10) would be from pressure transducer measurements, as described previously, while those from Eq. (2.19) would be from direct measurement of height of water in the column. The two calculations disagree with each other and with trueZ£(r) between 6:00-16:30 PST. Fig. 2.4 shows that dmjdt < 0 from 6:00-12:30 PST but Fig. 2.7 shows that normal operation resumes only after 16:30 PST, the added delay being due to the excess water that accumulates on the tension plate during the constant ma phase. Until that water evaporates the system cannot function normally. We did not collect data to test this anomalous behaviour, since we modified the system to avoid it, but observed many of the symptoms, i.e., excess water on the tension plate, increased pressure at the air inlet, and large apparent evaporation rates just after sunrise. We suspect that this behaviour is evident in the original test data presented by Arkin et al. (1974) (Fig. 2.8, which reproduces their Fig. 4). Although cumulative evaporation at the end of the day was inversely related to mulch thickness, as expected, up until 12:00 PST the reverse was true, even though cumulative solar at 12 :00 PST was about half that at the end of the (clear) day. For the 10 t ha"1 mulch, maximum evaporation rate occurred between 8:00-9:00 PST and rates were slightly negative between 13:00-16:00 PST. If true of actual evaporation in the field, then these results are Chapter 2. Improved tension-plate system 15 difficult to explain. The results for the 10 t ha"1 mulch are however in qualitative agreement with the predictions in Fig. 2.7. Although Arkin et al. (1974) reported that they minimized air temperature fluctuations in the water columns by enclosing them in a reflective styrofoam box, it is unlikely, considering that the measurements were made in Texas in August, that such fluctuations were completely eliminated. 0 8 12 16 20 24 f(h PST) Fig. 2.7. Apparent values of latent heat flux density calculated with Eq. (2.10) (from the pressure transducer) and Eq. (2.19) (from height of water) in the mass-flow analysis of the Arkin et al. (1974) tension-plate system compared with measurements using the improved tension-plate system for August 25, 1994. Chapter 2. Improved tension-plate system 16 I8 O % 6 o > W 4 > o • " I 1 1 Incoming Solar i I • • 1 • • lOt ha"1 Q -+ 41 ha"1 • © 11 ha"1 • A Bare Plate A A~ EJ A A A © ©_ • A © © © • A © + + + - A O + + -ft | -8 10 12 14 16 18 t(h) Fig. 2.8. Cumulative evaporation measured by Arkin et al. (1974) using tension plates in a bare soil and under 1, 4, and 10 t ha"1 straw mulches on August 17, 1973. Incoming solar is expressed as equivalent cumulative evaporation. 2.2.3. Improved tension-plate system One way to avoid these difficulties is to keep rKa(0 and PJf) strictly constant. This is possible for 7ka(0 with significant expense, but not for PJt) since the system must be exposed to the atmosphere. A simpler choice is to add a second flow line out of the water column in parallel with the tension plate, effectively increasing LE(t). The flow in this line must either be kept strictly constant or monitored precisely if it varies. Then operation is normal (dmjdt > 0) for all t regardless of variations of rK a(/) and PJt). If the Chapter 2. Improved tension-plate system 17 equivalent latent heat flux density for the flow in the second line is LEs(t) and that for the flow out of the water column is LEc(t), then LE(t) = LEc(t)-LEs(t). (2.20) Eq. (2.20) is used to calculate LE(f), which could even be negative (condensation). Fig. 2.9 shows dmjdt calculated after differentiating Eq. (2.11) with respect to t, with LE(t) replaced by LEJJ) and LEs(t) = 102 W m"2 (1.35 x 10"5 m3 h"1), which was the approximate rate actually used on that day and in our studies. As expected, dmjdt > 0 for all t. All values of dmjdt are above a critical value, defined as 2 x 10"9 kg s"1, which yields 6 -/ bfj © 4 . 0 0 8 12 16 20 24 t (h PST) Fig. 2.9. Rate of change of water column air mass calculated with the mass-flow analysis of the Arkin et al. (1974) tension-plate system modified to include a parallel flow line for August 25, 1994. Measured data in Fig. 2.5 were used with PJJ) = 100 kPa and LEs(f) = 102 W m"2. Also shown is the critical value of dmjdt. Chapter 2. Improved tension-plate system 18 an intake rate of about 3 air bubbles min"1. Based on our experience, this is the minimum rate of bubbling required for accurate averaging of the pressure transducer signal, which as shown in Fig. 2.3 varies greatly on short time scales due to bubble entry. The second flow line is shown schematically in Fig. 2.1. Outflow from this line, which is regulated by a precision needle valve, drips into a flask placed about 0.5 m below the bottom of the water column. Because the pressure at the base of the column is constant the flow rate should remain constant if the hydraulic conductance of the valve does not change and even if Pa(t) varies. Although it was found that using de-aired distilled water minimizes valve clogging, some variation of flow rate does occur and so it is monitored continuously. Each drop completes a simple electric circuit by falling between two wires, generating a pulse which is counted. Since distilled water is a poor conductor, the water passes through a salt solution in a sealed container to increase its electrical conductivity adequately for the drop-counting technique. Our tension plate is somewhat different from the Arkin et al. (1974) system. The evaporation surface, which is nominally 30 by 30 cm, is covered with 1-2 mm layer of local soil spread on a 0.5 mm thick piece of blotting paper. The blotting paper is placed on a polyester membrane (105 um mesh, yielding a measured air-entry tension of about 800 Pa, equivalent to 8 cm height of water) which is attached to the walls of the tension plate so that it forms an air-tight seal. The blotter protects the membrane from damage by the soil. The membrane is supported by a 6 mm thick layer of 0.5-1 mm diameter sand. The inflow tube, which protrudes into and across the plate through a hole in one wall, contains many 0.3 mm diameter holes which pass water freely but protect the tube from Chapter 2. Improved tension-plate system 19 back-filling with sand. The bottom of the plate is made of 3 mm thick copper plate to minimize distortion of soil temperature. Using an infrared thermometer in differential mode, less than 0.5 °C difference in surface temperature was measured between the tension plate and surrounding bare soil under high evaporation rate conditions. The tension plate is positioned relative to the water column so that tp is in the range 300-500 Pa. The water storage rate;</(^ >), for our plates is typically between an upper limit of 9 x 10"3 kg Pa"1 for free water on a 0.09 m2 plate and a lower limit of 4 x 10"6 kg Pa"1 estimated from the soil water retention curve for tp in the range 2.5-5 kPa (Hares, 1988) assuming a 2 mm thick layer of soil on the plate (Fig. 2.6). Measurement of/(2j>) was done in the laboratory using the inflow tube as a hanging column. Most of the water release associated WithJltp) is attributed to deformation of the membrane surface, which the soil possibly contributing significantly at the higher tensions. Hydraulic conductance (for equivalent latent heat flux) of the flow path from the water column to the tension-plate surface, Kp, is governed by LE(t) = Kp(pb - pp). (2.21) For the tension plate in Fig. 2.6, Kp was about 66 W m"2 Pa"1, which if limited by vertical flow through the sand layer only yields a saturated hydraulic conductivity of about 2xl0"4 m s"1. Based on our experience, this is reasonable for the sand used. 2.2.4. Measurement errors in the improved tension-plate system Chapter 2. Improved tension-plate system 20 Major sources of error in the improved tension-plate system are the accuracies of the pressure transducer, drop-counting technique, and data logger, and storage effects in the tension plate as the evaporation rate varies. The pressure transducer was calibrated by applying various constant pressure differences and measuring voltage with the data logger. The drop-counting technique was calibrated by manually weighing outflow rate with the outflow tube below the bottom of the column as in the field; essentially this determined the volume of water in each drop. Drop size is a function of geometry of the outlet and is independent of flow rate. Total accuracy is then readily measured by closing off the flow to the tension plate, so that LE(t) = 0 exactly and any measured values are errors. The mean error using this method was < 1 W m"2 with a range of ±4 W m"2 for half-hour values both in the laboratory and in the field, with LE&(i) varying from 100 to 400 W m"2. These errors are for the system as described above; accuracy can be improved by increasing the surface area of the tension plate or decreasing the cross-sectional area of the water column but both options require more frequent filling of the water column. The error expressed as equivalent latent heat flux density due to water storage at the tension plate is given by Fig. 2.6 shows that when % is in the range 300-500 Pa,/^) < 7 x 10"5 kg Pa"1. Therefore, with ^ p = 66 W m"2 Pa"1 and assuming an upper limit for dLE(t)/dt of about 0.05 W m" s" L d S p = Z / ( r „ ) d r p 4, d7 Ap dt (2.22) Combining Eqs. (1), (3), (21), and (22) yields L dSp = Lf(tp) dLEjt) A dt ApKp dt (2.23) Chapter 2. Improved tension-plate system 21 (from the bare soil measurements in Fig. 2.10) then according to Eq. (2.23) the maximum error associated with storage of water on the tension plate is about 1.5 W m"2. This error would be even smaller under a thick mulch where LE(t) changes more slowly than for a bare soil. 2.3. Field tests Field tests were done on selected days within a series of micrometeorological field experiments conducted at the University of British Columbia Plant Science Research Station in Vancouver during summer and early fall in 1992, 1993, and 1994. The site was a 25 by 40 m bare area in which was located a circular mulch plot of about 14 m diameter. The site was surrounded by generally unirrigated bare and cropped fields. Straw mulches were applied successively in time at rates of 2, 5, 10, and 15 t ha"1, resulting in layers roughly 1, 3, 6, and 9 cm thick, respectively. Each mulch application rate was studied for a number of days on the same plot. The surface of the surrounding bare area, which was used as a reference plot, was generally maintained wet by manual and sprinkler irrigation, although on some days this was not possible because of high evaporation rates coupled with the sandy loam soil texture. The soil under the mulches was wet enough, deduced from the soil water retention curves (Hares, 1988) and gravimetric water contents, that evaporation always proceeded at the potential rate. 2.3.1. Bare soil Chapter 2. Improved tension-plate system 22 Daytime latent heat flux density measured with improved tension-plate systems and micro-lysimeters (Boast and Robertson, 1982) for a bare surface are compared in Fig. 2.10. July 20, 1994, was a mostly clear day with the experimental site completely bare (no mulch) and wet. Two tension-plate systems were located within a meter of each other near the middle of the site, and surrounded by four micro-lysimeters (7.3 cm id., 3.7 cm deep stainless steel cores with a 1 mm thick steel bottom plate) about 3 m away. The micro-lysimeters were manually weighed hourly using an accurate digital balance (0.005 g resolution, equivalent to < 1 W m"2 for hourly measurements) located in a nearby hut. 600 Tension Plate o. 0 4 8 12 16 20 24 / (h P S T ) Fig. 2.10. Latent heat flux density measured with two improved tension-plate systems and four micro-lysimeters in a bare soil on July 20, 1994. The breaks in tension-plate data occurred when manually refilling the water columns. Chapter 2. Improved tension-plate system 23 They were kept under cover during transfer to and from the hut and while waiting to be weighed to minimize water loss when out of the soil, and corrections were made for the time lost during weighing. Agreement is within 35 W m"2 between the two tension-plate systems and within 80 W m"2 among the four micro-lysimeters. Considering the variation within each method the tension plates and micro-lysimeters agreed very well. Evett et al. (1995) suggest that stainless steel micro-lysimeters should consistently underestimate evaporation but this is not evident in our results. Latent heat flux density measured with the improved tension-plate system and the Bowen ratio/energy balance method (Fuchs and Tanner, 1970) for a bare surface are compared in Fig. 2.11. During October 16-18, 1993, the weather was mostly cloudy with the experimental site completely bare and wet. The tension-plate system was located near the middle of the site with the Bowen ratio/energy balance sensors within a few meters of it. The Bowen ratio was calculated half-hourly from vertical air temperature and vapour pressure differences between the 1 and 5 cm heights measured using fine-wire thermocouples (25 urn chromel/constantan) and capacitance-type humidity sensors (Vaisala HMM-20D with 75 urn chromel/constantan thermocouple installed within its protective permeable cap, painted white with standard membrane filter removed, to convert relative humidity to vapour pressure), respectively. Both sensors were naturally ventilated and fixed at the two heights; no attempt was made to take advantage of regularly reversing their positions. Net radiation was measured with a net pyrradiometer (Swissteco, type S-l) mounted at 50 cm height and soil surface heat flux density was Chapter 2. Improved tension-plate system 24 measured with a 0.6 by 3 by 10 cm home-made heat flux plate (copper/constantan thermopile wound on a high conductivity epoxy resin plate and sandwiched between Fig. 2.11. Latent heat flux density measured with an improved tension-plate system and the Bowen ratio/energy balance method (a) and vapour pressure gradient between 1 and 5 cm heights measured with capacitance-type humidity sensors (b) for a bare soil on October 16-18, 1993. The breaks in tension-plate data occurred when manually refilling the water column. anodized aluminum plates using the same epoxy resin) installed at 1 cm depth with corrections for heat storage above the plate made from soil temperature measured at 0.5 cm depth (single 250 u.m chromel/constantan thermocouple fixed with epoxy resin in 2 mm o.d. by 10 cm long stainless steel tubing) and soil volumetric heat capacity estimated as in Hares and Novak (1992). Unrealistically large magnitude values of LE(t) calculated Chapter 2. Improved tension-plate system 25 by the Bowen ratio/energy balance method when the Bowen ratio was near -1 (generally at night) were excluded from Fig. 2.11. The two methods agreed very well during daytime. Differences occurred at night although the fluxes according to both methods were then small. Comparison with the measured vapour pressure gradient (multiplied by -1), also presented in the figure, shows that the Bowen ratio/energy balance method was often incorrect at night, since the sign of LE(f) usually disagreed with the sign of the gradient. Such errors are not uncommon with this method when fluxes and gradients are small and small systematic errors can change the direction of calculated LE(t). The signs of LE(i) and the vapour pressure gradient were in good agreement for the tension-plate system. 2.3.2. Non-wetted straw mulch Daytime latent heat flux density measured with an improved tension-plate system and four micro-lysimeters under a dry straw mulch applied at 10 t ha"1 are compared in Fig. 2.12. September 17, 1992, was a clear day on which the mulch was quite dry during daytime but did gain moisture at night, from both dew and evaporation from the soil. The micro-lysimeters were manually weighed every two hours as described for the bare soil. The two methods do not agree, the micro-lysimeters yielding on average 56% greater latent heat flux density during the daytime. Variability among the micro-lysimeters is large, typically between 50 and 100%. For 2 and 5 t ha"1 mulches measured similarly (not shown) the micro-lysimeters overestimated latent heat flux density by 16 and 24%, Chapter 2. Improved tension-plate system 26 respectively. These differences are ascribed to systematic errors with the micro-lysimeter method. Although evaporation during the weighing procedure was minimized some water loss is unavoidable (shown later). Since LE(t) under mulches decreases considerably with increasing mulch thickness these small losses become more significant at higher mulch application rates. In addition, removal of the micro-lysimeters every two hours disturbs the overlying mulch, which dries out more quickly and becomes less dense, introducing greater variability. 60 50 40 30 20 10 0 -10 1 1 1 Tension Plate "Micro-lysimeter o #1 0 8 12 16 20 24 t (h PST) Fig. 2.12. Latent heat flux density measured with an improved tension-plate system and four micro-lysimeters under a non-wetted 10 t ha"1 straw mulch on September 17, 1992. The break in tension-plate data occurred when manually refilling the water column. Chapter 2. Improved tension-plate system 27 This suggests that some of the latent heat flux density measurements in Hares and Novak (1992), for which micro-lysimeters were used exclusively, are in error. This will be discussed in another manuscript but we note that correction of this overestimate brings mulch diffusivities calculated by them into better agreement with those calculated in the present studies using the tension-plate system. Our contention that the micro-lysimeter measurements in Fig. 2.12 are in error is supported by longer term measurements made under 2, 5, and 10 t ha"1 mulches with the tension-plate system and micro-lysimeters (Fig. 2.13). Four micro-lysimeters were used and each point shown is an average of these replicates. The micro-lysimeters were manually weighed at 7:00-17:00 PST only, and were otherwise not disturbed. Both nighttime and daytime periods are presented separately. Overall agreement between the two methods, especially during daytime when the disturbance error would be maximum, is excellent for all mulch application rates. Further supporting evidence that the improved tension-plate method works well under dry straw mulches is provided in Fig. 2.14, which compares LE(t) and the vapour pressure gradient between 0 and 1.5 cm heights (multiplied by -1) measured within the 10 t ha"1 mulch on August 25, 1994. The pressure gradient was calculated by assuming saturation at the soil surface at a temperature extrapolated from soil temperature measured at 0.5 cm depth and soil heat flux density at 1 cm depth (both measured as for the bare soil) using Fourier's law. Vapour pressure was measured at 1.5 cm using a Vaisala HMM-20D sensor as for the Bowen ratio measurement but with the bottom half and end piece of the standard protective cap removed to promote natural ventilation. The Chapter 2. Improved tension-plate system 28 sensor was protected from dew and drops falling from above it by the remaining half of the cap, rendered water proof with white paint, and oriented vertically to minimize condensation on the sensing surface, and the thermocouple was located very near the sensing surface. Fig. 2.13. Comparison between daytime (7:00-17:00 PST; unfilled symbols) and nighttime (17:00-7:00 PST; filled symbols) average latent heat flux density under non-wetted 2, 5, and 10 t ha"1 straw mulches measured with an improved tension-plate system and with micro-lysimeters (average of four replicates). Measurement dates were September 20-22, 1992 (2 t ha"1 mulch), September 12-15, 1992 (5 t ha"1 mulch), and September 16-18, 1992, and August 29-September 1, 1994 (101 ha"1 mulch). Chapter 2. Improved tension-plate system 29 «3 AH i t-i O 8 12 16 20 24 f (hPST) Fig. 2.14. Latent heat flux density measured with an improved tension-plate system under a non-wetted 10 t ha"1 straw mulch and vapour pressure gradient between 0 and 1.5 cm heights within the mulch measured as described in the text on August 25, 1994. The break in LE(f) occurred when manually refdling the water column. Although fluxes and gradients are not necessarily expected to be proportional to each other within a mulch because of, in part, near-field effects (Raupach, 1989), turbulent diffusivities determined at times when the mulch was dry and near-field effects were negligible suggest that scalar transfer in the 1.5 cm layer adjacent to the soil surface is dominated by molecular diffusion. Therefore, good correlation between LE(f) and vapour pressure gradient across this layer, at least with respect to sign, is expected, and this is shown to be reasonably true in Fig. 2.14. Not all the features of this figure are understood Chapter 2. Improved tension-plate system 30 at present, e.g., why the vapour pressure gradient between 12:00-16:00 PST is about 3 times that at night even though LE(f) is only about 35% greater (which could be due to buoyancy effects since the 0-1.5 cm layer is stable during daytime and unstable at night), why the gradient is so large relative to flux between 9:00-11:00 PST when LE(t) is negative, and why the reversals of sign of LE(t) and the gradient do not occur simultaneously. The figure is presented only to show that the temporal trends of both measurements, which were completely independent, are well correlated. 2.3.3. Artificially wetted straw mulch To test the ability of the improved tension-plate system to measure condensation rate, the 10 t ha"1 mulch was wetted thoroughly by sprinkler irrigation during the night of August 28, 1994. Latent heat flux density measured with the improved tension-plate system and two micro-lysimeters from 18:00 PST, August 29 to 18:00 PST on September 1, 1994, a series of clear days, is shown in Fig. 2.15. Measurement error associated with water loss during manual weighing of the micro-lysimeters was corrected as follows. Each micro-lysimeter was weighed twice successively in time, i.e., the micro-lysimeters were removed, weighed, replaced in the soil, and then these steps were repeated. One half of the difference in the successive weights was either subtracted from the second weight (for the initial weight in a time period) or added to the first weight (for the final weight in a time period) so that corrected LE(t) is given by (2.24) Chapter 2. Improved tension-plate system 31 where subscripts 1 and 2 refer to the first and second successive weights, W, subscripts i and f refer to initial and final times, and = 0.0042 m2 is the surface area of the micro-lysimeter. The magnitude of this correction was in the range 5-10 W m"2. The micro-lysimeters were weighed hourly during daytime; nighttime values are averages based on the last measurement of the previous day and the first measurement of the next day. The tension-plate system and micro-lysimeters agreed very well at night and fairly well during daytime on the first two days when the mulch was still wet. Underestimates by the micro-lysimeters on the first two days may have been due to water dripping onto the lysimeters upon removal for weighing. On all three days, but especially the third, LE(t) measured by the micro-lysimeters in the afternoon exceeded that measured by the tension-plate system by as much as 50%, similar to the results in Fig. 2.12 and despite the correction for water loss during weighing. During this experiment, it became obvious that the straw overlying the micro-lysimeters was drying more rapidly than the rest of the plot because of the repetitive removal of the lysimeters. Some substitution with straw from elsewhere on the plot was done but not systematically. The results show that the error associated with this drying is at least as large as the correction for water loss during weighing. Hares and Novak (1992) reported condensation rates under straw mulch strips that were similar to those in Fig. 2.15 (their maximum rate, which was an average for 10:00-12:0 PST on April 7, 1985, was equivalent to 19 W m"2). The good agreement between micro-lysimeters (corrected for weight loss during weighing) and tension-plate system in this figure suggests that their condensation rates should be increased by 5-10 W m"2, since Chapter 2. Improved tension-plate system 32 they did not correct for weight loss. Temporal trends measured by Hares and Novak (1992) are very similar to those measured on the last two days of this experiment. 40 20 0 -20 -Micro-lysimeter #1 Micro-lysimeter #2 Tension Plate 0 12 0 12 t (h PST) o-0 12 Fig. 2.15. Latent heat flux density measured with an improved tension-plate system and two micro-lysimeters under an artificially wetted 101 ha"1 straw mulch from August 29-September 1, 1994. Unfilled symbols are daytime values and filled symbols are nighttime values. The breaks in tension-plate data occurred when manually refilling the water column. Comparison between LE(t) from the tension-plate system and vapour pressure gradient between 0 and 1.5 cm heights within the mulch (multiplied by -1), measured as described previously, during the wetting experiment is shown in Fig. 2.16. As in Fig. 2.14, the temporal trends of these independent measurements are similar which adds further evidence that the tension-plate system measures condensation rates well. Again, Chapter 2. Improved tension-plate system 33 not all the features in this figure are fully understood at present and data analysis is still continuing. Fig. 2.16. Latent heat flux density measured with an improved tension-plate system under an artificially wetted 101 ha"1 straw mulch and vapour pressure gradient between 0 and 1.5 cm heights within the mulch measured as described in the text from August 29-September 1, 1994. The breaks in LE(t) occurred when manually refilling the water column. 2.4. Evaporation under and above a non-wetted mulch Latent heat flux density above a 101 ha"1 mulch was determined by adding LE(t) measured by the tension plate under the mulch to that calculated from total weight loss for the mulch layer, LEJf). This weight loss was a sum of losses for six 1 cm thick layers (cross-Chapter 2. Improved tension-plate system 34 sectional area Am = 0.0139 m2) stacked in perforated acrylic containers within the mulch (2 replicate profiles) so that AnV'f 'i/6 layers Mulch weight loss on August 29, 1993, was measured every one hour during daytime, but for nighttime only average loss between 17 and 7 h was measured. Latent heat flux density above bare and mulch surfaces in Fig. 2.17 are typical for such surfaces (e.g., Novak and Black, 1985; Bussiere and Cellier, 1994). Attempts to measure LE(t) above Fig. 2.17. Latent heat flux density measured with improved tension-plate systems in a bare soil and under a non-wetted 10 t ha'1 straw mulch on August 29, 1993. Also shown is LE(t) above the mulch calculated from mulch weight loss as described in the text. The breaks in LE(t) occurred when manually refilling the water columns. Chapter 2. Improved tension-plate system 35 the mulch using the Bowen ratio/energy balance method as for the bare soil were unsuccessful, which was attributed to differences in source height for vapour and heat. These were significant because sensors were located less than 5 cm above the mulch due to the restricted fetch in our studies. At night, LE(t) under the mulch is much larger than that in the adjacent bare area. However, above the mulch LE(t) is negative (the mulch having gained weight) indicating condensation. About 45% of this condensation comes from soil evaporation, the rest from the atmosphere. Immediately after sunrise, LE(i) above the mulch increases sharply, greatly exceeding that from the bare soil. This is attributed to the low thermal conductivity and heat capacity of the mulch compared to wet soil, which causes mulch surface temperature to increase more rapidly than bare soil surface temperature. At this same time LE(i) under the mulch decreases to near zero. However, by 10:00 PST availability of water from the mulch becomes limiting and LE(i) above the mulch declines while under the mulch LE(t) increases, becoming equal to that above the mulch by 13:00 PST. This remains so until 17:00 PST when the mulch starts to absorb moisture and transition to the nighttime pattern begins. 2.5. Summary and Concluding Remarks Mass-flow analysis of the tension-plate system in Arkin et al. (1974) has shown that their system is subject to large errors when evaporation rates are low or negative, as Chapter 2. Improved tension-plate system 36 typically occurs under thick straw mulches. The errors are associated with variations of atmospheric pressure and, more importantly, temperature of the air in the water column. Although it is possible to regulate this temperature (but not atmospheric pressure), we found that it is simpler and cheaper to add a second outflow line from the water column in parallel with the tension plate in which flow rate is either maintained strictly constant at a specified value or monitored accurately if it varies. The flow rate out of the water column is then high enough for all evaporation rates at the tension plate, including negative values, that the measurements are always independent of variations due to atmospheric pressure and water column air temperature. Error analysis of the improved system shows that latent heat flux density is measured to within 5 W m"2. Comparison of the tension-plate system against micro-lysimeter and Bowen ratio/energy balance methods showed good agreement for bare soil during daytime. Short-term (every 1-2 hours) comparison with micro-lysimeters for daytime measurements under non-wetted straw mulch did not show good agreement, which was attributed to errors in the micro-lysimeter method associated with water loss during manual weighing and disturbance of the mulch with repetitive removal. When the micro-lysimeters were weighed only twice a day, agreement with the tension-plate measurements was excellent for both daytime and nighttime. Condensation rates measured under artificially wetted straw mulch with the tension-plate and micro-lysimeter methods were in good agreement after the micro-lysimeter measurements were corrected for water loss during manual weighing. As the mulch dried the methods diverged because of disturbance of the mulch during repetitive removal of the micro-lysimeters. Chapter 2. Improved tension-plate system 37 2.6. References Adams, J.E., 1966. Influence of the mulch on runoff, erosion, and soil moisture depletion. Soil Sci. Soc. Am. Proc, 30: 110-114. Aiyelaagbe, I.O.O. and Fawusi, M.O.A., 1986. Growth and yield response to mulching. Biotronics, 15: 25-29. Arkin, G.F., Ritchie, J.T. and Adams, J.E., 1974. A method for measuring first-stage soil water evaporation in the field. Soil Sci. Soc. Am. Proc, 38: 951-954. Boast, CW. and Robertson, T.M., 1982. A "micro-lysimeter" method for determining evaporation from bare soil: Description and laboratory evaluation. Soil Sci. Soc. Am. J., 46: 689-696. Bristow, K.L., Campbell, G.S., Papendick, R.I. and Elliott, L.F., 1986. Simulation of heat and moisture through a surface-residue soil system. Agric For. Meteorol., 36: 193-214. Bussiere, F. and Cellier, P., 1994. Modification of the soil temperature and water content regimes by a crop residue mulch: experiment and modeling. Agric. For. Meteorol., 68: 1-28. Dugas, W.A. and Bland, W.L., 1989. The accuracy of evaporation measurements from small lysimeters. Agric. For. Meteorol., 46: 119-129. Evett, S.R., Warrick, A.W. and Matthias, A.D., 1995. Wall material and capping effects on microlysimeter temperatures and evaporation. Soil Sci. Soc. Am. J., 59: 329-336. Chapter 2. Improved tension-plate system 38 Fuchs, M. and Tanner, C.B., 1970. Error analysis of Bowen ratios measured by differential psychrometry. Agric. Meteorol., 7: 329-334. Grimmond, C.S.B., Isard, S.A. and Belding, M.J., 1992. Development and evaluation of continuously weighing mini-lysimeters. Agric. For. Meteorol., 62: 205-218. Hares, M.A. and Novak, M.D., 1992. Simulation of surface energy balance and soil temperature under strip tillage: II. Field test. Soil Sci. Soc. Am. J., 56: 29-36. Hares, M.A., 1988. Effects of Mulching on the Surface Energy Balance and Soil Thermal Regimes. Ph.D. Diss., Univ. of British Columbia, Vancouver, Canada. Novak, M.D. and Black, T.A., 1985. Theoretical determination of the surface energy balance and thermal regimes of bare soils. Boundary-Layer Meteorol. 33: 313-333. Raupach, M.R., 1989. A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies. Q. J. R. Meteorol. Soc, 115: 609-632. Russel, J.C., 1939. The effect of surface cover on soil moisture losses by evaporation. Soil Sci. Soc. Am. Proc, 4: 65-70. Stigter, C.J., 1984. Mulching as a traditional method of microclimate management. Arch. Meteorol. Geophys. Bioclim. Ser. B, 35: 147-154. Tanner, C.B. and Shen, Y., 1990. Water vapour transport through a flail-chopped corn residue. Soil Sci. Soc. Am. X, 54: 945-951. Chapter 3. Ramp model 39 Chapter 3 Coherent eddies and temprature structures functions for three constrasting surfaces. Part I: Ramp model with finite microfront time 3.1. Introduction The dominance of large-scale, intermittent, coherent turbulent eddies in the exchange of momentum, heat, and mass within and above plant canopies has been recognized in recent years (Raupach et al., 1989 and 1991). These structures are evident in time traces of air temperature, vapour density, and other scalars as 'ramp' patterns in which a slow nearly steady increase or decrease is followed by a relatively rapid change back to a baseline level (Gao et al, 1989; Paw U et al., 1992; Qiu et al., 1995). Analysis of these patterns is improving our understanding of turbulence and has led to the development of surface renewal models of turbulent transfer (Brunet and Raupach, 1987; Paw U et al., 1995; Spano et al., 1996). Van Atta (1977), hereafter referred to as 'VA', developed a theory to describe the coherent and random parts of a temperature time series measured in the surface layer of the atmosphere. The coherent part consisted of intermittent ramps with a constant rate of increase (when the underlying surface was warmer than the air) followed by an instantaneous, or step, change back to baseline level. The random part consisted of small-scale turbulent fluctuations assumed to be locally isotropic. Coherent and random parts Chapter 3. Ramp model 4 0 were assumed to be statistically independent with the complete temperature trace a linear superposition of them. VA then used his model to analyse even- and odd-order temperature structure functions (defined later) for measurements made in the atmospheric boundary layer over the ocean. Subsequent analysis of temperature and other scalar time traces and application to renewal models have largely been based on VA's results (e.g., Spano et al., 1996).. In this chapter we present a model in which the relatively rapid change at the end of each ramp is not instantaneous but occurs in a finite 'microfront' time. The existence of microfronts separating air sweeping into the canopy from above and within canopy air has been described by Gao et al., (1989). Structure functions with the new model are derived and compared with high frequency air temperature data measured above and within a Douglas-fir forest and above a straw mulch and bare soil. The VA ocean data are similarly compared with the new model. Ramp frequencies and microfront times determined using the Mexican Hat wavelet transform are compared with values from the new model calculated by fitting to the 3rd-order temperature structure function. This chapter is the first of a two part study of coherent eddies and temperature structure functions associated with a Douglas-fir forest, straw mulch, and bare soil, three surfaces of contrasting scale. In the second part (Chapter 4), a new air renewal model for sensible heat flux density is developed using results from this paper. 3.2. VA Theory and temperature ramp model Chapter 3. Ramp model 41 Assumptions made by VA in proposing his temperature structure theory are as follows (adopting our notation): (1) Measured air temperature, T, can be separated into a random part, TT, and a coherent part, Tc, such that T = Tt+Tc. Similarly, AT = T(t)-T(t-At), where t is time and At is a time lag, can also separated into two parts such that AT= ATr+ATc. (2) The two parts are statistically independent, so that (A7^ )m(A7^ )" = (A7 )^m(A7 )^", where the overbar stands for an appropriate averaging procedure for the turbulence, generally a time average over periods long enough to include all important turbulent scales and short enough to exclude long term trends, such as diurnal variations. The Arth-order structure function is given by (AT)", which is of even or odd order depending upon whether n is even or odd, respectively. (3) The random part is locally isotropic, so that (ATT)m = 0 for m odd. (4) The coherent part can be represented by a sequence of identical uniform ramps of amplitude M and duration tr, separated by a constant time, ts (Fig. 3.1). Each ramp ends with a step change down to baseline level. The time interval between the brginning of each ramp is T- ts+tt. The first three assumptions yield the following general relationships for the 2nd-, 3rd-, and 5th-order structure functions: (Alf = (AfJ + (ALy, (ATj = (KtJ, (3.1) (AT? = 10(A~fJ (KtJ + (AfJ. Chapter 3. Ramp model 42 M 0 0 MAt/tt 0 < -M+MAt/t • -M .z: Fig. 3.1. Temperature ramp model ofVA showing definitions ofM, ts, tT, and rand Tc(t) and ATc(t), for 0 <At<ts. Combining the ramp model in Fig. 3.1 with the temporal averaging procedure given by (AfJ^-JAATJdt (3.2) yields the following equations for the 2nd-, 3rd-, and 5th-order coherent structure functions (similar expressions exist for other values of«, but only these three are used to calculate M and t): Chapter 3. Ramp model 43 (A7/c)" = (3.3) for 0 < Ar < ts. For At« tr, Eqs. (3.3) become (ATC)" = (-\)nM"AtIT, n = 2,3,or 5, (3.4) so that (A7^ )" in this range is a linear function of At for all «. After combining Eqs. (3.1) and (3.4), VA arrived at the following equations for Mand T. With M and T known, the linearized coherent structure functions can be calculated for all A* and n using Eq. (3.4). Although Eq. (3.4) should become increasingly more accurate as At decreases, Fig. 2 of VA and our data (Fig. 3.2) show that this is not true for n = 3 at least. The data in Fig. 3.2 are typical of all our above surface measurements (123 half-hour periods above a Douglas-fir forest, 9 10-min periods above the straw mulch, and 9 10-min periods above the bare soil). VA found that for his data the 3rd-order temperature structure function, which as Eqs. (3.1) show are the only one that is directly comparable to measurements, is linearly dependent on At for an intermediate range of A7 only. He did not comment on the increasingly large disagreement as At decreases below this range. M 3 + (10(Ar)2 - (AT)51 (AT)3)M+ 10(AT)3 = 0, (3.5) T=-M3Atl(ATf. (3.6) Chapter 3. Ramp model 44 0.1 -10" P 10 10" 10"' 10" — 1 Bare Soil 1 — — z = 3 cm 15:00-15:10 o September 17,1994 0.01 0.1 1 i _ Straw Mulch z = 9.6 cm _ ' D 14:50-15:00 -August 23, 1994 0.01 0.1 1 i i _ Douglas-fir Forest i —-' ss8**"" z = 23 m 11:30-12:00 -A — I 1 July 19,_ 1990 0.1 1 10 A? (s) Fig. 3.2. Typical plots of measured -(Ar) 3 versus Ar for above the Douglas-fir forest, straw mulch, and bare soil. Also shown is the V A linearized ramp model (dashed lines with unit slope) and his full model (solid lines) calculated as described in the text. The experiments during which the air temperature data were measured are fully described in Chapter 4 and for the forest also in Lee and Black (1993). For the Douglas-fir forest sampling was at 9.9 Flz during daytime only and air temperature was measured with either a 13 urn diameter chromel/constantan thermocouple (z = 23 m, where z is height above ground) or a 3-dimensional sonic anemometer/thermometer (z = 2, 7, 10, and 16.7 m). Tree height was 16.7 m. For the straw mulch and bare soil the highest frequency sampling was at 80 Fiz and air temperature was measured with 25 um diameter Chapter 3. Ramp model 45 chromel/constantan thermocouples. The mulch was applied at a 10 t ha"1 rate and its thickness was 6.6 cm. The 80 Hz measurements were made near midday at only one z, 3 cm above each surface. No data smoothing or filtering were done for any of the three surfaces. The fitting to the measured data in Fig. 3.2 was done following VA. A straight line of unit slope was drawn tangent to -(AT) 3 versus At on a log-log plot. This determined the At at which Eqs. (3.5) and (3.6) were used to calculate M and rfrom measured (AT)2, (AJ) 3, and (AT)5. Also shown is -(AT) 3 calculated from Eqs. (3.3), i.e., VA's model without truncation of terms of order At/tr and higher. It was assumed that 4 = 0.251, which agrees with Qiu et al.(1995), and the same M and rfrom the linear solution were used. For the straw mulch and bare soil, the effect of this truncation is important, the two forms disagreeing in the range where the truncated equation applies. As we shall see, this implies that M and t are not calculated correctly for these surfaces using VA's procedure. (Further difficulties with his method are that Eq. (3.5) does not always have a real root, although this is rare, and calculating TfiromM3 with Eq. (3.6) means that a small error inMleads to a relatively large error in T.) An alternate way of viewing these relations is to plot -(AT) 3 / At versus At (Fig. 3.3). The measurements then exhibit a well-defined maximum at roughly the At at which Eq. (3.4) with n = 3 is tangent to the data in Fig. 3.2. We denote this At by A4*. Chapter 3. Ramp model 46 0 1 1 0.0 0.1 0.2 At (s) F i g . 3.3. Typical plots of measured -(Ar)3 / At versus At for above the Douglas- f i r forest, straw mulch , and bare soi l (same data as i n F i g . 3.2). A l so shown is the V A l inearized ramp model (dashed horizontal lines) and his fu l l model (solid lines) calculated as described i n the text. 3.3. Ramp model with finite microfront time We propose a model in which the relatively rapid change at the end of each ramp is not instantaneous but occurs in a finite microfront time, tf (Fig. 3.4). For simplicity, the ramps are assumed to follow each other without any delay (ts = 0), because including a separation time between ramps does not change the values of -(AT)3 / At. A schematic diagram of a microfront sweeping into a canopy is shown in Fig. 3.5, based on Gao et al.(1989). It shows why the microfront is associated with the large change in temperature Chapter 3. Ramp model 47 at the end of each ramp and that tf is a small fraction of total sweep time. The finite microfront time is typically evident in ramps measured above all three surfaces (Fig. 3.6). T-t{ 0 -MAt S h MAt < T-tf 0 -M(r-At) 0 At M(r-At) 0 -M(r-At) At-t, f For 0<At<L T-t{-At For/f< At< r-t{ f 6 ^  At T-'t{ T For r- tf < At <t T-L 0 At-tf \AtT t-t{ t Fig. 3.4. Temperature ramp model with finite microfront time showing the definition of tc and Te(f) and ATc(t) for 0 < At < t{, t{<At< r-t{, and t-tc <At<r. Chapter 3. Ramp model 48 Fig. 3.5. Schematic diagram of the vertical cross-section of air temperature and wind vectors at one height for a single ramp structure during daytime. Contour lines are temperature and arrows are typical wind vectors near the top of the canopy. The tilted narrow region with dense contours is the microfront (after Gao et al., 1989). Chapter 3. Ramp model 49 Fig. 3.6. Typical air temperature ramp structures for above the Douglas-fir forest, straw mulch, and bare soil from the data sets in Fig. 3.2 (after subtraction of average temperature, T). The time interval between successive data points is 0.101 s for the forest and 0.0125 s for the mulch and bare surfaces. According to Fig. 3.4, ATc(t) varies with the relative magnitudes of At, tf, and x. (The VA ramp model should similarly differ for At > ts but we only needed the A? < ts form.) The new model yields f M Mr At + 1, tf (T-t{) M At A7^(/) = T-tf M At-MT T-t{ (T-tf)t{ M A At, tf 0<t<At, At<t<T-t{, (t-t+tf), T-t{<t<T-t{ + At, T-tf + At<t<T, (3.7) Chapter 3. Ramp model 50 for 0 < At < tt, ' M(r-At) (T-tf) ' M(r-At) Mr Ar c(0 = 0<t<At-t M + ——(t-At + L), At-L<t<At, At T-t( M Mr , At-- — (t-t+tf), r-tf (r-t{)t{ At<t<r-t{, T-tf<t<T, (3.8) for tf<At< t-tf, and AT c(0 = ' M(T-At) (T-t{) ' M(T-At) (T-t{) T ( T - / F X M(r-At) Mr 0<t<At-t{, (t-At + t{), At-tf<t<r-t{, M(T-At) At-Mr (r-tf)t, (t-r+tA, At<t<r-tf, r-tf<t<r. (3.9) for r-tf < At < r. Substituting Eqs. (3.7)-(3.9) into Eq. (3.2) and carrying out the integration yields the following expressions for the 2nd-, 3rd-, and 5th-order temperature structure functions divided by At: 7^ _[(ATJdt At rAt ( _ i r ^ [ ( A £ r ( 1 + ^ ) _ Z l z i ( A l ) 2 ( 1 _ ^ - ^ T t{ ' ' T-tf n +1 t{ ' T-t{ „ M" T(r-At)n + (-\)"(r- At)At"~] n-l t{ r"fn 0< At<tf, (3.10) (-1)" [ r (r-tj n + \At (r-tA -], tf<At<r-tf, M" (r-At)" n-\(T-At)n+] t/"At n + l t"At r -1 { < At < r, with Chapter 3. Ramp model 51 1, n = 2, \-2Atlt, n = 3, (3.11) \-9AtI2T+15(A?/ T)2 /2-5(Ar /rf, n=5. Because the integrations were performed analytically, these structure functions are exact for temperature data that are continuous in time. However, measured data are in discrete form, limited by sampling rate. The integral in Eqs. (3.10) is then approximated as a sum over the measurement period so that, most generally, ( A D " 1 Ktf/jyi A „ , „ . n I [T(ji-j+l + k)-T(ji-j+l)r, (3.12) At At[I(NI 1=1 where N is the total number of data points for the measurement period, j-l is the number of data points skipped when evaluating the sum, /' is the summation index, k = At/Ats, where A4 is the sampling time interval, i.e., k is the number of sampling time intervals in At (which for discrete data are an integer > 1), and I(N I j) is the whole number of times that j divides into N. We compared Eq. (3.12) to the analytical solution with n - 3 for N and j appropriate to our data. Differences were negligible for both j - l , which gives the maximum accuracy because all data points are used, and j = k, which is the case when accumulating and averaging on-line at the optimum sampling rate to avoid storing large amounts of data (Chapter 4). Eqs. (3.10) and (3.11) with n = 3 were fitted for At/r< 0.3 to nearly all available high frequency data for the three surfaces (in addition to the above surface data there were 41, 28, 27, and 26 half-hour periods at z = 2, 1, 10, and 16.7 m, respectively, within the Douglas-fir forest). For a small number of periods (about 5%) both above and within the Douglas-fir forest the fitting was not done because the shape of-(AT) / A* versus At did Chapter 3. Ramp model 52 not look at all like in Fig. 3.3. A standard nonlinear least squares fitting routine (Marquardt-Levenberg algorithm in SigmaPlot, Jandel Scientific Software, without any weighting of data) was used to determine the best M, t, and tf for each measurement period. The r2 values were in the ranges of 0.82-0.98, 0.72-0.97, 0.95-0.99, and 0.93-0.99 for above and within the forest and above the mulch and bare surfaces, respectively. Comparison with the same typical data as in Fig. 3.3 demonstrates that the new model describes the 3rd-order structure function very well for all At, including the maximum and the decline for A* < Atm (Fig. 3.7). Also shown is the full VA model, i.e., the n - 3 expression in Eqs. (3.3), with 4 = 0.251, using M and t determined by fitting the finite microfront time ramp model. These results show that the decrease in modelled -(A7)3 / At for small At is associated with the finite microfront time. The good agreement between both models and the data for At > Atm shows that VA's full model can be used to calculate M and r if fitted to At > Atm data only. However, his linearized theory, given by Eqs. (3.4)-(3.6), overestimates M by 10-30% and overestimates rby a factor of 2-4 (Table 3.1). Some of the error for r is because Eq. (3.6) requires an additional correction factor, as seen next. Chapter 3. Ramp model 53 0.0 0.1 0.2 0.0 0.1 0.2 0.3 0.06 i 1 1 1 -0.00 1 1 1 •—1 0 5 10 15 At (s) Fig. 3.7. Typical plots of measured -{AT f I At versus At for above the Douglas-fir forest, straw mulch, and bare soil (same data as in Fig. 3.3). Also shown is the fitted ramp model with finite microfront time (solid lines) and the full VA ramp model with the same M and rand ts = 0.25r(dashed lines). An alternate way of presenting these results is to normalize both ordinate and abscissa as shown in Fig. 3.8. This collapses the data to the right of the peaks fairly well. Also included is the ocean data of VA, which were read off a scanned and digitized image of his Fig. 3.2 and then treated as for our own data. One evident feature is that the maximum value of [-(AT)31 At]/(]vf/T) is not constant but varies between 0.5 and 1. This variation is not related systematically to surface roughness and remains unexplained. The cube-root of the inverse of the maximum value of [-(AT)31 At]/(A^/f), denoted as % is shown as a function of Atjtfox above surface data (for the forest, calibration days only, Chapter 3. Ramp model 54 see Chapter 4) in Fig. 3.9. This parameter, which is used in the renewal model of Chapter 4, varies by less than 25% from unity. Some of the forest values are less than 1, because variability for At > Atm caused the peak of the fitted model to fall below the measured one. The factor ^contributes to some of the error for rin Table 3.1. At/T Fig. 3.8. Typical plots of normalized measured -(AT)31 At versus normalized At for above the Douglas-fir forest, straw mulch, and bare soil (same data as in Fig. 3.7). The ocean data of V A are included (z = 3.81 m). Also shown is the fitted normalized ramp model with finite microfront time (various lines). Chapter 3. Ramp model 55 Table 3.1. Ratios of M, t, and Mix determined with VA's linearized cubic structure function theory to those determined using the ramp model with finite microfront time above the Douglas-fir forest, straw mulch, and bare soil. Five extreme outliers for r calculated with VA's method were not included in the averages because they were 1-2 orders of magnitude larger than the rest and would have distorted the ratios Bare Soil Straw Mulch Douglas-fir Forest MVA/Mfm 1.19 1.08 1.43 Tyjr^ 2.68 2.27 3.68 (M lr\hl(M lx)(m 044 048 0.39 *Overbar indicates an average over all measurement periods. 1.4 1.2 -1.0 o o 0.8 i 1 O Bare Soil • Straw Mulch A Douglas-fir Forest 0.00 0.02 0.04 0.06 0.08 0.10 m Fig. 3.9. Correction factor y= (M/r"l3)/[-(AT)31 At]V3 at At = Atm versus Atjtfoi above the Douglas-fir forest (z = 23 m, calibration days only, see Chapter 4), straw mulch (z = 9.6 cm), and bare soil (z = 3 cm). Chapter 3. Ramp model 56 3.4. Comparison with ramp detection by wavelet transform Wavelet analysis is used frequently to detect coherent structures in intermittent stochastic data, including turbulence signals (Collineau and Brunet, 1993a and b; Qiu et al., 1995). We used the Mexican Hat (MHAT) wavelet transform to detect ramp structures in our temperature data. The MHAT wavelet, g(a,b,p,t), is defined as the second derivative of a Gaussian function: where a is the (positive) scale dilation parameter that affects the width and amplitude of the wavelet but not its shape, b is the translation parameter that sets the origin of the function, and p is a power coefficient that affects only the amplitude of the wavelet. Following Collineau and Brunet (1993a), we chosep=\. The MHAT wavelet transform, F(a, b), filters a time series, such as T(t), with the wavelet g(a,b,t) at each point b and scale dilation a, i.e., When the MHAT wavelet encounters (through changes in b) a sharp drop in T(t), F(a, b) changes sign with a negative slope. Therefore, every such sign change should indicate a coherent structure. However, if a is too small the wavelet transform identifies small fluctuations in temperature that are associated with random turbulence, while if a is too large only the biggest structures are identified. The optimum a is determined from the wavelet variance, W(d), defined as follows: (3.13) (3.14) Chapter 3. Ramp model 57 W(a)= f [F(a,b)fdb. (3.15) Because W(a) vanishes as a —»0 and a —»°o, there is a maximum, at cr = am, where the MHAT wavelet and T(i) are best correlated (Fig. 3.10). This am is then used in Eq. (3.14) to objectively identify ramp structures. Fig. 3.10. Determination of optimum a = am at the maximum of MHAT W(a), illustrated for the straw mulch. Average T was determined for each measurement period above and within the forest and above the mulch and bare surfaces by dividing the total time by the number of ramps detected. Fig. 3.11 shows typical segments of T(i)-T and corresponding F(am,b) from above the forest, mulch, and bare surfaces. In plotting F(am,b), b is treated as the Chapter 3. Ramp model 58 time variable. Ramp structures are clearly defined at 3 cm above the bare soil and the straw mulch. This agrees with the suggestion of Paw U et al. (1992) that well defined ramps would be evident immediately above smooth surfaces (they failed to see any at z = 1 m above a bare soil). Ramp structures are also clearly defined above the Douglas-fir forest. Collineau and Brunet (1993b) pointed out that the MHAT wavelet technique might miss some structures that are very close to one another or identify too many during long ramp-free periods. Both problems occur in the sample data shown but overall such errors were not very significant. 2 0 -2 Douglas-fir Forest ill •'. m-. i . .. i T • i i 50 100 t(s) 150 200 Fig. 3 .11. Typical segments of air temperature time series (after subtraction of T) and MHAT F(am,b) from the data sets in Fig. 3.2 for above the Douglas-fir forest, straw mulch, and bare soil. Every zero-crossing with a negative slope for F(am,b) signifies a ramp event. Chapter 3. Ramp model 59 Probability distributions of r, determined with the MHAT wavelet transform for all periods above the forest, mulch, and bare surfaces are shown in Fig. 3.12. Since 1/r scales with friction velocity, (Fig. 4.1), the distributions were calculated after normalizing each rby multiplying it by / where is the average of all measurement periods for each surface. The shapes of the probability distributions are similar for all three surfaces and in agreement with those reported by Qiu et al. (1995). Average rfor the forest is about 50 times that for the mulch and bare surfaces and in all cases the average exceeds the most frequent value because of the long distribution 'tail' for large r. 0.0 0.5 1.0 1.5 2.0 2.5 0 25 50 75 100 125 r(s) Fig. 3.12. Probability distributions of T determined with the MHAT wavelet transform above the Douglas-fir forest, straw mulch, and bare soil. Average rfor each surface is also indicated. Chapter 3. Ramp model 60 Despite the large difference in scale between the Douglas-fir forest and the straw mulch (a factor of 253 for canopy height, h), \/T measured above these surfaces with the MHAT wavelet transform scales remarkably well against ujh, where Wh is the average horizontal wind speed at the top of the canopy (Fig. 3.13). Vertical profiles of wind speed u, including wh, were measured with sensitive cup anemometers for the Douglas-fir forest (Lee and Black, 1993) and with home-made miniature hot wire anemometers for the mulch (Orchansky et al., 1994). According to Raupach et al. (1989), linear stability theory predicts that uh I (rh) = 0.13, although this is normally rounded off to 0.1, as shown. This assumes that Ls = uh/ (du I dz) at z = h is equal to h/2, often a good approximation, and that the horizontal convective velocity for the large eddies is ub. The first assumption is satisfied approximately for the forest but we suspect from the large displacement height (5.6 cm or 0.85/Y) that Ls for the mulch may be smaller than h/2 (the u profile did not have enough vertical resolution to be sure). According to Shaw et al. (1995) the convective velocity at z = h is almost twice Wh- After accounting for these effects, the uh / (rh) in the range 0.1-0.3 indicated is still compatible with linear stability theory as described by Raupach et al. (1989), although they point out a number of reasons that agreement should only be order-of-magnitude anyway. Recent measurements that we made in the wind tunnel with 15 cm high model trees at different densities (see Liu et al., 1996, for a description of the methodology) are also shown, and are in the similar range 0.13-0.25. For the wind tunnel, 1/rwas assumed equal to the peak spectral frequency of u and the Uf,/h in the range 13-23 is even higher than for the mulch. Chapter 3. Ramp model 61 Fig. 3.13. Plot of lit determined with the MHAT wavelet transform versus uh/h above the Douglas-fir forest, straw mulch and model forest. The solid line is the prediction of linear stability theory according to Raupach et al. (1989). According to Raupach et al. (1989), the large turbulent eddies associated with the ramp structures are of the order h in size, which implies that r, and therefore wh / (rh), should not vary with z. Although there is a lot of scatter, this is supported by the Douglas-fir data determined with the MHAT wavelet transform which shows little systematic variation with z, especially at z = 16.7 m (Fig. 3.14). The larger values that are more frequent as z decreases may be because only the biggest eddies are detected with the MHAT technique deep within the canopy. Chapter 3. Ramp model 62 % z = 23 m (s) Fig. 3.14. Comparison between average r determined with the MHAT wavelet transform within and above the Douglas-fir forest The measurements within and above were made simultaneously. The range in which values differ by less than a factor of 2 is indicated. Comparison of r determined with the MHAT wavelet transform and by fitting the ramp model with finite microfront to the 3rd-order temperature structure function for all three surfaces is shown in Figs. 3.15 and 3.16. Agreement is quite good except for about half the data within the forest. It is not clear whether this was mainly due to difficulties with only one of the techniques, or both. The 3rd-order structure function for these points typically displayed at least two maximums (Fig. 3.17), implying different sized ramp structures. Since we generally fitted to the first well-defined maximum, as indicated, T was underestimated relative to the MHAT wavelet transform which we have seen was perhaps biased towards large ramps. Chapter 3. Ramp model 63 % MHAT (s) Fig. 3.15. Comparison between average r determined with the MHAT wavelet transform and T determined by fitting the ramp model with finite microfront time to the 3rd-order temperature structure function for above the Douglas-fir forest, straw mulch, and bare soil. The range in which values differ by less than a factor of 2 is indicated. Chapter 3. Ramp model 64 Fig. 3.16. Same as Fig. 3.15 but for within the Douglas-fir forest. The data point surrounded by a square for z = 7 m is considered in Fig. 3.17. Chapter 3. Ramp model 65 "«> 3 >S2 P < 1 Y 0 0 Douglas-fir Forest, z = 7 m 8:30-9:00, July 28, 1990 Measured Fitted 10 15 20 At (s) 25 30 Fig. 3.17. Variation of measured -(AT f I At with At within the Douglas-fir forest for a time period for which ramp model and MHAT rare in poor agreement (Fig. 3.16). Also shown is the fitted ramp model with finite microfront time. To compare tf determined by fitting the ramp model to the 3rd-order temperature structure function with direct (manual) measurement from ramp structures detected with the MFfAT wavelet transform would have been extremely tedious and was not done. (There were about 550 ramps per 10-min period for the bare and mulch surfaces and about 40 ramps per half hour for the forest.) We did, however, randomly select 10 well-defined ramp structures from one measurement period above each surface (same periods as in Fig. 3.2) for such a comparison (Table 3.2). After normalizing to account for the Chapter 3. Ramp model 66 larger than average size of the 10 selected ramps, agreement is reasonably good between tf determined by both methods. Although the normalization may be questionable, both methods predict similar ratios of tf between the three surfaces. This directly supports the previous result that the decrease of measured -(AT)31 At for small A* is a signature of the finite microfront time in the ramp structures. Table 3.2. Comparison between t{, M , and r determined from the ramp model with finite microfront time for the indicated time periods and L measured directly on 10 selected well-defined ramps in each time period. Normalized L is calculated by multiplying ts from the 10 ramps by the ratio of M from the finite microfront model to M from the 10 ramps Bare Soil z = 3 cm 15:00-15:10 September 17, 1994 Straw Mulch z = 9.6 cm 14:50-15:00 August 23, 1994 Douglas-fir Forest z = 23 m 11:30-12:00 July 19, 1990 Ramp Model tf(s) 0.021 0.057 0.18 M(°C) 1.68 3.17 1.45 t(s) 0.86 1.03 49.4 Measured *Tt (s) 0.038 0.11 0.30 M (°C) 2.45 4.61 2.18 T(S) 1.08 1.20 52.5 Normalized T((s) 0.026 0.077 0.20 *Overbar indicates an average of 10 selected ramps. 3.5. Summary and concluding remarks Chapter 3. Ramp model 67 We have shown that the ramp structure model and theory of VA cannot fully explain measurements of the 3rd-order temperature structure function made above and within a Douglas-fir forest, a straw mulch, and a bare soil. Our measurements show that -(AT)3 / At versus At generally reaches a well-defined maximum at some At = Atm, which was also true of the ocean data reported by VA. Neither his linear expressions nor his complete ramp model can describe this behavior. We have presented a new ramp model with finite microfront time that generally describes -(AT) 3 / At for all At very well. The value of Atm 11 varied between surfaces in a non-systematic manner. Values of M and r determined with the VA linearized structure function expressions, often used in the literature, disagreed with values from the new ramp model. However, his full model agrees if fitted to the 3rd-order structure data for At > Atm. Values of rand U determined by fitting the new ramp model to the 3rd-order temperature structure function for all At were shown to be in good agreement with those determined directly from ramps detected with the MHAT wavelet transform. The only exception was within the forest, especially at the lowest z, which may have been a combination of the inability of the MHAT wavelet transform to detect smaller more frequent ramps and exclusion of less frequent structures when fitting the ramp model to the -(AT) 3 / At data. The good agreement for tf is strong evidence that the microfront time in the model is physically real and that the peak in the 3rd-order structure function is its signature. Our results are in accordance with the ideas in Raupach et al. (1991) that coherent turbulent temperature structures just above and within the roughness elements of rough Chapter 3. Ramp model 68 surfaces are shear driven and of universal character after appropriate scaling. Despite the large differences in scale, ramp frequencies above both the Douglas-fir forest and straw mulch were in remarkably good agreement with linear stability theory as described by Raupach et al. (1989). The straw mulch and bare soil experiments uniquely extend measurements of temperature structure functions and ramp frequency to the smallest scales possible in the field. 3.6. References Brunet, Y. and Raupach, MR., 1987. A simple renewal model for transfer in plant canopies, Abstracts, International Symposium of Flow and Transport in the Natural Environment: Advances and Application, Canberra, 2 pp. Collineau, S. and Brunet, Y., 1993a. Detection of turbulent coherent motions in a forest canopy, Part I: Wavelet analysis. Boundary-layer Meteorol., 65: 357-379. Collineau, S. and Brunet, Y., 1993b. Detection of turbulent coherent motions in a forest canopy, Part II: Time-scales and conditional averages. Boundary-layer Meteorol., 66: 49-73. Gao, W., Shaw, R.H. and Paw U, K.T., 1989. Observation of organized structure in turbulent flow within and above a forest canopy. Boundary-layer Meteorol., 47: 349-377. Chapter 3. Ramp model 69 Lee, X. and Black, T.A., 1993. Atmospheric turbulence within and above a Douglas-fir stand. Part I: Statistical properties of the velocity field. Boundary-layer Meteorol., 64: 149-174. Liu, J., Chen, J.M., Black, T.A. and Novak, M.D., 1996. E-e modelling of turbulent air flow downwind of a model forest edge. Boundary-Layer Meteorol., 77: 21-44. Orchansky, A.L., Lee, X. and Novak, M.D., 1994. Miniature hot wire anemometer to measure very low wind speeds. Preprints, 21st AMS Conf. Agric. For. Meteorol., San Diego, CA, 201-202. Paw U, K.T., Brunet, Y., Collineau, S., Shaw, R.H., Maitani, T., Qiu, J. and Hipps, L., 1992. Evidence of turbulent coherent structures in and above agricultural plant canopies. Agric. For. Meteorol., 61: 55-68. Paw U, K.T., Qiu, J., Su, H.B., Watanabe, T. and Brunet, Y., 1995. Surface renewal analysis: A new method to obtain scalar fluxes without velocity data. Agric. For. Meteorol., 74: 119-137. Qiu J., Paw U, K.T. and Shaw, R.H., 1995. Pseudo-wavelet analysis of turbulence patterns in three vegetation layers. Boundary-Layer Meteorol., 72: 177-204. Raupach, M.R., Finnigan, J.J. and Brunet, Y., 1989. Coherent eddies in vegetation canopies. Proc. Fourth Australian Conf. on Heat and Mass Transfer, Christchurch, NZ, 75-90. Raupach, M.R., Antonia, R.A. and Rajagopalan, S., 1991. Rough-wall turbulent boundary layers. Appl. Mechanics Revs., 44: 1-25. Chapter 3. Ramp model 7 0 Shaw, R.H., Brunet, Y., Finnigan, JJ. and Raupach, M.R., 1995. A wind tunnel study of air flow in waving wheat: Two-point velocity statistics. Boundary-Layer Meteorol., 76: 349-376. Spano, D., Duce, P., Snyder, R.L. and Paw U, K.T., 1996. Verification of structure function approach to determine sensible heat flux density using surface renewal analysis. Preprints, 22nd AMS Conf. Agric. For. Meteorol. Atlanta, GA, 163-164. Van Atta, C.W., 1977. Effect of coherent structures on structure functions of temperature in the atmospheric boundary layer. Arch. Mech., 29: 161-171. Chapter 4. Renewal model 71 Chapter 4 Coherent eddies and temperature structure functions for three contrasting surfaces. Part II: Renewal model for sensible heat flux 4.1. Introduction Our understanding of soil-atmosphere interactions has benefited greatly from recent advances in methodology and instrumentation used to measure fluxes of sensible and latent heat and other scalar fluxes over a variety of land surfaces. However, these fluxes cannot be measured within very dense and short canopies, such as grasses or straw mulches (of particular interest to our research group), with standard approaches such as eddy-correlation, Bowen ratio/energy balance, aerodynamic, and variance methods. Eddy-correlation (Moore, 1986), which is increasingly favored by experimentalists because fluxes are measured directly, cannot be used within grass canopies or straw mulches because current sensors are too large and wind speeds within such canopies are very low. Bowen ratio/energy balance (Fuchs and Tanner, 1970) and aerodynamic methods (Monteith and Unsworth, 1990) are also inapplicable because fluxes are generally not proportional to gradients within canopies (Raupach, 1989). Variance methods (de Bruin et al., 1993) calculate fluxes of sensible and latent heat from standard deviations of temperature and water vapor fluctuations but they can only be used in the inertial sublayer. Chapter 4. Renewal model 72 Organized (or coherent) structures have recently been described in turbulent flows above and within plant canopies (Gao et al, 1989; Paw U et al, 1992). They are responsible for the majority of vertical momentum, heat, and mass transfer (Shaw et al., 1989; Qiu et al., 1995) which provides a means for determining fluxes, as illustrated by the development of surface renewal models (Brunet and Raupach, 1987; Paw U et al., 1995; Spano et al., 1996). In these models, turbulent exchange is idealized as the regular replacement of air in contact with the surface canopy by 'fresh' air from above the canopy. During the relatively long quiescent period between exchanges, air in the canopy is enriched or depleted of momentum, heat, water vapour, and other gaseous components. The replacement with fresh air is associated with a large coherent event which occurs rapidly compared to the length of the quiescent period. The scalar flux density from the surface is then the average rate of change of storage in the canopy volume associated with these events. In this chapter, which is the second part of a study on coherent eddies and temperature structure functions associated with three contrasting surfaces (Douglas-fir forest, straw mulch, and bare soil), we present a new air renewal model that calculates sensible heat flux density, H, at any height, z, either within or above a canopy. The model uses results from the analysis of turbulent temperature structures described in the first part (Chapter 3) and determines H from the exchange of heat at z only, and not from changes of storage in the canopy volume. Standard surface renewal theory is based on a Lagrangian approach (Paw U et al., 1995) while the new model is Eulerian in nature, H being determined as the net vertical flow of heat at the z of interest. Therefore, we Chapter 4. Renewal model 73 interpret the new model as a crude (but accurate) description of the eddy exchange (correlation) process at z. The model is calibrated using very high frequency data and selected days of lower frequency data measured above and within the Douglas-fir forest and above the straw mulch and bare soil. It is then tested with other lower frequency data that encompass the complete range of measured conditions for these surfaces. 4.2. Model derivation Coherent turbulent structures are associated with 'ramp' events in the time series of temperature and other scalars. For unstable conditions, a typical temperature ramp is characterized by a slow, nearly constant rate of increase and a relatively sharp drop (Chapter 3). The increase is associated with the quiescent period during which the air is warmed by small-scale transport (both laminar and turbulent) from canopy elements and the underlying surface. The sharp drop in temperature indicates the occurrence of a large turbulent eddy that replaces the warmed air with cooler air from above. For stable conditions, the air cools during the quiescent period and is replaced by warmer air from above. It is assumed that for each ramp event most of the heat exchange is associated with the large-scale turbulent eddy, with very little occurring during the quiescent period. For a typical measurement period (e.g., a half hour), the average H at any z is the net heat exchange associated with all ramps in this period. This leads to the following equation for H: H= pcpaz— (4.1) Chapter 4. Renewal model 74 where p and cp are the density and specific heat of air, respectively, M and T are the average ramp temperature change and time between ramps, respectively, and a z is the volume of air per unit ground area exchanged on average for each ramp. We assume, therefore, that this volume scales with z. The coefficient a is independent of height, which we will show is confirmed by our measurements, although it varies between canopies. In Chapter 3 it is shown how M and r can be determined from high frequency measurements of air temperature fluctuations. From the cubic temperature structure function we have where T is air temperature, t is time, ATm = T(t+Atm)-T(t), the overbar implies a time average for the measurement period, and Atm is the sampling time interval at which -[(AT)31 Atf3 is a maximum. The coefficient % which corrects for the difference between M/r 1' 3 and the maximum value of -[(AT)31 At]1'3, is in the range 0.9-1.25 for the forest, mulch, and bare surfaces plus the ocean data of Van Atta (1977). Note that for routine application of the model, only -[(AT)31 Atf3 is ultimately required from high frequency temperature data. In most data logging systems -(AT)3 can be accumulated and averaged on-line during sampling, which avoids the need for storing large amounts of data. The average value and range (in brackets) of appropriate sampling rate (1/A m^) determined from the time periods considered in Chapter 3 are 1.2 (0.2-5), 9 (9-11), and 15 (10-26) Hz for the forest, mulch, and bare surfaces, respectively, which should define the (4.2) Chapter 4. Renewal model 75 range for all surfaces. Determination of the required rate for any surface can be done with just a few hours of high frequency monitoring. But the results are not very sensitive to sampling rate if one errs on the low side. In Chapter 3 it is shown that rabove the three surfaces is determined equally well by either direct detection with the MHAT wavelet transform or by fitting the ramp model with finite microfront time to -[(AT)31 At]m versus At data. Both approaches require storage and analysis of high frequency temperature data. Raupach et al. (1989) predicted that within canopies 1/r should scale with maximum wind shear (dw/dz at z = h, where u is mean wind speed and h is canopy height) and that transport of momentum and scalar fluxes in the canopy and roughness sublayer is dominated by eddies of length scale comparable with h while in the inertial sublayer dominant eddies scale with z-d, where d is the displacement height. We assume then that 1/r can be scaled as follows: where is an empirical coefficient and is the friction velocity. Under neutral conditions uj(z-d) is directly proportional to wind shear at any z and ujh is well correlated with maximum wind shear; both forms determine wind shear from measurements at only one z. The roughness sublayer is assumed to be between z = h and z - h+2(h-d) following Sellers et al. (1986); for d = 2/3/?, a standard approximation, the expressions for 1/r are then continuous at z = h+2(h-d). The layer adjacent to the soil within canopies (z < 0.2h) T 1 for z >h + 2(h-d) or z< 0.2//, for0.2h<z<h + 2(h-d), (4.3) Chapter 4. Renewal model 76 is treated the same as the inertial sublayer with and d appropriate to the soil or understory (Lee, 1992; Lee and Black, 1993c; Jacobs et al., 1994). However, 1/ris not necessarily continuous at z = 0.2// and Eqs. (4.3) should be viewed as only valid far from this z. We did not consider a 'matching' expression that would connect the two layers continuously. Substituting expressions for M and rfrom Eqs. (4.2) and (4.3) into Eq. (4.1) yields: H = \ -a(32nrPcp[ (AT)3 I Atf3^3^, for 02h<z<h + 2(h-d), (4.4) -ap2l3ypcp[(AT)3 I Atf3wf for z > h + 2(h-d)ovz< 0.2/?. (z-d) According to the model H is proportional to z in the canopy and roughness sublayers while in the inertial sublayer(s) it is proportional to z / (z - d)m. The empirical coefficient ap2l3y is a common factor in both forms. 4.3. Field experiments 4.3.1. Douglas-fir forest Micrometeorological measurements were made in a Douglas-fir forest near Courtenay on Vancouver Island, British Columbia, during July 19-20 and July 26-August 1, 1990 (Lee and Black, 1993a and b). The period from July 6 to August 1 was rainless and the trees were moderately stressed with Bowen ratios between 1 and 2. The stand, Chapter 4. Renewal model 77 which was planted in 1962 and thinned and pruned in 1988, had a (projected) leaf area index of 5.4, a height of 16.7 m, and was located on a 5° slope. Air temperature was measured with fine-wire thermocouples (chromel/constantan, 25 um in diameter) at z = 0.9, 2, 4.6, 7, 10, 12.7, 16.7 and 23 m throughout the experiment. Data were sampled at 10 Hz and averaged on-line half-hourly throughout each day. Friction velocity and H were measured with two eddy-correlation units mounted 1.5 m from a 25-cm wide, 24-m tall guyed triangular open-lattice tower. The first unit, which consisted of a 3-dimensional sonic anemometer (Applied Technologies Inc., model BH-478B/3, 25 cm path length) and a fine-wire thermocouple (chromel-constantan, 13 um in diameter), was mounted permanently at z• = 23 m. The second unit, which consisted of a 3-dimensional sonic anemometer/thermometer (Applied Technologies Inc., model SWS-211/3V, 10 cm path length), was operated at z = 2, 7, 10, and 16.7 m for two or three days at each level during the experiment. All eddy correlation data were sampled and recorded at 9.9 Hz during daytime only. The maximum value of -(AT)3/At was determined from the eddy correlation temperatures by varying At until A/ m was found, as shown in Chapter 3. Subsidiary data included net radiation flux density, Rn, measured with a net radiometer (Swissteco Instruments, model S-l) at z = 24 m, and soil heat flux density, G 0 , measured with a pair of commercial heat flux plates (Middleton Instruments, model F) and a pair of home-made plates placed at 3 cm depth and corrected for heat storage above this depth (Lee and Black, 1993b). There were 9 measurement days, yielding 41, 28, 27, 26, and 123 half-hour periods at z = 2, 7, 10, 16.7, and 23 m, respectively. Calibration days were selected Chapter 4. Renewal model 78 randomly so that there was one day for each z. Calibration of /? and y (Chapter 3 and Table 4.1) was done with data measured at z = 23 m only while or was calibrated at each z. The remaining data were used for model testing. Table 4.1. Air renewal model calibration (J3 and a) and testing statistics for the Douglas-fir forest, straw mulch, and bare soil. Al l linear regressions were forced through zero. The n indicates the number of measurement periods (half-hour except for /? for the mulch and bare surfaces, which were 10 min) Calibration z (m) p r2 n Douglas-fir Forest 23 0.705 0.052 55 Straw Mulch 0.09 0.538 0.288 9 Bare Soil 0.03 Calibration 0.398 0.273 Test 9 z(m) a r2 n r2 n Douglas-fir 2 0.550 0.318 14 0.829 27 Forest 7 0.502 0.488 15 0.659 13 10 0.546 0.709 13 0.495 14 16.7 0.520 0.885 16 0.966 10 23 0.517 0.846 58 0.843 65 Straw 0.076 0.542 0.973 48 0.976 48 Mulch 0.096 0.509 0.976 48 0.975 206 0.111 0.526 0.972 48 0.978 48 0.126 0.465 0.972 48 0.982 48 Bare 0.01 0.724 0.965 48 0.990 48 Soil 0.03 0.684 0.974 48 0.910 671 0.05 0.663 0.976 48 0.990 48 0.07 0.691 0.975 48 0.989 48 Chapter 4. Renewal model 79 4.3.2 Straw mulch and bare soil Experiments were conducted on adjacent straw mulch and bare plots at the University of British Columbia Plant Science Research Station in Vancouver during July 19-September 18, 1994. This was the third successive year of such measurements. The straw mulch plot was a circular area 14 m in diameter and the bare plot was about 25 by 25 m. Site preparation consisted of ploughing, levelling, and packing and the site was surrounded by generally non-irrigated bare and cropped fields. Barley straw was applied at 10 t ha*1 to the mulch plot on July 22, resulting in a layer 6.6 cm thick, and measurements were made simultaneously at both plots from August 7-September 1 (July 22-August 7 was used for instrument set up and for measurements in a small bare opening located near the middle of the mulch plot). Most of this period was rainless and the mulch was quite dry during the daytime, except early in the morning when it was still wet with dew. On the night of August 28 the mulch was wetted completely by sprinkler irrigation and then allowed to dry out naturally until the evening of September 1, after which the mulch was removed. Therefore, during July 19-21 and September 2-18 the whole site (about 25 by 40 m) was bare and intensive bare soil measurements were made without (possible) interference from the mulch. Up until August 1 the bare plot, which was considered as a reference for the mulch, was irrigated daily in an effort to maintain evaporation at potential rate. This was abandoned after this date because the high potential evaporation rates coupled with the sandy loam soil texture made it fruitless. Chapter 4. Renewal model 80 Air temperature was measured with fine-wire thermocouples (chromel/constantan, 25 um in diameter) at various locations (above and within the mulch, in the small bare opening in the mulch plot, and above the bare soil), sampling rates, and recording rates for both surfaces. The cubic structure function, -(AJ) , was often calculated on-line with At = 0.1 s and recorded along with other averages. As shown above, this At was near (mulch) or somewhat greater (bare) than A*m for both surfaces. Friction velocity was calculated with (Stathers et al., 1988) u^kuj{[\n(zx-d)lz0]-rm}, (4.5) where k is von Karman's constant, ur is the wind speed at reference height zr, z0 is the surface roughness length, and is the diabatic profile function for momentum, given by f21n[(l + x)/2]-l-ln[(l-r-x2)/2]-2arctanx-i-^/2, unstable conditions, Y = < (46) m (-4.7 ,^ stable conditions, where x = (1 - 1 6 £ ) 1 / 4 , C, = zxl Z^ 0 = -kzrgHI (pcpTul), JMo is the Monin-Obukhov length, J is the mean absolute temperature between d+z0 and zt, and g = 9.8 m s"2 is the gravitational acceleration. The values of z0 and d were determined from mean horizontal 'cup' wind speed profiles measured on a few days in 1994 using home-made miniature hot wire anemometers (Orchansky et al., 1994). The measurements were made simultaneously at four different z, resulting in at least three days data at z = 7.6, 8.6, 9.6, 10.6, 11.1, 11.6, 12.6, and 13.6 cm above the straw mulch and at z = 4, 7, 10, and 13 cm above the bare soil (Chapter 6). Only wind speeds for nearly neutral conditions, i.e., at dawn (6:00-7:00 PST) and dusk (17:00-18:00) were used to calculate z0 and d. The Chapter 4. Renewal model 81 standard technique of fitting to the logarithmic law (Eq. (4.5) with *Fm = 0) was used, and the fits were excellent (r2 > 0.97). The values of z0 and d were 0.0052 and 0.056 m for the straw mulch and 0.0050 and 0 m for the bare soil, respectively. Reference wind speed was measured with a sensitive cup anemometer (C.W. Thornthwaite Assoc., model 901-LED) at zr = 0.57 m. This was outside the boundary layers of both surfaces but similar measurements made at z = 0.24 m were less reliable because of sensor stalling at the lower wind speeds. Eq. (4.5) could not be used explicitly because is in the expression for £. Iteration of Eqs. (4.5) and (4.6) was done by setting *Fm = 0 initially, calculating with Eq. (4.5) and then calculating ¥ m with Eq. (4.6), and then repeating this procedure until convergence was achieved. Measured H was used in the expression for £ for both calibration and testing of the model. Sensible heat flux density above the straw mulch was calculated from measured components of the surface energy balance as follows: H=Rn-G0-LE, (4.7) where LE is the latent heat flux density above the mulch, which is the sum of LE from soil and mulch layers. Net radiation was measured with a net radiometer (Swissteco Instruments, model S-l) mounted at z = 0.5 m near the centre of the mulch plot. Soil heat flux density was measured with a home-made heat flux plate (copper/constantan thermopile wound on a 0.6 by 3 by 10 cm high conductivity epoxy resin plate and sandwiched between anodized aluminum plates using the same epoxy resin) installed at 1 cm depth with corrections for heat storage above the plate made from soil temperature Chapter 4. Renewal model 82 (single 250 |j,m chromel/constantan thermocouple fixed with epoxy resin in 2 mm o.d. by 10 cm long stainless steel tubing) measured at 0.5 cm depth and soil volumetric heat capacity estimated as in Hares and Novak (1992). Latent heat flux density from the soil was measured with an improved tension-plate system (Chapter 2). Gravimetric water contents and measured soil water retention curves (Hares, 1988) showed that the soil in the mulch plot stayed wet enough throughout the experiment that evaporation was always energy-limited, as required by the tension-plate technique. During daytime, LE from the mulch was determined by manually measuring weight loss of six 1 cm thick layers of straw mulch (0.0139 m2 cross-sectional area) stacked in perforated acrylic containers within the mulch (2 replicate profiles). Total weight loss divided by time interval between weighings (generally 1-2 hours) and cross-sectional area was converted to LE by multiplying by the latent heat of vaporization, Z, = 2.45xl06J kg"1. During nighttime, LE above the mulch was measured using the Bowen ratio/energy balance method. The Bowen ratio was calculated from vertical air temperature and vapour pressure differences measured between z = 6.6 and 9.6 cm, i.e., just above the mulch, using the 25 fim fine-wire thermocouples and capacitance-type humidity sensors (Vaisala, model HMM-20D, with 75 |im chromel/constantan thermocouple installed within its protective permeable cap, painted white with standard membrane filter removed, to convert relative humidity to vapour pressure), respectively. Both sensors were naturally ventilated and fixed at the two heights. The Bowen ratio/energy balance method agreed well with the combined tension-plate and mulch weight loss method on average for nighttime (we only measured total mulch weight loss Chapter 4. Renewal model 83 between dawn and dusk). The two methods did not agree during daytime, which was ascribed to errors in the Bowen ratio/energy balance method because of the large difference in source height for H and LE; at night this was not a problem because the sink for both H and LE was near the top of the mulch. Sensible heat flux density above the bare soil was measured using the Bowen ratio/energy balance method with air temperature and vapour pressure differences measured between z = 1 and 5 cm as for above the mulch. This method was in excellent agreement during daytime with the energy balance method using LE measured with the tension-plate system when the bare soil was wet and evaporation was energy-limited. Discrepancies at night were ascribed to normal uncertainty in the Bowen ratio/energy balance technique when fluxes and gradients are small. Net radiation and Go for the bare soil were measured as for the mulch plot. Except as otherwise indicated, all data were sampled at 10 Hi; throughout the day and averages and other statistics recorded every 10 min (although reporting herein is half-hourly unless indicated otherwise). For the straw mulch, there were 6 days with all required measurements yielding a total of 254 half-hour periods at z = 9.6 cm and 96 half-hour periods at z = 7.6, 11.1, and 12.6 cm. For the bare soil, there were 15 days with all required measurements yielding a total of 719 half-hour periods at z = 3 cm and 96 half-hour periods at z = 1, 5, and 7 cm. In addition, there were 9 10-min measurement periods on 1 or 2 days for each surface during which air temperature was sampled and recorded at 80 Hz. These were done near midday at z = 9.6 and 3 cm for the mulch and bare surfaces, respectively. Calibration of ft and (^Chapter 3 and Table 4.1) was done with all available Chapter 4. Renewal model 84 80 Hz data. Calibration of a was done using one selected day for each surface on which -(AT)3 data were available at all four z above the surfaces. The remaining data were used for model testing. 4.4. Model calibration 4.4.1. Determination of (5 The coefficient /? for each surface was obtained from the slope of a linear regression of ramp frequency, 1/T, against either u*/h (forest) or u% I (z-d') (mulch and bare surfaces), where for the bare soil d' = d = 0 m while for the mulch d" - 2(h - d) is such that z-d' = h at z = h+2(h-d), i.e., 1/r is continuous at the top of the roughness sublayer. This modification to Eqs. (4.3) for the mulch was done because with the measured d = 0.056 m, z-d was much smaller than h just above the roughness sublayer so that the unmodified equations were clearly incorrect. Furthermore, the top of the roughness sublayer is at z = 0.086 m which places z = 0.096 m in the inertial sublayer although in Chapter 3 it is shown that the lit from this height scales as in the roughness sublayer. Since there is some uncertainty about the precise height of the roughness sublayer, estimates ranging up to z = 2h (Raupach et al., 1989), with d' = 2(h- d) = 2.0 cm there is little difference between roughness and inertial sublayer formulations in the Chapter 4. Renewal model 85 first few cm above the roughness sublayer and correct scaling is achieved for large z. The regression line was forced through zero (Fig. 4.1; r 2 coefficients in Table 4.1). The values of 7 were determined with the MHAT wavelet transform (Chapter 3). Fig. 4.1. Calibration of ft according to modified Eqs. (4.3) as described in the text for the Douglas-fir forest, straw mulch, and bare soil. Also shown are fitted straight lines. All P values (Table 4.2) are of the same order of magnitude (within a factor of 2) but they suggest an increase with surface roughness and/or higher values in the roughness sublayer compared to the inertial sublayer. The r2 coefficients are low, however, and there is quite a bit of scatter, especially for the forest. This is typical of such data in the literature (Qiu et al., 1991). As we shall see, the final model agrees with measured H better than might be expected from the scatter in Fig. 4.1, suggesting that much of this scatter is inherent in the direct measurement of r, which is avoided in the final model Chapter 4. Renewal model 86 because Eqs. (4.3) are substituted. The /? values estimated from Fig. 4.5 of Qiu et al. (1991) are roughly 0.06, 0.1, and 0.3 for the maize, orchard, and forest surfaces, respectively, which are 3-10 times lower than our values. In a later chapter, Qiu et al. (1995) show that when the scaling is expressed in terms of % lh, where un is the wind speed at h, 1/Tfalls below the prediction of linear stability (Raupach et al., 1989) for large U\Jh. This disagrees with our findings (Chapter 3). Collineau and Brunet (1993) report /J = 0.56 for a pine forest which agrees with our results. Table 4.2. Average coefficients a, ft, and /(from Chapter 3) and the combined coefficient a/32ny for the Douglas-fir forest, straw mulch, and bare soil a P r ap2l'y Bare Soil 0.691 0.398 0AU Straw Mulch 0.511 0.538 1.175 0.397 Douglas-fir Forest 0.527 0.705 1.001 0.418 4.4.2. Determination of a The coefficient a for each surface at various z was obtained from the slope of a linear regression (forced through zero; r 2 coefficients in Table 4.1) of measured //versus the appropriate right-hand-side of Eqs. (4.4) with a = 1 for all half-hour measurement periods on the selected calibration days. Fig. 4.2 shows that oris virtually independent of z Chapter 4. Renewal model 87 for all three surfaces. For the Douglas-fir forest H varied by more than a factor of 3 between above and within canopy values. For z = 2 m (0.12/?) in the forest the second of Eqs. (4.4) was used with it* = crw/1.25, where c w is the measured variance of vertical wind speed, because measured shear stress was negative (Lee and Black, 1993a). This made a significant difference as a calculated with the first of Eqs. (4.4), used at all other z for the forest, is 1.62. For the straw mulch, the first of Eqs. (4.4) was used at z = 7.6 cm while the second equation was used at all other z. For the bare soil, the second of Eqs. (4.4) was used at all z. The a reported in Table 4.2 for each surface is an average of the values shown in Fig. 4.2. 10 o Bare Soil • Straw Mulch w 2D . 4 Douglas-fir forest - 8 o A 0.0 0 0.0 0.5 1.0 a Fig. 4.2. Calculated a (calibration) versus z/h ^Douglas-fir forest and straw mulch) or versus z (bare soil). Vertical lines are the average values for each surface. Chapter 4. Renewal model 88 The a values are about a factor of 2 less than those reported by Spano et al. (1996) who calculated M and r using the structure function theory of Van Atta (1977). Some of their values were greater than 1, which according to our interpretation does not make physical sense. According to Chapter 3, the Van Atta (1977) method underestimates Ml r by about a factor of 2 which would result in a values about 2 times too large. With these considerations, the a values in Table 4.2 are in rough agreement with those of Spano et al. (1996). Diurnal variations of measured and modelled H on the calibration days are presented in Figs. 4.3 (forest) and 4.4 (mulch and bare surfaces). Model calculations in 600 -400 -~i r July 20, 1990 A A 0 V <?. 200 h s 23 m i 1 r July 28, 1990 23 m i 2m_ Douglas-fir Forest August 1, 1990 4 . ^ 12 16 20 8 12 t (h PST) 16 20 Fig. 4.3. Measured (symbols) and modelled (lines) half-hour H versus t for the Douglas-fir forest on the calibration days. Model uses average a in Fig. 4.2. Also shown is measured Rn-G0 (filled triangles). Chapter 4. Renewal model 89 these figures use the average or in Table 4.2 at all z, and not the calibrated a shown in Fig. 4.2. Because the variation of a with z is small, this makes little difference but agreement for diurnal variations with the calibrated values is a little better than shown. The model is in excellent agreement with the measurements on a half-hourly basis despite large changes in H, u, and atmospheric stability. It is interesting that for the forest both measured and modelled H vary considerably from half hour to half hour even on clear days when Rn-Go shows little such variation. According to Lee and Black (1993b), at the top Fig. 4.4. Measured (open circles) and modelled (lines) half-hour H versus t for the straw mulch and bare soil on the calibration days. Model uses average values of a shown in Fig. 4.2. Also shown is measured Rn-G0 (filled triangles). Chapter 4. Renewal model 90 and above the forest this is a symptom associated with failure to achieve energy balance closure using the eddy correlation technique, which occurred on many days during the study. They did not attribute this to errors in measured H but to the inability of a single point measurement to represent the forest surface adequately. 4.4.3. Combined coefficient ap2l3y Table 4.2 shows that the combined coefficient afi2ny that appears in both forms of Eqs. (4.4) is roughly constant at about 0.4 for all three surfaces. This result is striking considering that vertical scales vary by 2-3 orders of magnitude between the bare soil and forest, and measurements are from both canopy and inertial sublayers. The similarity to von Karman's well known constant, k, is provocative but is probably coincidental, since k is associated with turbulence in the inertial layer only. We do not have a physical argument that directly connects afi2l3y with k. In any event, the apparent universality of apmy makes application of Eqs. (4.4) particularly simple. 4.5. Model tests We tested the model for the three surfaces with data from all available days other than those used for calibration using the average ap2/3y appropriate to each surface. For the forest, this was not a strong test as meteorological conditions were similar throughout Chapter 4. Renewal model 91 the experiment. Measured and modelled diurnal variations of H (Fig. 4.5) compare generally as well or better than for the calibration days, as also indicated by the regression coefficients in Table 4.1. Note that daytime H > 0 at all z in the forest. According to Lee and Black (1993b), potential air temperature, 9= T+Tz , where r= 0.01 °C m"1 is the adiabatic lapse rate, generally increased with z for 4.6 m < z < 10 m, so that heat flow was 'counter-gradient'. The air renewal model predicts upward heat flow, as measured, which places a lower limit on the size of the average eddy causing the exchange (Fig. 4.6). The minimum height of the exchange eddy is about 10 m, since the difference in average 0 between z = 7 and 16.7 m is approximately equal to M. If some mixing of the air occurs during the exchange then the vertical dimension would be greater. 600 400 200 0 I I S3 &3 July 26, 9^90 July 27, 1990 23 m 2 m July 30, 1990 Douglas-fir Forest July 30, 1990 8 12 16 20 8 12 r(hPST) 20 Fig. 4.5. Difference of # between z = 7 m and indicated height above it versus M at 7 m calculated by fitting the ramp model with finite microfront time to the cubic temperature structure function for the Douglas-fir forest on July 27 and 28, 1990. Only data such that TXom > Tlm > T4.6m and H > 0 are shown. Chapter 4. Renewal model 92 < 0.0 0.5 1.0 M a t z = 7 m ( ° C ) Fig. 4.6. Measured (symbols) and modelled (lines) half-hour H versus t for the Douglas-fir forest on the test days (one day not shown). Model uses average Ocp2ny in Table 4.2 for the forest. Also shown is measured Rn-G0 (filled triangles). Fig. 4.7 shows measured and modelled half-hour H above the mulch for four consecutive mostly clear days following wetting of the mulch with sprinkler irrigation. Surface conditions in this period were very different from the calibration day which provides a stronger test of the model. Agreement is excellent between measurements and model during both daytime and nighttime although the model overestimates daytime H on day 1 and underestimates it on day 4 by about 10%. Both measurements and model show that daytime H increased as the mulch dried out, so that on the last day it almost equaled Rn-Go, and that H was negative at night. The regression coefficients of a direct Chapter 4. Renewal model 93 comparison between measured and modelled H (forced through zero) on all available test days (Table 4.2) are similar to the calibration values. / (h PST) Fig. 4.7. Measured (symbols) and modelled (lines) half-hour H versus / for the straw mulch on four successive test days (11:00, August 29 to 18:00, September, 1, 1994) following overnight sprinkler irrigation of the mulch. Model uses average a/3my in Table 4.2 for the straw mulch. Also shown is measured R„-G0 (filled triangles). Fig. 4.8 shows measured and modelled half-hour H above the bare soil for the same four successive days as in Fig. 4.6. Surface conditions were only slightly different during this period from the calibration days and so the test is not as strong as for the mulch. Agreement is excellent during the daytime but not as good at night, although H is small then in any case. Comparison of the Bowen ratio/energy balance method with our improved tension-plate system when the soil was wet showed that the former was often in error at night (Chapter 2), which was attributed to the usual uncertainties of the method Chapter 4. Renewal model when gradients and fluxes are small and Bowen ratio is near -1. Except for z = regression coefficients in Table 4.1 are similar to the calibration values. 94 3 cm, the / (h PST) Fig. 4.8. Same as Fig. 4.7 but for the bare soil. A further partial test of the model is afforded by the ocean air temperature data presented by Van Atta (1977). As shown in Chapter 3, these data are described very well by the ramp model with finite microfront time which after fitting to his -(AT) 3 /At versus At data yield M = 0.21°C, r = 2.93 s, and / = 0.98. Determination of was done simultaneously with zo by solving Eq. (5.5) with d = 0 and *Fm = 0 and z0 = 0.0l5u2Jg (4.8) given by Charnock (1955). According to Van Atta (1977), ur = 4.95 m s'1 at zr = 3.81 m. The model with afivly = 0.4 predicts H = 35 W m"2, which is in the range 15-55 W m"2 measured by Hold and Raman (1986) for the ocean (Arabian Sea). Chapter 4. Renewal model 95 4.6. Sensible heat flux profiles within the mulch and a bare opening in the mulch Typical daytime and nighttime vertical profiles of H within the straw mulch predicted using Eqs. (4.4) are shown in Figs. 4.9 and 4.10, respectively. The coefficient ap2ny = 0.397 was used, as for above the mulch (Table 4.2). For z < 0.2/7, measured was divided by 3 which was a rough estimate since turbulence was not measured within the mulch. Also shown are profiles of H due to molecular diffusion, calculated from the measured profile of T as H = -pcp DdT/dz, where D = 2.2 x 10"5 m2 s"1 is the thermal diffusivity of still air, profiles of total H, equal to the sum of the air renewal and molecular diffusion profiles, and profiles of measured T (differences between 6 and T are significant only for the forest). Average wind speed within the mulch measured with the home-made hot wire anemometers varied from 0.1 to 0.3 m s"1 from the bottom to the top of the mulch for the daytime period and from 0.07 to 0.15 m s"1 for the nighttime period. Average wind speed at zr = 0.57 m was 2.1 and 0.9 m s"1 for these respective periods. There are no direct measurements of H available for comparison. The daytime profile of T shows a strong inversion throughout all but the top 15% of the mulch. Total H is negative for the lowest 40% of the mulch and positive elsewhere. Therefore, similar to the Douglas-fir forest, counter-gradient flow occurs in the middle and upper half of the mulch. Air renewal H is positive at all measurement heights except z = 1.1 cm, where it is slightly negative (this was a consistent feature of the daytime results). Chapter 4. Renewal model 96 Molecular diffusion is important in the bottom 60% of the mulch, becoming rapidly insignificant as total H increases rapidly with z above this layer. 2 1 0 0 100 200 20 30 40 H(Wm2) T(°C) Fig. 4.9. Daytime vertical profiles of predicted air renewal (dashed line), molecular diffusion (dotted line), and total (solid line) H within the straw mulch as described in the text. Also shown is the concurrent vertical profile of measured T. The nighttime profile of T is reversed, showing a strong lapse rate throughout the mulch. Total H is positive throughout most of the mulch, counter-gradient flow being confined to the upper 15%. Air renewal H is negative at all measurement heights except at z = 1.1 cm, where it is slightly positive. Molecular diffusion is significant throughout the mulch. 1 1 i r 12:30-13:00, August 23, 1993 Within and Above Straw Mulch Chapter 4. Renewal model 97 Considering the daytime profile of T, the air renewal H is consistent with the idea that large-scale eddies of vertical dimension of order h cause most of the heat transfer within the mulch. Clearly, if the transfer was dominated by smaller-scale eddies the sign of air renewal H would be reversed above z = 1.1 cm. Similar remarks apply to the nighttime profile for 0.7/7 < z <h but below z = OJh the results cannot by interpreted in this way because Tin the mulch is greater than Tabove, at least to z = 1.9/7, and yet air renewal H < 0 (but very small, i.e., < 5 W m"2). 3:30-4:00, August 24, 1994 Within and Above Straw Mulch 2 0 1 -20 -10 #(Wm"2) 0 10 15 T(°C) Fig. 4.10. Same as Fig. 4.9 but for nighttime. The daytime profiles within the mulch are in contrast to profiles measured similarly in the centre of an 18 cm diameter circular bare opening located near the middle of the mulch plot (Fig. 4.11). This was part of a study of micro-scale advection which the results Chapter 4. Renewal model 98 of Hares and Novak (1992) suggested was potentially important in strip tillage. The H values in the opening were calculated as for within the mulch. 2 1 0 0 20 40 60 30 35 H(Wm2) T(°Q Fig. 4.11. Same as Fig. 4.9 but for the centre of an 18 cm diameter circular bare opening in the straw mulch. The corresponding measured (energy balance method) H above the surrounding mulch was 280 Wm"2. The profile of T shows a positive lapse rate for z < 2.2 cm, a slight inversion for 2.2 < z < 4.4 cm, and a positive lapse rate for z > 4.4 cm. Total and air renewal H are positive for all z, and strongly increase with z as within the mulch. Molecular diffusion is only significant for z < 1.1 cm. Therefore, counter-gradient flow also occurs in this case at about the same z as within the mulch. The major difference between the opening and J i i Chapter 4. Renewal model 99 within the mulch occurs near the soil surface; in the opening total H = 29 W m"2 while in the mulch total H=-6W m"2. The positive value of H near the surface of the opening is in contradiction with H determined with the energy balance method using independent measurements of Rn, Go, and LE that yields H = - 16 W ra"2 for this time period which was typical of such measurements for previous years (Novak et al., 1994). This suggests that there is a systematic error in our application of the energy balance method to these openings which we are still investigating. 4.7. Summary and concluding remarks We have derived, calibrated, and tested a new air renewal model for sensible heat flux density using data from three surfaces of strongly contrasting vertical scale and turbulent flow regime. The results show that the model determines H remarkably well in the inertial sublayer and within the canopy, for both stable and unstable atmospheric conditions. The combined empirical coefficient, apl2/3y « 0.4, that appears in the model varies by less than 10% for different heights and surfaces, even though the factors within it vary significantly between surfaces (but not with z). The model calculates H at any z from the cubic structure function of T measured at a moderately high frequency and from average u* for the time period of interest. The cubic structure function can be accumulated and averaged on-line so that storage of large amounts of data are not necessary. Therefore, the model has a particularly simple and apparently universal form, Chapter 4. Renewal model 100 and its routine use for measuring H, or the flux of any scalar, is convenient and relatively cheap. It would be an attractive method for measuring vertical profiles and horizontal variability within and above canopies because many sensors could be deployed and monitored easily. The physical interpretation of the model given in the derivation may not be the best. Instead of interpreting az as the volume of air per unit ground area exchanged per rarrip, a z/r can be interpreted as the average vertical exchange velocity associated with each ramp. Since the exchange actually occurs in a small time interval, 4, at the end of each ramp (ts is larger than 4, the microfront time described in Chapter 3, but much smaller than T) then H=pcpMwe(tS/T) (4.9) where we = az/ts is the effective vertical exchange velocity during the coherent event. Further work is needed to test whether Eq. (4.9) represents a more fundamental form of the model that roughly describes the eddy exchange and correlation process of turbulent transfer. We are undertaking further tests of the model in conjunction with our studies of more sustainable forest harvesting strategies in the B.C. interior (Sicamous Creek) and of heat, water vapour, and carbon fluxes in a deciduous stand in the boreal forest of Saskatchewan (BOREAS). 4.8. References Chapter 4. Renewal model 101 Brunet, Y. and Raupach, MR., 1987. A simple renewal model for transfer in plant canopies. Abstracts, International Symposium of Flow and Transport in the Natural Environment: Advances and Application, Canberra, 2 pp. Charnock, H., 1955. Wind stress on a water surface. Q.J.R. Meteorol. Soc, 81: 639. Collineau, S. and Brunet, Y., 1993. Detection of turbulent coherent motions in a forest canopy, Part II: Time-scales and conditional averages', Boundary-Layer Meteorol., 66: 49-73. de Bruin, H.A.R:, Kohsiek, W. and van Den Hurk, B.J.J., 1993. A verification of some method to determine the fluxes of momentum, sensible heat, and water vapour using standard deviation and structure parameter of scalar meteorological quantities. Boundary-Layer Meteorol., 63: 231-257. Fuchs, M. and Tanner, C.B., 1970. Error analysis of bowen ratios measured by differential psychrometry. Agric. Meteorol., 7: 329-334. Gao, W., Shaw, R.H. and Paw U, K.T., 1989. Observation of organized structure in turbulent flow within and above a forest canopy. Boundary-Layer Meteorol., 47: 349-377. Hares, M.A., 1988. Effects of mulching on the surface energy balance and soil thermal regimes. Ph.D. Thesis, University of British Columbia, Vancouver, British Columbia. Hares, M.A. and Novak, M.D., 1992. Simulation of surface energy balance and soil temperature under strip tillage: II. Field test. Soil Sci. Soc. Am. J., 56: 29-36. Chapter 4. Renewal model 102 Hold, T. and Raman, S., 1986. Variation of turbulence in the marine boundary layer over the arabian sea during Indian Mnsoon (MONEX 79). Boundary-Layer Meteorol., 37: 71-87. Jacobs, A.F.G., van Boxel, J.H. and Shaw, R.H., 1994. Wind speed and air temperature characteristics within a dense vegetation canopy. Preprints, 21st AMS Conf. Agric. For. Meteorol., San Diego, CA, 309-312. Lee, X., 1992. Atmospheric turbulence within and above a coniferous forest. Ph.D. Thesis, University of British Columbia, Vancouver, British Columbia. Lee, X. and Black, T.A., 1993a. Atmospheric turbulence within and above a douglas-fir stand. Part I: Statistical properties of the velocity field. Boundary-Layer Meteorol., 64: 149-174. Lee, X. and Black, T.A., 1993b. Atmospheric turbulence within and above a douglas-fir stand. Part II: eddy fluxes of sensible heat and water vapour', Boundary-Layer Meteorol., 64: 369-389. Lee, X. and Black, T.A., 1993c. Turbulence near the forest floor of an old-growth Douglas-fir stand on a south-facing slope. Forest Sci., 39: 211-230. Monteith J.L. and Unsworth M.H., 1990. Principles of environmental physics. 2nd edition, Edward Arnold, Hodder and Stoughton, London, 291pp. Moore, C.J., 1986. Frequency response corrections for eddy correlation systems. Boundary-Layer Meteorol., 37: 17-45. Chapter 4. Renewal model 103 Novak, M.D., Chen, W.J., Orchansky, A.L. and Ketler, R., 1994. Micro-scale advection to a circular bare wet opening in a straw mulch. Preprints, 21st AMS Conf. Agric. For. Meteorol., San Diego, CA, 52-55. Orchansky, A.L., Lee, X. and Novak, M.D., 1994. Miniature hot wire anemometer to measure very low wind speeds. Preprints, 21st AMS Conf. Agric. For. Meteorol., San Diego, CA, 201-202. PawU, K.T., Brunet, Y., Collineau, S., Shaw, R.H., Maitani, T., Qiu, J., and Hipps, L.: 1992. Evidence of turbulent coherent structures in and above agricultural plant canopies. Agric. For. Meteorol., 61: 55-68. Paw U, K.T., Qiu, I, Su, H.B., Watanabe, T. and Brunet, Y., 1995. Surface renewal analysis: a new method to obtain scalar fluxes without velocity data. Agric. For. Meteorol., 74: 119-137. Qiu J., Shaw, R.H. and Paw U, K.T., 1991. Comparison of turbulence statistics and structures at four vegetation canopies. Preprints, 20th AMS Conf. Agric. For. Meteorol., Salt Lake City, Utah, 66-67. Qiu J., Paw U, K.T. and Shaw, R.H., 1995. Pseudo-wavelet analysis of turbulence patterns in three vegetation layers. Boundary-Layer Meteorol., 72: 177-204. Raupach, M.R., 1989. A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies. QJ.R. Meteorol. Soc, 115: 609-632. Raupach, MR., Finnigan, J.J. and Brunet, Y., 1989. Coherent eddies in vegetation canopies. Proc. Fourth Australian Conf. on Heat and Mass Transfer, Christchurch, NZ, 75-90. Chapter 4. Renewal model 104 Sellers, PJ., Mintz, Y., Sud, Y.C. and Dalcher, A., 1986. A simple biosphere model (SiB) for use within general circulation models. J. Atmos. Sci., 43: 505-531. Shaw, R.H., Paw U, K.T. and Gao, W., 1989. Detection of temperature ramps and flow structures at a deciduous forest site. Agric. For. Meteorol., 47: 123-138. Spano, D., Duce, P., Snyder, R.L. and Paw U, K.T., 1996. Verification of structure function approach to determine sensible heat flux density using surface renewal analysis. Preprints, 22nd AMS Conf. on Agric. For. Meteorol., Atlanta, GA, 163-164. Stathers, R.J., Black, T.A. and Novak, M.D., 1988. Modelling surface energy fluxes and temperatures in dry and wet bare soils. Atmosphere-Ocean, 26:59-73. Van Atta, C.W., 1977. Effect of coherent structures on structure functions of temperature in the atmospheric boundary layer. Arch. Mech., 29: 161-171. Chapter 5. Radiation distribution 105 Chapter 5 Simulating radiation distribution within a straw mulch 5.1. Introduction Crop residues conserve soil and water effectively when left on a soil surface as mulch, and are valuable animal foods, fuels, and manufactured materials when harvested as hay (Unger, 1994). The effectiveness of mulching on soil and water conservation, is largely controlled by radiation distribution and turbulent transfer processes in the soil-mulch system. Likewise, the quality of hay is mainly determined by the speed of hay drying, which is also a function of radiation distribution and turbulent transfer processes in the hay layer. As part of a series of studies concerned with energy and mass exchange in soil-mulch systems, this chapter is devoted to the study of radiation distribution in straw mulches. In simulating radiation distribution, some researchers have treated a mulch canopy as one layer (e.g. Chung and Horton, 1987; and Hares and Novak, 1992). This simplistic approach, however, does not provide details of radiation distribution within the mulch canopy. Others (e.g., Ross et al., 1985; Bussiere and Cellier, 1994) have divided mulch canopies into multiple layers, and used plant canopy radiation models (e.g., Norman and Jarvis, 1975; Norman, 1979; Ross, 1981) to simulate the detailed radiant energy absorption by mulch layers and soil. In these multiple layer models, residue elements were Chapter 5. Radiation distribution 106 assumed to be randomly distributed, and yet, within-canopy radiation flux data were not measured to test the validity of this assumption. Furthermore, indirect results, such as measurements of evaporation from soil under a sugar-cane mulch (Bussiere and Cellier, 1994), suggest that the radiation simulation results within the sugar-cane mulch canopy may be erroneous. Their simulations predicted small soil evaporation rates (AE), but measured AE values were quite large (i.e., 150-200 W m"2). One possible reason for this error is the underestimation of solar radiation fluxes arriving at the underlying soil surface. To improve the simulation of radiation distribution in a soil-mulch system, a general plant canopy radiation model should be revised to fit the specific features of a mulch canopy (Tanner and Shen, 1990). First, residue elements are piled on top of each other, unlike plant leaves that hang in space, supported by branches. Overlapping or clumping of elements is more likely to occur in a mulch layer than in a plant canopy where some degree of clumping exists (Chen and Black, 1991). Another feature is that dead residue elements have a much smaller element transmittance than live leaves. For example, flail-chopped corn residue elements have element transmittances of 0.005 and 0.02 in the visible and near-IR bands, respectively, compared to 0.07 and 0.36 for senesced corn leaves (Tanner and Shen, 1990). Finally, unlike a live leaf, for which transpiration is an important component in temperature regulation, there can be a great difference between its upper surface temperature and air temperature for a residue element. This difference can be accentuated by low winds within the mulch canopy, and the small thermal conductivity of residue elements. In this chapter, a radiation model for a Chapter 5. Radiation distribution 107 horizontal straw mulch, that incorporates these features, is presented and its accuracy is tested using field and laboratory measurements. 5.2. Materials and methods 5.2.1. Clumping index For a canopy consisting of horizontal elements, the transmission of direct radiation can be described as follows (Nilson, 1971; Ross, 1981): where T{R\) is the transmittance of direct radiation flux through a canopy layer having a residue area index R, - iAR, AR is the projected residue area index of an "elemental" layer, within which no mutual shading occurs among residue elements, / is the number of elemental layers in the mulch canopy layer, and Q is the clumping index which describes the way in which residue elements are distributed in the mulch canopy, as illustrated by the following limiting and special cases (Ross, 1981): (1) £2(AR) = 0, when the highest degree of clumping occurs. This implies that a shaded area can only be present in a given layer where there is also a shaded area in the overlying layer. Thus, shading elements in all layers must be arranged one on top of the other. Such an arrangement of residue elements provides maximum mutual shading and, consequently, maximum penetration. From Eq. (5.1), we obtain the following: 0<Ri<AR, AR<R„ (5.1) Chapter 5. Radiation distribution 108 1-RI, 0<^<AJ?, l-AR, ARKR,. (5.2) It follows that the penetration of radiation is determined by the arrangement and number of residue elements in the first layer and lower layers will have no effect. (2) £2(AR) - 1, when residue elements are randomly distributed. Equation (5.1) becomes: (3) JO(AR) = l/AR, when the lowest degree of clumping or the highest degree of regularity exists. This special case is the situation where no mutual shading exists between elements in different layers, which gives: In our experiments, a typical piece of straw had a length of about 30 cm and a diameter of about 0.3 cm. The projected element area per unit mass of the mulch was 5.6 m2 kg"1 (Leaf Area and Analysis Programme, Skye Instruments Ltd.), with resulting residue area density ~ 90 m2 m"3. The ratio of mulch canopy height to application rate is about 0.6 cm f 1 ha (see details later). Assuming that the depth of an elemental layer equals 0.3 cm, the diameter of a piece of straw, we have AR = 0.28. Therefore, the theoretical range of £2(AR) lies between 0 and about 3.5 (i.e., 1/ AR). For /-»«>, Eq. (5.1) is conventionally approximated by: 0<RI<AR, ARKR^. (5.3) 0<^<1, ^>1. (5.4) r(^)=exp[-i2(i^]. (5.5) Chapter 5. Radiation distribution 109 With this equation, values of £2LR) can be readily calculated from measured values of Measurements of t(R\) were made in the summer of 1984 by mounting a square (1.5 m by 1.5 m) wooden frame, lined with transparent acrylic plastic film, at about 1 m above the bare ground (Hares, 1988). Fresh dry straw was distributed on the film at rates of 0.5, 1, 2, 5, 10, and 20 t ha"1, while an up-facing solar radiometer (Kipp and Zonen, Delet, Holland, model CM5) was positioned 0.13 m below the frame. The ratio of solar radiation transmitted to radiation above the mulch (tu) was recorded at 10 min intervals during the daytime on clear days (one mulch rate per day) for an average of 7 hours, from 8:00 to 15:00 PST. Significant scatter (0.35 to 0.87) in the 10-min values existed for application rates lower than 5 t ha"1, mostly due to the non-uniform distribution of radiation transmitted through the mulch. Final transmittances (f) were obtained after making two corrections. The first correction was for the transmittance of the acrylic film and frame, namely, r ci = Tu/0.88. Values of r ci were then corrected for the effect of reflection from the bare ground and back-reflection downward from the mulch. The correction of back-reflection was based on the relation (Tanner and Shen, 1990): ^ 0 = r S 0 + / ^ , (5-6) where So is the measured solar radiation incident to the mulch, Rg the radiation reflected from the ground up to the mulch layer, and rm the reflectance of the mulch layer. The rm value was approximated by assuming a constant ratio between reflectance and absorbance (1-r) of a mulch layer, i.e, Chapter 5. Radiation distribution 110 1 = 1' 0 - * c l)/ (1 - f ) = 0.30(1 - T o 1 ) / 0.97. (5.7) where /*m' (= 0.30) is the reflectance of a thick mulch and t (= 0.03) is the transmittance of this mulch. The value of Rs is given by: Rs=re(fTclS0+(l-f)S0), (5.8) where rg is reflectance of the ground (measured as 0.16), / is the view factor between the bottom surface of the mulch and the area shaded by the suspended mulch, estimated to be 0.15 (which includes shade from the frame and solar radiometer). Table 5.1 summarizes corrected values as well as the clumping index, Q, which are well within the theoretical range from 0 to 3.5. Table 5.1. Transmittances fa, un-corrected; %\, corrected for the influence of underlying acrylic film and the frame; t, further corrected for the mulch layer back-reflection of the ground reflection) of a fresh straw mulch at various application rates. Also included is the clumping index , Q, calculated from these r values using Eq. (5.5) rate (t ha'1) R %. T n 0.5 0.28 0.6776 0.7700 0.7590 0.9847 1 0.56 0.4488 0.5100 0.4875 1.2828 2 1.12 0.2992 0.3400 0.3106 1.0440 5 2.80 0.1496 0.1700 0.1340 0.7177 10 5.60 0.0792 0.0900 0.0511 0.5310 20 11.20 0.0616 0.0600 0.0304 0.3119 Chapter 5. Radiation distribution 111 The value of R was a projected area index measured using a camera (Leaf Area and Analysis Program, Skye Instruments Ltd.), instead of the intercepting area index used by Chen and Black (1992). This index was used because the straw was firmly packed in bales before being used; a large fraction of the straw was flat, while some remained cylindrical. The difficulty in determining the ratio of flat to cylindrical straw prevented the use of the intercepting area index. When RAI is small, Q >1 may be partly due to the use of the projected area index (Chen et al. 1992). Tanner and Shen (1990) measured values of Q\o be 1.74 and 1.66 (based on direct and diffuse radiation, respectively). Chen and Black (1992) argued that the intercepted area was 15-30% larger than the projected area since elements might not have been flat. However, even when these values of Q are reduced by 15-30%, they are still larger than 1.0. When R < AR, no mutual shading exists between elements and elements are distributed randomly so that Q ~ 1. As a second elemental residue layer is applied, the effects of regularity and overlapping co-exist, with regularity more likely to dominate, resulting in a value of Q > 1. This is probably a result of the effort of trying to distribute the elements as uniformly as possible when mulch was applied onto the frame. As R further increases, Q becomes < 1, indicating that more overlap occurs between mulch elements. The relationship between Q and R can be represented by the empirical equation: %<AR, Ri>2AR, (5.9) Chapter 5. Radiation distribution 112 which fits with r2 = 0.999 (Fig. 5.1). Note that these values of Q are for fresh straw mulch. In our field experiments, one mulch application rate generally lasted for less than a week, and consequently, the mulch consisted predominantly of fresh straw. 0 2 4 6 8 10 12 R Fig. 5.1. Clumping index, Q, as a function of residue area index, R, for a horizontal straw mulch. Transmittances calculated from Eq. (5.5) with measured i2(i.e., Eq. 5.9) and with Q= 1 (i.e., random distribution as often assumed in the simulation of radiation distribution within a mulch) are compared with measurements (Fig. 5.2). Interestingly, for R < 1.5, both calculations agree well with measured r, but rwas significantly underestimated for R > 1.5 when £2=1 was used. Such an underestimated r would lead to an underestimation of solar radiation arriving at the soil surface below the mulch. Assuming Eq. 5.9 is also Chapters. Radiation distribution 113 applicable to the sugar-cane mulch (R = 4) studied by Bussiere and Cellier (1994), we calculate T= 0.086 through the mulch. The underestimation of solar radiation arriving at the soil surface if Q = 1 is used, which gives r= 0.018, may be as large as 70 W m"2 (corresponding to the maximum solar radiation of 1000 W m"2). This may help explain why Bussiere and Cellier's (1994) model greatly underestimated the evaporation rate under their mulch. Fig. 5.2. Solar radiation transmittance, % as a function of residue area index, R. Lines are calculated from Eq. (5.2) using different 12 values: 12 = 1 (i.e., random distribution) and £2 from Eq. (5.9) (i.e., measured). 5.2.2. Mulch radiation model Chapter 5. Radiation distribution 114 In addition to using the above £2(R), accounting for different temperatures at upper and lower surfaces of a residue element, neglecting the transmission of radiation through a residue element, and dividing the mulch canopy into N elemental layers, with layer 0 denoting the atmosphere and layer N+l denoting the ground (Fig. 5.3), the model is derived using the following assumptions: (1) Multiple short-wave refections between layers are negligible. (2) The Q value is the same for direct short-wave, diffuse short-wave, and long-wave radiation fluxes (Tanner and Shen, 1990; Shen and Tanner, 1990). (3) Emissivities of residue elements and the soil surface are unity, because the scattering of thermal fluxes is negligible (Norman, 1979; Bristow et al., 1986). Atmosphere t I t I 1 Mulch /Elemental Layers f u 7d N ] t , J N .....! 1. N N Soil Fig. 5. 3. Schematic representing fluxes of radiation in a soil-mulch-atmosphere system. The net radiation flux at the /th layer, R„i, then is defined as S? - S" + Z? — H . Chapter 5. Radiation distribution 115 From Eq. (5.2), the downward transmitted direct solar radiation arriving at the z'th layer, Sf, is given by: ^ = r i , = exp[-i2(^1)^_1], forl</<A^ + l (5.10) where S* is the solar flux density above the mulch canopy. Equation (5.10) gives To = 1. The sum of upward reflected short-wave radiant fluxes leaving z'th layer, equals: with S^+x = S^r , where re\ is the reflectance of mulch elements and rg is the reflectance of the ground beneath a mulch canopy. The quantity (Sf - ) is the solar radiation flux intercepted by the jth layer. Intercepted fluxes are then reflected upward and pass through the layers between the rth and y'th layer (inclusive), which comprises the first part of the right hand side in Eq. (5.11). The second part is similar, except that it is reflected from the ground. Mulch element reflectance, rei, was measured directly using a 40 x 40 cm2 mulch plane. The mulch plane was constructed by arranging fresh dry barley straw piece by piece (touching or slightly overlapping each other in order to avoid any gaps) on a wooden plate. Incident and reflected solar radiation fluxes were measured using a pyranometer (Kipp & Zonen, Delet, Holland, model CM5) at about 10 cm above the mulch plane for solar zenith angles between 0 and 70°. The values of re\ were 0.46±0.04, after correcting for the shading effect of the pyranometer dome. In this study, we used 0.46 for mulches consisting of pure barley straw. For mulches consisting of a mixture of Chapter 5. Radiation distribution 116 components, we determined the value of rei by matching the modeled net radiation flux density to the observed value at the mulch top during 12:00-13:00 on September 26, 1993, a clear day. This value then was used for all other times and mulch application rates (Table 5.2). These re\ values were similar to those of other residue types. For example, re\ = 0.46+0.06 for a flail-chopped corn residue (Tanner and Shen, 1990), and re\ = 0.31 for a sugar-cane residue (Bussiere and Cellier, 1994). The value of r g is estimated to be 0.1 based on previous measurements (Hares, 1988). The net short-wave flux density radiation at the upper-surface of the ;th layer, Sni, is thus computed as: Sn.=S*-S°, l<i<N+l (5.12) Table 5.2. Mulch composition (barley straw or a mixture of barley, clover, and weeds), canopy height Qi), average diameter of the mulch element (de{), reflectance of the mulch element (re]) and soil (rs) for various application rates in the 1993 experimental season 21 ha"1 lOt ha"1 15tha_1 21 ha"1 5 t ha"1 test period Aug. 17-19 Aug. 28-31 Sept. 10-13 Sept. 21-24 Sept. 25-28 composition barley barley barley mixture mixture h (cm) 1.2 6 9 1.2 3 del (cm) 0.3 0.3 0.3 0.3 0.3 re\ 0.46 0.46 0.46 0.33 0.33 0.1 0.1 0.1 0.1 0.1 Chapter 5. Radiation distribution 117 The total long-wave irradiance of each layer has components originating at the soil surface, neighboring residue layers, and the atmospheric layer. The view factor between the upper surface of zth layer and the jth overlying layer is given by: fi,i = ^ - H - T H , forO</</, (5.13) and the view factor between the upper surface of zth layer and the atmosphere is i-i A i = - r i - u o r 1 ~ £7j,i- Similarly, the view factor between the upper surface of the zth J=I layer and the jth underlying layer is given by: Ai = ^ -rH, fori<j<N+l, (5.14) and the view factor between the upper surface of the zth layer and the ground is AT fiN+i = TN+i-f o r ~2Zfji- Using these view factors, we can write the downward long-wave radiation flux density arriving at the plane of the zth layer' upper surface as: ^ = fo,^(TS + ttf1MT>)4' for2<z<# + l, (5.15) 7=1 with /Jj1 = £ a(j(7") 4. The first term on the right-hand-side of Eq. (5.15) is due to radiation originating from the atmosphere, and the second term due to radiation originating from overlying mulch layers. Similarly, the upward long-wave radiation flux density leaving the zth layer is expressed as: ^ = f^(Ts)4 + itfl,Jo(^;)\ forl<z</V, (5.16) with ZJ,+1 = cr(Ts) 4. The first term on the right hand side of Eq. (5.16) is due to radiation originating from the ground and the second term due to radiation from underlying mulch Chapters. Radiation distribution 118 layers. In Eqs. (5.15) and (5.16), a is the Stefan-Boltzmann constant, Ta and Ts are absolute temperatures of air at the Stevenson screen height and of the soil surface, and £, is the atmospheric emissivity. The value of €a is determined from the Ta and water vapor pressure (ea, in mb) at screen height for clear sky conditions (Idso, 1980; Novak and Black, 1985): €a = 0.6 + 5.95 x 10"5 ea exp(l 500 / Ta). (5.17) For cloudy conditions, the atmospheric emissivity can be calculated from (Bristow et al., 1986): eac = (l - 0.84C>, + 0.84C, (5.18) where C is the mean fraction of cloud cover (ranging from 0 to 1). The daily average cloud cover can be estimated from % (the ratio of daily solar radiation flux density to total hemispherical solar radiation flux density incident on a horizontal surface at the outer edge of the earth's atmosphere) via the expression (Bristow et al., 1986): 1, Z<035, 2.4 -Ax, 0.35 <;*r< 0.6, (5.19) 0, ^>0.6. The net long-wave radiation flux density at the upper-surface plane of the z'th layer is given as: Z n i =L\-L\, fori (5.20) The net radiation flux density at the upper-surface plane of the z'th layer then is computed by: ^ i = ^i+A , i- ( 5 - 2 1 ) Chapter 5. Radiation distribution 5.2.3. Experiments 119 Field tests for the mulch radiation model were carried out at the University of British Columbia Plant Science Research Station in Vancouver from August 17 to September 30, 1993. From August 17 to September 13, 1993, pure barley straw was the predominant residue. From September 22-30, 1993, the residue was a mixture of barley straw, clover, and weeds; the clover and weeds were of a darker appearance than the barley straw. The mulch plot was a 14 m diameter circle in a 25 by 40 m2 bare area generally kept wet by irrigation. Mulch application rates of 2, 5, 10, and 15 t ha"1 (resulting in mulch layers of about 1.2, 3, 6.6, and 9 cm in thickness) were each studied for a number of days on the same plot (Table 5.2). Net radiation flux density (Rn) at the mulch canopy top was measured using a net radiometer (Swissteco Instruments, Oberriet, Switzerland, Model S-l) mounted at about 0.5 m above the ground near the center of the mulch plot. The instrument was calibrated prior to the experiment in the field with a solar radiometer (Kipp and Zonen, Delet, Holland, Model CM-5), using the conventional shading technique (Fritschen and Gay, 1979). The net radiometer was most accurate during daytime measurements; R„ may have been overestimated at night because of condensation of moisture on the upper polyethylene dome. Total downwelling radiation flux density beneath the mulch canopy were measured using a miniature net radiometer of diameter 1.2 cm (Swissteco, Oberriet, Switzerland, Type Minor MK II S-14). The sensor of the radiometer was aligned with the soil surface Chapter 5. Radiation distribution 120 so that the top polyethylene dome protruded into the mulch layer by 0.6 cm. The bottom dome was replaced with a black-body temperature sensor positioned in a hole in the soil. Therefore, the measured flux density was applicable to some depth between z = 0 and 0.6 cm. The miniature net radiometer was also calibrated using the conventional shading technique. Because of its location, the miniature net radiometer dome was likely free of dew at night. Solar radiation fluxes were recorded hourly at 10 m above ground at an auto-climate station about 100 m from the experimental site using a solarimeter (LI-COR, Type LI-200SB). Hourly air temperatures and relative humidity were also recorded in a Stevenson screen at the climate station. They were measured with a 25-um diameter fine-wire thermocouple and a Vaisala humidity transmitter (Type HMM-20D), respectively. Upper-surface temperature of residue elements was measured by positioning a 250-um coarse-wire thermocouple in contact with the surface of an element using transparent tape. Measurement heights were z = 1.2 cm in the 2 t ha"1; 1.1, 2.2, and 3.3 cm in the 5 t ha"1; 1.1, 2.2, 3.3, 4.4, 5.5, and 6.6 cm in the 10 t ha"1; and 1, 2, 3, 4, 5, 6, 7, 8, and 9 cm in the 15 t ha"1 mulch. Air temperatures were also measured at the same heights using 75-um diameter fine-wire thermocouples. The lower-surface temperature of the residue element was assumed to be equal to the air temperature at the same height. This assumption was tested in 1994 using the same experimental layout at the same site for a 10 t ha"1 barley straw mulch. In Fig. 5.4, T4-!* and T-Ta are plotted against Rn at the top of the 10 t ha'1 mulch canopy. Generally, 7d-7a is small (< 3 °C) and nearly independent of Rn, indicating that the assumption of T1« Ta is valid. In contrast, T-Ta is Chapter 5. Radiation distribution 121 highly correlated with Rn, reaching more than 15 °C at mid-day, when Rn is at its maximum value, and falls to about -3 °C during the night when Rn becomes negative. 20 i i T r - r a 1 1 1 CT 15 - o ^ • T 1 1° • • 1 "V, l-H o 5 1 3 0 5 T O O o ° 0 -5 1 I i i i -100 0 100 200 300 400 500 tfn(Wm-2) F i g . 5.4. Difference between lower- (or upper-) surface temperature and air temperature, Td — Ta (or T1 — Tj, plotted against the net radiation f lux (Rn) at top of a 10 t ha' 1 straw mulch (i.e., z = 6.6 cm). r d - Tt (or 7 " - Ta) was measured dur ing 0:00, August 18 to 24:00, August 22, 1994 (or 8:00, August 28 to 24:00, August 31, 1993). 5.3. Results and discussions 5.3.1. Comparison with field measurements Chapter 5. Radiation distribution 122 Simulated results were compared with observations made at the canopy top and beneath the mulch (z = 0.6 cm) for application rates of 2, 5 10 and 15 t ha"1. In Fig. 5.5, examples of diurnal variations of hourly net radiation fluxes R„ at the canopy top were plotted for each application rate. The calculated Rn agree well with measurements made during the day and early in the night (19:00-24:00 PST), for all application rates. Discrepancies, however, are clearly found from 0:00-6:00 PST on September 11 (15 t ha" *), September 22 (2 t ha"1), and to a lesser degree on September 26 (5 t ha"1). Two reasons for these discrepancies are possible. One was condensation on the upper dome of 400 200 2tha"' A ^ X , September22 / A 1993 " Q L A A A ± ± ^ \ • , K . . A A A A 400 • 1 — 1 5tha_1 -A" I — i i September 26 f A. 1993 4> A A A A A A ^ i 400 200 0 400 200 0 tyb* A A A, A , 15tha l r l ^ - A A A ifr-A-A-AH - 1 1 lOt ha"1 ^ " " ^ X ^ August 29 \ 1993 K A A A A A J ^~A_^_A-A^ i September 11 1993 8 12 16 20 24 / (h PST) Fig. 5.5. Diurnal variation of hourly net radiation flux, at the top of a mulch. Lines are calculations and symbols are measurements. Chapter 5. Radiation distribution 123 the net radiometer. Such a water film or droplets on the surface would have an emissivity close to unity and consequently the net radiometer would greatly overestimate Rn. On three of the four days (September 11, 22, and 26), relative humidity RH at the climate station was high (> 90%) between 0:00 to 6:00 PST, but otherwise was below 80%. During August 29, RH was below 80% all day. These measurements of RH may explain the discrepancies between calculated and observed values of R^. Our experience with the net radiometer is that condensation occurs in general. Another possible explanation for the discrepancy between calculated and observed values of Rn was an increase in cloudiness at night. The model would then greatly underestimate downcoming atmospheric long-wave radiation during cloudy periods. Most discrepancies were likely caused by the condensation problem rather than variations due to cloudiness. Despite these discrepancies, good overall agreement was found between measurements and calculations for all four mulch application rates (Fig. 5.6). Table 5.3 shows the linear regression statistics (intercept = 0) describing the agreement between calculated and measured values for all available data. Chapter 5. Radiation distribution 124 0 200 400 0 200 400 Rn Measured (Wm"2) Fig. 5.6. Comparison of measured and calculated hourly net radiation flux, R„, at the top of a mulch. Statistics for the figure are listed in Table 5.3. Table 5.3. Linear regression (intercept = 0) statistics describing the agreement between measured and calculated net radiation fluxes (Rn) at top of, and total downwelling radiation fluxes (S*+L d) at z = 0.6 cm within a mulch of application rates 2, 5, 10, and 15 t ha"1 r2 Slope Standard Error (W m"2) Range (W m'2) Number of hours Ra(21 ha1) 0.964 0.978 29.59 -91-407 112 Rn (5 t ha"1) 0.985 1.022 16.24 -75-279 86 yRnOOtha"1) 0.989 1.088 16.45 -78-331 89 tfnOStha"1) 0.937 0.960 31.67 -76-274 73 tf+L* (21 ha"1) 0.876 0.988 50.21 297-782 112 Sf+L* (5 t ha"1) 0.870 0.957 24.63 334-532 86 S?+Ld (101 ha"1) 0.982 0.997 5.99 369-492 89 S'+r'OStha 1) 0.966 1.000 5.39 357-456 73 Chapter 5. Radiation distribution 125 Comparisons between measured and calculated total downwelling radiation fluxes at z = 0.6 cm are illustrated in Fig. 5.7. Excellent agreement was found for thick mulch canopies having application rates > 10 t ha"1. Fluctuations can be seen clearly for thin mulch canopies with application rates < 5 t ha"1 during daytime hours, but not during night hours. These fluctuations resulted mainly from spatial heterogeneity of solar radiation flux distributions beneath the thin mulch canopies. Tram systems have been generally used to overcome this heterogeneity problem when measuring radiation fluxes within forests. Fig. 5.7. Diurnal variation of hourly total downwelling downward radiation flux, Si+Ld, at z = 0.6 cm within a mulch. Lines are calculation and symbols are measurement. Note the different scales on y-axes. Chapter 5. Radiation distribution 126 For example, Black et al. (1991) found that the more open the forest crown, the longer the pathway of the tram should be in order to obtain good spatial averages for fluxes. Because a mulch canopy is much denser than a forest, we obtained quite smooth total downwelling radiation fluxes under thick mulches even without the use of a tram system. These data are plotted along with all other available data in a 1:1 fashion (Fig. 5.8), which may be interpreted similarly to Fig. 5.7. Table 5.3 lists the statistics which describe the comparison between model and measurements. Standard errors of estimation were small (<10 W m"2) for thick mulches of application rates > 10 t ha"1, but large (20-50 W m"2) for thin mulches of application rates < 5 t ha"1, due to the spatial non-uniformity. 400 600 800 400 600 800 400 500 400 500 tf+L6 Measured (W m"2) Fig. 5.8. Comparison of measured and calculated hourly total downwelling radiation flux, 5?+L d, at z = 0.6 cm beneath a mulch (see statistics in Table 5.3). Chapter 5. Radiation distribution 5.3.2. Model sensitivity analysis 127 Inputs to the model include variables and parameters. Variables are solar radiation above the canopy (So), upper- and lower-surface temperatures (T and T4) of straw elements at various heights within the canopy, and soil surface temperature (Ts), all given as functions of time in the period of interest. Parameters include mulch element reflectance (rei), soil surface reflectance (rg), mulch layer clumping index (H), and atmospheric emissivity (f^ c). Outputs of the model include such terms as net radiation and absorbed radiation fluxes. Here, we choose to perform the sensitivity test for net radiation fluxes at the canopy top, middle, and at the underlying soil surface using the fractional sensitivity method (McNaughton and Spriggs, 1986). Fractional sensitivity^ to a fractional change in other variables p of an output variable such as net radiation flux Rn, is defined as: ft = jhp(dRB/^yAt/j\dt. (5.22) Fractional sensitivity of Rn to input variables So, T-I4, ea and Ta via and input parameters re\, rg, and Q are shown in Table 5.4. They are calculated for daytime (6:00-19:00 PST) and night-time (19:00-6:00 PST) averages over a four-day period for the 10 t ha"1 mulch. Results for other application rates are similar (not shown). Average net radiation fluxes at different levels are also included in the table. During the day, the average net radiation is sensitive to So, and £ c^, especially at the top and upper parts of the canopy. This result was also reported by Tuzet et al. (1993), who used evapotranspiration Chapter 5. Radiation distribution 128 rate as an output of model sensitivity analysis. While rei has a significant impact on the average net radiation at the canopy top and soil surface, rg has little to do with average Rn, except at the soil surface. The clumping index, however, plays an important role during daylight hours, especially in the lower part of the canopy and at the soil surface. During night, average Rn is mainly determined by £,c and Q. Other factors have little effect. Table 5.4. Fractional sensitivity of Rn to variables So, T-l*, e^, parameters reU rg, and 12for the 101 ha" mulch, as defined in Eq. (5.22) daytime daytime daytime night night night top middle bottom top middle bottom So 1.721 1.205 0.913 -0.007 -0.004 -0.003 /"el -0.682 -0.025 0.252 0.002 0.000 -0.001 -0.001 -0.006 -0.083 0.000 0.000 0.000 -0.059 -0.005 0.000 -0.022 0.033 0.000 1.688 0.918 0.622 -4.268 -1.991 -1.381 Q -1.106 -1.924 -2.665 -0.122 -1.307 -1.789 From Table 5.4, we see that Rn is insensitive to V - T4. The question then arises as to how large will the error be if the difference between T and T* in the simulation is neglected. At the canopy top, the simulation shows that the daytime average Rn is 6% higher when it is assumed that T = T1 than when measured values of T and 1* (= Ta) are used. For hourly Rn values, the maximum difference is 10%. Within the canopy, this difference decreases, becoming negligible at the soil surface. During night, the error is Chapter 5. Radiation distribution 129 small (<5%). Thus, though not as important as So, £aC, rei, and Q, T - T1 should be considered if a 10% error is deemed significant in the simulation. 5.3.3. Model application examples Once values of Q, re\, rg, and £ c^ are determined, the mulch canopy radiation distribution model can be used to describe various radiation components in great detail when solar radiation fluxes and surface temperatures are known. Fig. 5.9 shows a simulation of S*, S", Ld, Lu, and Rn in the 10 t ha"1 straw mulch canopy from 12:00-13:00, on August 29, 1993. The largest component is Si. It attenuates quickly in the top 1/3 of the mulch canopy, indicating a strong interception of solar radiant energy. A fraction of the intercepted solar radiation is reflected upward in short-wave radiation and the rest is lost as long-wave radiation, resulting in Rn ~ 5*72 near the canopy top. In the lower part of the mulch canopy, 5*1 decreases slowly due to the high degree of clumping of mulch elements. Rn decreases even slower than S* because of long-wave radiation gain and a decrease in upward short-wave reflection. The shift from loss to gain in long-wave radiation occurs near mid-canopy, corresponding to the temperature distribution in which V reaches a maximum at the canopy top and decreases downward, while has a maximum value near zlh = 2/3 (Chapter 4). A considerable amount of S* arrives at, and is absorbed by the soil surface. The positive net long-wave radiation flux at soil surface also increases the total available energy there. Chapter 5. Radiation distribution 130 0 200 400 600 800 Radiation Flux (W m"2) Fig. 5.9. An example of simulated downward short- and long-wave (S*1 and Z,d), upward short- and long-wave (5" and Lu), and net radiation flux (Rn = 3d- + Ld - V1) within a 10 t ha"1 straw mulch during 12:00-13:00 PST, August 29, 1993. During night, the radiation regime in a mulch canopy is determined by long-wave radiation components only (Fig. 5.10). Although the mulch surface temperature is significantly lower than air temperature, R„ at the canopy top is negative because the atmospheric emissivity is much lower than that of the residue elements. As zlh decreases, residue elements "see" an increasing number of overlying elements, and Rn thus increases slowly. Nevertheless, Rn is still negative at ground level. Chapter 5. Radiation distribution 131 1.0 0.8 0.6 0.4 0.2 0.0 -100 0 100 200 300 400 Radiation Flux (W m" ) Fig. 5.10. An example of simulated downward long-wave (Z,d), upward long-wave (Z u), and net radiation flux (R„ = L d - Lu) within a 101 ha"1 straw mulch during 0:00-1:00 PST, August 29, 1993. In the foregoing examples, all radiation components were calculated using the measured clumping index Q. In conservation tillage practices, the degree of clumping among residue elements may change from one situation to another. The model was used to investigate the impact of clumping among mulch elements on radiation regimes within a mulch canopy. A complete assessment of this impact requires that the effect of variations in long-wave components be known, i.e., and 7" must be specified or determined with a turbulent transport model. These complex interactions are not presented here. In Fig. 5.11, net short-wave radiation fluxes (^-S") are plotted for the following four conditions: elements positioned exactly on top of each other (£2 = 0), elements randomly distributed Chapter 5. Radiation distribution 132 (Q = 1), elements having no mutual shading (£2 = 3.5), and the measured Q. The first case yields the largest amount of radiation energy reaches the soil surface; a large evaporation rate from soil would be expected if the soil is wet. Consequently, this kind of mulch element arrangement is not efficient in conserving soil moisture, but may be good to warm the soil at high latitudes where low soil temperatures in early spring are a problem. Both the second and third cases eliminate short-wave radiation at the soil surface beneath the 10 t ha"1 straw mulch, and are effective for water conservation. In the fourth case, mulch elements are clumped to a moderate degree, and so an intermediate radiation o.o*-* 0 200 400 600 ^ - ^ ( W m " 2 ) Fig. 5.11. Variations of net short-wave radiation flux (S^ S") profiles corresponding to different clumping degrees of mulch elements within a 10 t ha'1 straw mulch during 12:00-13:00 PST, August 29, 1993. Chapter 5. Radiation distribution 133 distribution is observed. Clearly, clumping greatly alters radiation distribution patterns within a mulch, which can be modified in accordance to different needs. 5.4. Conclusions Measured solar radiation transmittances through a mulch layer of different application rates (0.5, 1, 2, 5, 10, and 20 t ha"1) demonstrate that the distribution of residue elements is generally non-random. Instead, regularity prevails for the distribution of residue elements (£2 > 1) when residue area index, R < 1, or alternatively, clumping becomes more important (£2 < 1) when R > 1. Measurements also show that temperature differences between upper and lower surfaces of a mulch element can be as large as 15 °C. Field tests for mulch canopies with application rates of 2, 5, 10, and 15 t ha"1 show that simulated Rn agrees well with measurements made at the canopy top. The ratio of estimation error to measurement range is less than 10%. Our model was further tested for total downwelling radiation fluxes (S* + Ld) beneath four mulch canopies (at z = 0.6 cm). Despite the influences of spatial non-homogeneity, the ratios of estimation error to measurement range of S* + L d , is less than 15% for mulches of low application rate (< 5 t ha"1), and reduces to less than 10% for thick mulches (> 10 t ha"1). Sensitivity tests indicate that £2 has a significant impact on Rn, as do S0 and £,c. Neglecting the difference between V and I4 may result in a 10% error in R„. In addition, Rn is quite sensitive to rei, but is sensitive to r% only at the soil surface. Chapter 5. Radiation distribution 134 Details of the radiation components in a horizontal mulch canopy can be obtained using this model, as shown by simulation examples. Changing the clumping index through the rearrangement of mulch elements, can change radiation distributions within a mulch canopy. This may provide ways to manage thermal and moisture regimes within soil-mulch-atmosphere systems. 5.5. References Black, A.T., Chen, J.M., Lee, X. and Sagar, R.M., 1991. 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Hares, M.A., 1988. Effects of mulching on the surface energy balance and soil thermal regimes. Ph.D. Thesis, the University of British Columbia, Canada. Hares, M.A. and Novak, M.D., 1992. Simulation of surface energy balance and soil temperature under strip tillage: II. Field test. Soil Sci. Soc. Am. J., 56: 29-36. Idso, S.B., 1980. On the apparent incompatibility of different atmospheric thermal radiation data sets. Quart. J. Roy. Meteorol. Soc, 106: 375-376. McNaughton, KG and Spriggs, T.A.W., 1986. A mixed-layer model for regional evaporation. Boundary-Layer Meteorol., 34: 243-262. Nilson, T., 1971. A theoretical analysis of the frequency of gaps in plant stands. Agric. Meteorol., 8: 25-38. Norman, J.M., 1979. Modeling the complete crop canopy. p249-277. In Barfield, B.J. and Gerber, J.F. (ed.) Modification of the aerial environment of crop. ASAE Monograph No.2. ASAE, St. Joseph. Norman, J.M. and Jarvis, P.G., 1975. Photosynthesis in Stika Spruce (Picea sitchensis (Bong) Carr. V. Radiation penetration theory and a test case. J. Appl. Ecol., 12: 839-878. Novak, M.D. and Black, T.A., 1985. Theoretical determination of the surface energy balance and thermal regimes of bare soils. Boundary-layer Meteorol., 33: 313-333. Chapter 5. Radiation distribution 136 Ross, J., 1981. The radiation regime and architecture of plant stands. Dr. W. Junk Publishers, The Hague, The Netherlands. Ross, P.J., Williams, J. and McCown, R.L., 1985. Soil temperature and the energy balance of vegetative mulch in the semi-arid tropics. I. Static analysis of the radiation balance. Aust. J. Soil Res., 23: 493-514. Shen, Y. and Tanner, C.B., 1990. Radiative and conductive transport of heat through flail-chopped corn residue. Soil Sci. Soc. Am. J., 54: 653-658. Tanner, CB. and Shen, Y., 1990. Solar-radiation transmittance of flail-chopped corn residue. Soil Sci. Soc. Am. X, 54: 650-652. Tuzet, A., Perrier, A. and Oulidaissa, A.K., 1993. A prediction model for field drying of hay using a heat balance method. Agric. For. Meteorol., 65: 63-90. Unger, P.E. (ed.), 1994. Managing agricultural residues. Lewis Publishers, Boca Raton, FL, USA. Wagner-Riddle C , Gillespie, T.J. and Swanton, C.J., 1996. Rye mulch characterization for the purpose of microclimatic modelling. Agric. For. Meteorol., 78: 67-81. Chapter 6. Turbulent statistics 137 Chapter 6 Turbulent exchange processes within and above a straw mulch. Part I: Statistics of the flow field 6.1. Introduction Mulching, which maintains soil surfaces covered with plant residues between successive crops or when the plant canopy cover is incomplete, is widely adopted in agriculture, forestry and horticulture (Stigter, 1984; Unger, 1994). Advantages of mulching include limiting soil erosion by wind and runoff, reducing water loss by evaporation, changing the soil temperature favorably, and enhancing soil productivity (Unger, 1994). Many studies to date have only considered the effects of mulching on the thermal and moisture regimes of the underlying soil, with different empirical models proposed to relate these regimes to mulch attributes (Bond and Willis, 1969; Unger and Parker, 1976). It is doubtful, however, that universal relationships can be obtained in this way. This approach, based on empiricism, requires an enormous amount of field work in order to begin to accommodate the complex way in which atmosphere, mulch, and soil interact. Recently, more promising simulation models have been developed that attempt to incorporate basic mass and energy exchange processes occurring in soil-mulch-atmosphere systems (Bristow et al., 1986; Hares and Novak, 1992; Bussiere and Cellier, 1994). These researchers successfully modeled exchange processes in the soil and Chapter 6. Turbulent statistics 138 atmosphere, but found it difficult to correctly simulate all detailed processes within a mulch. The most important cause of this difficulty is that mass and energy exchange processes within a mulch canopy involve not only molecular diffusion but also turbulent transfer (Kimball and Lemon, 1971; Campbell et al., 1980; Tanner and Shen, 1990). For example, Kimball and Lemon (1971) observed significant increases in heptane evaporation rates under various mulches with above-canopy wind speed. To simulate turbulent exchange processes within a mulch canopy, classical gradient-flux relationships (or K-theory) have been used in various forms (e.g., Bussiere and Cellier, 1994). They divided a sugar-cane mulch canopy into many layers, and assumed that the diffusivities decrease exponentially into the mulch. Their simulation predicted that soil evaporation beneath the mulch would be small, but their measured fluxes were large, around 150-200 W m"2. Similar discrepancies were also found between predicted and measured sensible heat fluxes above the canopy, with the former being about half the latter, for two clear days. The failure of the simulation was not unexpected since A"-theory is now widely admitted to be unsuitable to simulate canopy flows (Raupach, 1989). As alternatives to A"-theory, higher-order closure schemes (Meyers and Paw U, 1987) and Lagrangian models (Raupach, 1989) have been developed to improve the description of transfer within canopies. To evaluate the usefulness of these alternative models for a mulch canopy, measurements of turbulence and turbulent fluxes within a mulch must be made. Fluxes within mulch canopies, which are generally short (a few cm high) and dense (residue area Chapter 6. Turbulent statistics 139 density up to 85 m2 m"3), cannot be measured with current micrometeorological techniques, such as eddy correlation. To circumvent this technical difficulty, we developed several new methods to measure or estimate sensible heat, latent heat and radiative fluxes within and above straw mulch canopy (Chapter 2-5). This chapter and Chapter 7 characterize the regimes of turbulence and turbulent fluxes within and above a mulch canopy. Chapter 7 concentrates on turbulent fluxes of sensible and latent heat within and above the mulch canopy. This chapter reports statistical properties of the velocity field. 6.2. Methods 6.2.1. Experimental site and mulch properties Experiments were conducted at the University of British Columbia Plant Science Research Station, Vancouver, Canada, from July to October for three consecutive years (1992-1994). Data used in this paper is from the 1994 season, except where indicated. The site, a 25 m by 40 m area, was surrounded by short crops and bare areas. During the study, the dominant wind direction at the site was west to northwest. A circular area of 14 m diameter in the southeast corner was covered with barley straw at rates of 2, 5, 10, and 15 t ha"1 (resulting in mean thicknesses of 1.2, 3, 6.6, and 9 cm), while the surrounding area remained bare. Due to qualitative similarities among different application rates, only results from the 101 ha"1 mulch are reported. Chapter 6. Turbulent statistics 140 A typical piece of straw had a length of about 30 cm and a width of about 0.3 cm. The projected element area per unit mass of the mulch was 5.6 m2 kg"1 (Leaf Area and Analysis Programme, Skye Instruments Ltd.), with resulting residue area density ~ 90 m2 m"3. 6.2.2. Measurement of mean horizontal "cup" wind speed A short dense mulch canopy practically precludes the use of non-stationary sensors such as the servo-controlled split-film anemometers used in mature corn canopies (Shaw et al., 1974; Wilson et al, 1982). Therefore, we used stationary, home-made hot-wire anemometers (HW) and a triple hot-film constant-temperature anemometer (CTA) (Model 56C01, Dantec Electronik, Denmark) to measure wind velocities within the mulch canopy. An HW probe, with a vertical height of about 1 cm, has a response time of 3-5 s (Orchansky et al, 1994). Sensors were calibrated on a turntable, with the tangential velocity used as the known wind speed. The minimum wind speed which can be reliably measured with these HW's is about 5 cm s"1. Four HW's measured mean horizontal cup wind speeds, (s~ = [u2 + v2 f2, where u and v are average longitudinal and lateral wind components, respectively) simultaneously at various heights within and above the mulch canopy. At least three days of data were obtained at each of the following heights above ground: z = 1.1, 3.3, 6.6, 7.6, 8.6, 9.6, 10.6, 11.1, 11.6, 12.6, and 13.6 cm. For example, measurement heights were at z = 1.1, 3.3, 6.6, and 9.6 cm during August 23-25, 1994. This particular data set, which included a simultaneous measurement of wind speeds both Chapter 6. Turbulent statistics 141 within and above the canopy, was chosen for analysis of the relationships between wind regimes within and above the canopy. Throughout the experiment, wind directions were recorded with a propeller-vane wind monitor (R.M. Young Inc., Model 05103) at z = 40 cm. Above-canopy wind speeds at z = 24 and 57 cm were also recorded for the duration of the experiment, using cup anemometers (CW. Thornthwaite Associates, Model 901-LED). 6.2.3. Measurement of high-frequency wind components Longitudinal (u), lateral (v), and vertical (w) wind components were measured at high frequency (21 Hz) using the CTA at z = 1, 3, 5, 7.6, and 9.6 cm within and above the 10 t ha"1 mulch during the afternoon of August 25, 1994. At least three 10-min intervals were recorded at each height. During the measurements, the horizontal wind speed at z -57 cm, s51cm, varied between 1.3 and 2.0 m s"1, and the above-canopy H ranged from 120 to 220 W m"2. The wind monitor probe (Model 55R91) consists of three orthogonal nickel-coated, each 1.25 mm in length and 75 u.m in diameter, with a frequency response up to 17 kHz. The system was calibrated using the turntable technique as for the HW's for wind speeds ranging from 0 to 2 m s"1, and a Pitot tube and manometer in a wind tunnel for the range from 2 to 16 m s"1 (Liu et al., 1996). Air temperature near the probe was recorded simultaneously at the same frequency (using a fine-wire constantan/chromel thermocouple of diameter 13 p.m) to determine the zero wind voltage output which we had calibrated as a function of air temperature. Wind direction above the canopy was also Chapter 6. Turbulent statistics 142 measured at 21 Hz, to exclude data with wind directions outside a 30° cone about the longitudinal axis, within which the CTA probe measures accurately. To measure wind velocities within the canopy, the probe was lowered into the mulch through a small hole with a diameter of about 3 cm. Since actual distances between mulch elements are smaller (ranging from a few mm to 1-2 cm), measurements made in the hole could differ from those made in the undisturbed mulch canopy. In addition, wind directions in the mulch canopy are not necessarily the same as those above the canopy. Nevertheless, Aylor et al. (1993), who released smoke on the ground, found that flow reversals within a few cm of the ground in a grass canopy were rare, except in light winds. 6.2.4. Determination of turbulence statistics Surface friction velocity, , was determined by fitting above-canopy wind speeds measured with the HW's to a logarithmic profile (Thorn, 1975; Stathers et al., 1988), as follows: where k is von Karman's constant, JT is the mean horizontal cup wind speed at reference height zT, d and z0 are, respectively, the displacement height and roughness length, and *Fm is the diabatic profile correction factor for the momentum, given by: a* = ksr I [ln( zr-d ) - * U (6.1) 2 ln[(l + x)/2] + ln[(l + x2) / 2] - arctan x + n/2, for unstable conditions, -4.7£, for stable conditions, (6.2) Chapter 6. Turbulent statistics 143 where x = (1-16£) 1 / 4, zr/LMo = -kztgH/[p cpTaul], LMo is the Monin-Obukhov length, g is the gravitational acceleration, # is the sensible heat flux density above the canopy, p and cp are the density and specific heat of air, and Ta is the mean air temperature between zr and d + z0. The values of d and zo were determined using only measurements made under nearly neutral conditions (i.e., 6:00-7:00 and 17:00-18:00 PST) when Ym = 0. When high-frequency wind components are measured, surface friction velocities can be determined directly (w* = (-w'u')l/2). High-frequency wind components also give other turbulence statistics, such as variance (cr2 = f2 ), turbulence intensity (z'j = aj/w), for the horizontal (j = s) and vertical (J = w) velocity components, skewness (Sks = s* I cr 3), and kurtosis (Krs =s~*/crs4). To examine the intermittence of air flow within the mulch canopy, mean duration of gusts (rg), and of gust events (r) are calculated. A gust begins when the signal rises above a preset threshold (s = s + n<js, with n an integer in the range of 0 < n < 6) and ends when the signal drops below this threshold. Each time a gust occurs, an event is counted, and the duration of the event is the time between two consecutive gusts. Therefore, rg was determined from the number of data points that were above the given threshold speed, and r from the number of gusts in a period of interest. The time fraction that the horizontal wind speed exceeds the preset threshold, J(s), equals rg/r. The measured r g/r values were then compared to predicted values of the Gumbel extreme distribution (Brooks and Carruthers, 1953; Aylor et al., 1993; note that an error is present in Eq. (1) of Aylor et al., 1993), i.e., /(s)=l-exp{-exp[-s(s)]}, (6.3) where Chapter 6. Turbulent statistics g(s) = (1.283 / crs )(s - s) + 0.577. 144 (6.4) 6.3. Results 6.3.1. Diurnal patterns of mean horizontal cup wind speed Diurnal variations of 10-min average horizontal cup wind speeds within and above the 101 ha"1 straw mulch during August 23-25, 1994 are shown in Fig. 6.1 (note different Fig. 6.1. 10-min mean horizontal cup wind speed, 5 , measured using cup anemometers at z = 24 and 57 cm, and using hot-wire anemometers at four other heights within and above a 10 t ha"1 mulch from August 23-25, 1994. Chapter 6. Turbulent statistics 145 vertical scales). At all heights, wind speeds generally increased in daytime and decreased at night. Some exceptions occurred, e.g., the night of August 25 was quite windy. At low wind speeds, cup anemometers can stall, as seen at z = 24 cm, at night. As the height decreases, wind speeds attenuate accordingly, with the most rapid attenuation occurring near the canopy top. Despite the rapid attenuation, air movements within the canopy were considerable. The maximum 10-min mean wind speed at the lowest measurement height (1.1 cm) was 0.18 m s"1, which corresponds to 3.7 m s"1 at z = 57 cm. Air flows within and above the mulch canopy were well correlated, as indicated by the large correlation coefficients r2 (> 0.83) between wind speed at z = 57 cm and at a lower position (Fig. 6.2). The correlation between wind speeds at z = 57 cm and 24 cm was even better, with r 2 = 0.97 (not shown in Fig. 6.2). This result was consistent with similar measurements made using similar HW's in a standing wheat residue with a canopy height of 0.25 m and an above-ground biomass of 5.8 t ha"1 (Heilman et al, 1992). These authors found that wind speeds within and above the residue were closely related, and measured a 15-min mean wind speed of 25 cm s"1 at z = 1 cm in the residue, which corresponded to 6 m s"1 at z = 1 m above the ground. Chapter 6. Turbulent statistics 146 0.0 1 1 1 1 1 0 1 2 3 4 s at z = 57 cm (m s"1) Fig. 6.2. Wind speeds at various heights plotted against those at z = 57 cm for the same data set as Fig. 6.1. The numbers in bracket are r2 from linear regression between s values at the indicated height and at 57 cm. An alternate way to examine the relationship between wind speeds within and above a canopy is by calculating the ratio, I sout. In Fig. 6.3 this ratio is plotted against wind speed at a reference height (z = 57 cm). At high wind speeds (i.e., s51^ > 1.1 m s"1), which usually occurred in the daytime, the ratio was nearly constant. The ratio, however, increased sharply in lower wind speed conditions, which occurred most often at night. This suggests that because wind regimes within and above the mulch canopy in daytime Chapter 6. Turbulent statistics 147 high-wind and nighttime low-wind conditions are different, they should be investigated separately. 0.6 0.4 0.2 i2 0.0 c 0.6 0.4 0.2 0.0 Fig. 6.3. The ratio of wind speed within-canopy (z = 1.1 or 3.3 cm) to above-canopy (z = 9.6 cm) plotted against wind speed at z = 57 cm for the same data as in Fig. 6.1. The value 3j 7 c n i = 0.6 or = 1.1 cm s"1 is chosen as an approximate criterion to categorize low and high-wind speed conditions. 6.3.1.1. Daytime high-wind conditions During daytime, a strong inversion usually exists within the mulch canopy (Fig 6.4 and Chapter 7), suggesting that eddies above the mulch might, to some extent, be prevented from penetrating into the canopy. The extent to which a stable temperature Chapter 6. Turbulent statistics 148 profile inhibits penetration into a canopy should depend on inversion strength within the canopy. To examine this possibility, sm / sout was plotted against the average temperature gradient between z = 1.1 and 4.4 cm, where air temperatures reached maximum daytime values (Fig. 6.4). Only cases with positive temperature gradients are included in Fig. 6.4. The temperature gradient within the mulch canopy, which was as high as 3 °C cm"1, was much larger than in plant canopies such as a corn canopy (Jacobs et al., 1992). Despite Fig. 6.4. The ratio of wind speed within-canopy (z = 1.1 or 3.3 cm) to above-canopy (z = 9.6 cm) versus air temperature gradient between z = 1.1 and 4.4 cm. Data sets are the same as in Fig. 6.1 except for cases where ATJAz between 1.1 and 4.4 cm > 0. Chapter 6. Turbulent statistics 149 the fact that the temperature inversion in the bottom 2/3 of the canopy was strong, there was little or no dependence of wind speed ratio and temperature gradient, indicating that stable temperature profiles have little or no influence on within-canopy flows. The canopy flow appears to be dominated by large-scale eddies, so that air flows within and above the mulch canopy are highly coupled. This point can be made directly by computing the penetration depth, /p, defined by Jacobs et al. (1992) as follows: lp = crw^/N, (6.5) where <7W o u t is the standard deviation of the vertical velocity component above the canopy (assumed to be 1.25 w*), and N is the Brunt-Vaisala frequency (Plate, 1971), given by: N = gT(z2)-T(zym (6.6) where T is the average air temperature (in Kelvin) between Z2 (= 4.4 cm) and z\ (= 1.1 cm). The penetration depth was calculated and plotted against time in Fig. 6.5. The penetration depth was always larger than 4.4 cm (the depth of the stable air layer within the mulch canopy), and usually, / p ~ h. Thus, canopy height appears to be appropriate as a scale for canopy flow (Raupach et al., 1989; Jacobs, 1992). Chapter 6. Turbulent statistics 150 0 1 1 1 1 L—1 6 9 12 15 18 t (h PST) Fig. 6.5. Depth of penetration (/p = ( 7 W 0 U t / , where N is the Brunt-Vaisala frequency) into a 10 t ha"1 mulch canopy for the part of data in Fig. 6.1 when ATJAz between 1.1 and 4.4 cm > 0. Five lp > 30 cm points are excluded in this figure. 6.3.1.2. Nocturnal low-wind conditions To exclude high-wind data, in examining flow regimes under nocturnal low-wind conditions, we chose s51cm< 0.6 m s~l as the low-wind criterion (Fig. 6.3). Under these conditions, s at z = 57 cm and z = 1.1 or 3.3 cm were not well correlated, with r2 < 0.36 (Fig. 6.6). In other words, flows above and within the mulch were decoupled, which is similar to observations made in a corn canopy (Jacobs et al. 1992). These authors found that <TW was nearly constant within the canopy (zlh = 0.41), despite a decrease in <rw above Chapter 6. Turbulent statistics 151 t-i o 6 -T 1 1 1 1.1 cm (0.36) 3.3 cm (0.32) — i 1 1 — 1.1 cm (0.70) 3.3 cm (0.78) 20 30 40 50 60 7 8 9 10 11 12 Fig. 6.6. 10-min mean horizontal cup wind speeds at 1.1 or 3.3 cm versus (a) at 57 and, and (b) at 6.6 cm (mulch top). Data sets are the same as in Fig. 6.1 except for low-wind conditions (~f57cm < 60 cm s"1). Numbers in brackets are regression coefficients r2. the canopy from daytime to night (zlh = 2.65), and during some periods at night, ow>m > <7w,out. They attributed this result to within-canopy convective air flow induced by radiation cooling at the canopy top and the relatively warm soil surface, a situation which compares to the convective atmospheric boundary layer. To find out whether such an air flow also possibly occurred within the mulch canopy under nocturnal low-wind conditions, we calculated the Rayleigh number, Ra, for the mulch canopy under these conditions (j 5 7 c m < 0.6 m s"1 and 19:00-7:00 PST) as follows: Chapter 6. Turbulent statistics 152 Ra = f ^ ^ - z , ) \ (6.7) where v is kinematic viscosity, D™ is the molecular diffusivity for sensible heat, and z2 was chosen to be 6.6 cm (the minimum air temperatures normally occurred at the canopy top at night) and z\ = 1.1 cm. When Ra > Rac (the critical Rayleigh number = 1706), buoyancy work exceeds viscous dissipation, and as a result, air becomes unstable and motion takes place (Plate, 1971). For the mulch canopy, Ra was 1-2 orders of magnitude larger than R^ (Fig. 6.7). Therefore, free convective air flow within the mulch canopy Fig. 6.7. The Rayleigh number, Ra, in a 10 t ha"1 mulch canopy for the fractional data in Fig. 6.1 that meets the nocturnal low-wind-speed criterion (i.e., y 5 7 c m < 60 cm s - 1 and 19:00-7:00 PST). Also included is the critical Ra number (Rac = 1706). Chapter 6. Turbulent statistics 153 under nocturnal low-wind conditions was fully possible and expected. Wind speeds between two heights within the mulch canopy are thus well correlated, such as between z = 6.6 cmandz= 1.1 or 3.3 cm (Fig. 6.6). Convective air flows also resulted in sharp increases in 5 k / sm values as the above-canopy wind speed decreased (Fig. 6.3). Jacobs et al. (1992) found a good relation between <TW;u,/crw,out and the within-canopy bulk Richardson number Rim. Following their approach, we calculated Riin as follows: i T T X z ^ - ^ ) ! ( 6 8 ) where z2 = 6.6 cm and z\= 1.1 cm. In Fig. 6.8, sm 1yout was plotted against Rim for all data from the three days. Most data points (including all those from daytime observations) clustered around the near-neutral state (Rim = 0) in which the sin / yout ratio remained nearly constant. Only during the low-wind situations at night, when Ri m became large and negative (locally unstable), was there a clear dependence on this stability parameter. The ratio increased almost linearly with increasing negative values of the stability parameter, yielding a linear regression of J l l c m /s 9 6 c m = 0.16 - 0.011 Rim, r2 = 0.78, n = 430 and J33cm Is96cm = 0.16 -0.011 Rim, r2 = 0.73, rt = 430. This indicates that the ratio was determined mainly by within-canopy wind and thermal regimes (via the within-canopy bulk Richardson number). Chapter 6. Turbulent statistics 154 T 1 1 r 0.0 1 1 — 1 1 1 1 -40 -30 -20 -10 0 10 Fig. 6.8. The ratio (triangles are daytime values and circles are those at night) of wind speed within-canopy (z = 1.1 or 3.3 cm) to above-canopy (z = 9.6 cm) versus the within-canopy Richardson number Ri^ for the same data as Fig. 6.1. 6.3.2. Vertical profile of mean horizontal cup wind speed The vertical profile of mean horizontal cup wind speed varied logarithmically with height above the canopy, and exponentially with height within the canopy (Fig. 6.9). The logarithmic fit for average, above-canopy wind speeds (z = 7.6, 8.6, 9.6, 10.6, 11.1, 11.6, 12.6, and 13.6 cm) measured with FfW's under nearly neutral conditions (i.e., 7:00-8:00 and 17:00-18:00 PST) gives d = 0.87/j (or 0.0574 m) and z0 = 0.079/? (or 0.0052 m). Chapter 6. Turbulent statistics 155 These average wind speeds were calculated from the available data during 26 days in 1993 and 1994, after each 30-min period of mean wind speed was first normalized to that at z = 57 cm. If we assume the roughness sublayer is from h to h+2(h-d), as in Chapter 4, the lowest point (z = 7.6 cm) is within this sublayer. The exclusion of this point, however, does not change the logarithmic fitting significantly. Fig. 6.9. Vertical profile of mean horizontal cup wind speed, s , normalized by surface friction velocity, , within and above a 10 t ha"1 straw mulch. Measured wind speeds are average values for all available data, which meet the selection criterion (see the detailed description in the text), in 1993 and 1994. Since the thermal stratification effect on within-canopy wind is negligible for high wind condition as discussed above, we use all data with sUcm > 8 cm s"1 (corresponding to Chapter 6. Turbulent statistics 156 5 5 7 c m > 1.1 m s"1) to calculate the within-canopy vertical wind profile for high-wind conditions, with a best exponential function given as (Fig. 6.9): ff/i^ = 0.21exp.(2.16z/A). (6.9) The value of the attenuation factor(2.16) is somewhat smaller than the range of 2.6-4 found in plant canopies (Denmead, 1976; Wilson, 1982; Aylor et al., 1993). Denmead (1976) found that the attenuation factor decreases as wind speed at the canopy top decreases for various plant canopies. Wind speeds at the mulch top are generally quite small because of the high displacement height (d/h = 0.87, compared to 0.67 for a plant canopy), and thus, the attenuation factor of the mulch is expected to be smaller than that of a plant canopy. Under nocturnal low-wind conditions, within-canopy convective air flow occurs, which then further reduces the attenuation factor to about 0.5 for the mulch studied. Also plotted in Fig. 6.9 are CTA measurements of mean horizontal cup wind speeds within the mulch canopy. The agreement between the CTA and HW's is good. The comparison for above-canopy wind speeds between CTA and HW is presented in Table 6.1. Agreement is reasonable, considering that for only about 30% of the time during the measurement period, was the wind direction within 30° of the CTA probe axis and therefore suitable for analysis. Chapter 6. Turbulent statistics 157 Table 6.1. Mean cup wind speeds, s , at z = 9.6 cm measured with a triple hot-film constant-temperature anemometer (CTA) and a hot-wire anemometer (HW), and surface friction velocities, , at z = 7.6 and 9.6 cm above a 10 t ha"1 straw mulch measured using the CTA comparing those calculated from vertical wind profdes measured with HW's Run 1 2 3 s (m s"1) CTA, at 9.6 cm, 0.987 0.913 0.939 HW, at 9.6 cm, 0.813 0.721 0.958 (ms"1) CTA, at 9.6 cm 0.146 0.179 0.185 Profile 0.167 0.150 0.193 «*, (m s"1) CTA, at 7.6 cm 0.120 0.149 0.135 Profile 0.181 0.175 0.179 6.3.3. Turbulence statistics 6.3.3.1. Friction velocity and higher-order moments Good agreement was also found between measured values using the CTA at z = 9.6 cm and those calculated from vertical wind profiles (Table 6.1) using Eq. (6.1) with reference height = 57 cm. At z = 7.6 cm, however, measurements were only about 3/4 of calculated values. Standard deviations of CTA wind components, <7W and <7U, have similar vertical patterns with (Fig. 6.10). Although there is considerable scatter in the data, average values of ajand aju* of 1.26 and 3.02 at 9.6 cm agree reasonably well with Chapter 6. Turbulent statistics 158 typical surface-layer values (1.25 and 2.5, respectively, Lumley and Panofsky, 1964). Below this height, both cVw* and crju* decrease exponentially, described by: CTW/X = 0.026 exp[2.91z//?], r 2 = 0.81,« = 13, (6.10.a) CTU/^ = 0.153exp[2.06z//7], r2 = 0.71, n= 13. (6.10.b) 1.5 1.0 0.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ° W / W * > °JU* Fig. 6.10. Variation of oju^ (circles) and oju^ (squares) with normalized height zlh. The lines are given by Eqs. (6. lO.a) and (6. lO.b). Data at z = 7.6 cm were included in calculations because no measurements were taken at the canopy top. The rapid vertical attenuation of aju* and oj into the mulch are in general agreement with findings of others in corn or grass canopies (Wilson et al., 1982; Chapter 6. Turbulent statistics 159 Aylor et al., 1993). Aylor et al. (1993) found similar values for <7w/w* and oju* with attenuation factor -2.5, within a grass canopy. The simplest indicator of "turbulence strength" is turbulence intensity. Table 6.2 shows that turbulence intensity of the horizontal velocity component, zs, is 0.65 at zlh -1.5, and increases with decreasing height. The profile of zs reported here, is similar in shape and magnitude to observations of zs, made in a grass canopy (Aylor et al., 1993), but values were larger for the u component than those observed in a Douglas-fir forest (Lee and Black, 1993). Similar shapes for /'„ hold for the vertical velocity component, / w , in our measurements and those made in a Douglas-fir forest (Lee and Black, 1993). Lee and Black (1993), however, found that ?w = 0.34 above the forest, and reaches a maximum of 0.68 at zlh = 0.6, which is larger than our values of zw = 0.24 at zlh - 1.45 with a within-canopy maximum of 0.23 at zlh = 0.5. Table 6.2. Average values of wind speed (5 ), turbulent intensity (/'„ ;w), skewness (Sk,), and kurtosis (Krs) at heights within and above a 10 t ha"1 straw mulch during indicated time periods on August 25, 1994 9.6 cm 7.6 cm 5 cm 3 cm 1 cm Time 12:20-12:50 13:00-13:30 13:30-14:00 14:10-14:50 14:50-15:20 5 (m s'1) 0.95 0.56 0.12 0.07 0.04 h 0.65 0.72 0.64 0.75 0.91 iv, 0.24 0.26 0.17 0.23 0.15 Sk$ 1.85 2.01 2.88 3.31 4.36 Krs 5.02 5.79 18.13 35.74 52.83 Chapter 6. Turbulent statistics 160 Skewness (Sks) describes the asymmetry of a probability density distribution. The average value of Sks is 1.85 at zlh = 1.45 (Table 6.2), which is nearer to 1.15, the value for a Gumbel extreme value distribution, than zero, the value for a Gaussian distribution. As height decreases, the value of Sks increases. These features are concordant with observations in a grass canopy (Aylor et al., 1993), but differ from values for a Douglas-fir forest (Lee and Black, 1993). Lee and Black (1993) observed a maximum value of Sku at zlh = 0.6, where the wind speed is lowest. Since no secondary maximums in wind speed were measured within these dense grass or straw mulch canopies, a similar maximum is not expected. Positive values of Sks are consistent with the theoretical argument of Shaw and Seginer (1987) that the penetration of occasional sweeps of fast moving air from above, should give rise to positive Sks. Kurtosis is a measure of peakness or flatness of a probability density distribution. For a Gumbel extreme value distribution, kurtosis has a value of 5.37, while for a Gaussian distribution the value is 3. As shown in Table 6.2, kurtosis for the horizontal velocity component, Krs, was close to the value for a Gumbel extreme distribution at zlh = 1.45, as it was for above a grass canopy (Aylor et al., 1993). Higher values of kurtosis are observed within a mulch canopy, which indicates the existence of extreme events in this layer. As for skewness, the magnitude of kurtosis increases with decreasing height; a pattern also observed by Aylor et al. (1993) for the grass canopy. 6.3.3.2. Frequency distributions of wind speeds Chapter 6. Turbulent statistics 161 Air flow inside the mulch was highly intermittent (Fig. 6.11), as often observed in plant canopies (Shaw et al., 1983; Aylor et al., 1993). In the 1-min example, the mean wind speed at z = 1 cm was 7.7 cm s"1, with a maximum reaching 62 cm s"1. As a result, the fractions of time that s exceeded s by integer factors of cs were small (Fig. 6.12). For example, s exceeded s +cs only 13% of the time. The fraction of time was further reduced to 4% for a threshold wind speed = s+2cs. The Gumbel extreme value distribution predicted these measured fractions of time reasonably well. The only exception occurred at larger threshold speeds when the prediction tended to underestimate for z < h. Our findings were in general agreement with those observed in other experimental studies (Baldocchi and Meyers, 1988; Aylor et al., 1993). 60 -50 -„ ^ 4 0 -I 30 -20 -10 0 10 20 30 40 50 60 Fig. 6.11. An example of a longitudinal velocity component (u) time series at z = 1.1 cm within a 10 t ha"1 straw mulch, measured using the triple hot-film constant-temperature anemometer (CTA). Chapter 6. Turbulent statistics 162 10 u 10* H o o -l-> o ed u PH 1 Q - 3 10" 10" 1 1 1 1 1 1 - Gumbel o 9 cm • 7 cm A 5 cm \ V 3 cm \ A 0 1 cm O H & \ V 1 1 1 1 \ • • i 0 1 2 3 4 (5-5)/cT Fig. 6.12. Fraction of time occupied by gusts (s exceeds 5 by various amounts) at different heights within and above a 10 t ha"1 straw mulch. The line is a prediction based on the Gumbel extreme distribution (Eq. 6.3). If we assume that the frequency of large-scale eddies (or coherent structures) can be approximated by the frequency of gusts, then it is of great interest to examine the latter by setting a certain threshold speed. In Table 6.3, we show the mean duration of gust events T (the reverse of gust event occurrence frequency f) for different threshold wind speeds. Interestingly, we notice that the duration, T, is approximately constant with height for a each threshold speed. This result is consistent with general concepts of coherent structures (Raupach, 1989). As the threshold speed increases, values of ralso increase (i.e., less events are detected), which shows the arbitrariness in threshold setting. Average Chapter 6. Turbulent statistics 163 durations of large scale eddies are 0.58, 1.03, and 2.22 s, respectively, corresponding to (s-s)/crs = 0, 1, and 2. The Mexican Hat wavelet transform (MHAT) can determine T values more objectively (Collineau and Brunet, 1993a and b; Chapter 3). Applying the MHAT to 80 Hz air temperature time series at z = 9.6 cm, we found r « 1 s (Chapter 3). Therefore, in spite of the arbitrariness in setting the threshold speed, these two methods appear to agree, at least with respect to order of magnitude. Our result was also in concert with the theoretical argument of linear stability analysis of Raupach et al. (1989), who suggested that occurrence frequencies of coherent structures (J) near the canopy top, should be proportional to wind shear (dw/dz) near z = h. By approximating the local shear by Wh lh, they arrived at the expression: f = fiujh (6.11) where /? ~ 0.1, and Mh is the mean wind speed at canopy top. Their f3 values were determined from studies of an artificial canopy in a wind tunnel, and a corn canopy (Shaw et al., 1974). Finnigan (1979) observed the frequency,/, for the arrival of sweeps into a wheat canopy (h = 1.25 m) as about 0.35 Hz when wh = 2.0 m s"1, which gives a /? value of 0.22. By setting the threshold speed to s+os, Aylor et al. (1993) found /? = 0.07 for a grass canopy. Using measured wind speeds of z = h and average values for r, we calculated /? values to be 0.35, 0.19, and 0.10, respectively, corresponding to threshold speeds, (s-s )/<rs = 0, 1, and 2. Thus, their suggestion that wind shear occurs near the top of a canopy, might offer a reasonable basis for scaling the frequency of gusts, despite the fact that h differed greatly from canopy to canopy. Chapter 6. Turbulent statistics 164 Table 6.3. Mean duration of gust events, % for different threshold speeds at heights within and above a 10 t ha"1 mulch canopy during indicated time periods. Also listed is the mean duration of gusts (Tg) Threshold 9.6 cm 7.6 cm 5 cm 3 cm 1 cm Time 12:20-12:50 13:00-13:30 13:30-14:00 14:10-50 14:50-15:20 T(8) 5 0.57 0.42 0.44 0.71 0.76 S+<7S 0.95 0.70 0.81 1.13 1.55 s+2<js 2.26 1.59 2.04 2.36 2.85 7g(s) s 0.24 0.16 0.18 0.29 0.25 0.14 0.10 0.10 0.16 0.18 s+2cs 0.06 0.08 0.08 0.10 0.12 6.4. Conclusions and discussions Despite the fact that a straw mulch canopy is much denser and shorter than most plant canopies, considerable air flow occurs within it. At z = 1 cm within the TO t ha'1 mulch, we recorded an instantaneous wind speed of 62 cm s'1. Within-canopy wind speed is generally well correlated with that above when the latter is large enough (i.e., s57cm > 1.1 m s"1). Under high-wind conditions, which usually happens during the daytime, the ratio of within-canopy to above-canopy wind speed remains nearly constant for a variety of wind speeds. As a result, canopy flow may be characterized by a single above-canopy wind speed (w*), via a logarithmic profile, for above-canopy, and an exponential function for within-canopy. Thermal stratification inside the mulch in the daytime has little or no Chapter 6. Turbulent statistics 165 effect on the ratio, which indicates that canopy flow is controlled by eddies which are larger than 2/3/z, the within-canopy, stable layer depth. Depths of penetration, under these conditions, are about the same as the canopy height. Under nocturnal, low-wind conditions (i.e., at night when y5 7 c m < 0.6 m s'1), radiation cooling at the canopy top and relatively warm soil surface created within-canopy convective air flow. When the Rayleigh number exceeds its critical value (1706), within-canopy, convective air flow becomes possible. For the mulch canopy, we found that the Rayleigh number was generally 1-2 orders of magnitude larger than its critical value, under nocturnal low-wind conditions. Therefore, within-mulch air flow was very likely occurred. Consequently, the ratio of wind speed within-canopy to above-canopy increases sharply with decreasing above-canopy wind speeds. Variability of the ratio was accounted for by using the within-canopy bulk Richardson number. During daytime, the canopy flow is highly turbulent, with turbulence intensity of horizontal component being between 0.65 and 1. The turbulence regimes within and above the mulch canopy are dominated by large-scale eddies, as indicated by the penetration depths of eddies and large values of skewness and kurtosis within our mulch canopy. The frequency of large-scale eddies was computed by identifying gusts that were above a specified threshold value. With threshold wind speeds at s , ?+.CT, and 1 + 2ers, frequencies of large-scale eddies, / were 1.72, 0.97, and 0.45 Hz, respectively. By applying the MHAT wavelet technique to 80 Hz sampled temperature time traces, these values were determined to be within the same range as ramp occurrence frequencies (about 1 Hz) obtained at 3 cm above the mulch canopy. Linear stability analysis Chapter 6. Turbulent statistics 166 (Raupach, 1989) suggests that f=Pu\Jh, where f3~ 0.1. For the mulch canopy, Pvalues were found to be in concert with the suggestions of other authors, at least in order of magnitude (/?= 0.35, 0.19, and 0.10 for threshold wind speed = s , s + c s , and J + 2<7S, respectively). Our results provide experimental evidence for Raupach et al.'s (1989) suggestion that coherent structures are scaled appropriately to wind shear near the canopy top. 6.5. References Aylor, D.E., Wang, Y. and Miller, D.R., 1993. Intermittent wind close to the ground within a grass canopy. Boundary-Layer Meteorol., 66: 427-448. Baldocchi, D.D. and Meyers, T.P., 1988. Turbulence structure in a deciduous forest. Boundary-Layer Meteorol., 43: 345-365. Bond, J.J. and Willis, W. O., 1969. Soil water evaporation: Surface residue rate and placement effects. Soil Sci. Soc. Am. Proc, 33: 445-448. Bristow, K.L., Campbell, G.S., Papendick, R.I. and Elliott, L.F.: 1986. Simulation of heat and moisture through a surface-residue soil system. Agric. For. Meteorol., 36: 193-214. Brooks, C.E.P. and Carruthers, N., 1953. Handbook of statistical methods in meteorology. M.O. 538, Her Majesty's Stationary Office, London, 412pp. Chapter 6. Turbulent statistics 167 Bussiere, F. and Cellier, P., 1994. Modification of the soil temperature and water content regimes by a crop residue mulch: experiment and modeling. Agric. For. Meteorol., 68: 1-28. Campbell, G.S., McArthur, A.J. and Monteith, J.L., 1980. Wind speed dependence of heat and mass transfer through coats and clothing. Boundary-Layer Meteorol., 18: 485-493. Collineau, S. and Brunet. Y., 1993. Detection of turbulent coherent motions in a forest canopy. Part I: Wavelet analysis. Boundary-Layer Meteorol., 65: 357-379. Collineau, S. and Brunet. Y., 1993. Detection of turbulent coherent motions in a forest canopy. Part II: Time-scales and conditional averages. Boundary-Layer Meteorol., 66: 49-73. Denmead, O.T., 1976. Temperate cereals. In: Vegetation and the Atmosphere: Volume 2. Case Studies. J.L. Monteith (ed.), 1-30. Finnigan, J.J., 1979. Turbulence in waving wheat, Part I: Mean statistics and honami. Boundary-Layer Meteorol., 16: 181-211. Hares, M.A. and Novak, M.D., 1992. Simulation of surface energy balance and soil temperature under strip tillage: II. Field test. Soil Sci. Soc. Am. J., 56: 29-36. Heilman, J.L., Mclnnes, K.J., Gesch, R.W. and Lascano, R.J., 1992. Evaporation from ridge-tilled soil covered with herbicide-killed winter wheat. Soil Sci. Soc. Am. X, 56: 1278-1286. Chapter 6. Turbulent statistics 168 Jacobs, A.F.G., van Boxel, J.H., and Shaw, R.H., 1992. The dependence of canopy layer turbulence on within-canopy thermal stratification. Agric. For. Meteorol., 58: 247-256. Kimball, B.A. and Lemon, E.R., 1971. Air turbulence effects on soil gas exchange. Soil Sci. Soc. Am. Proc, 35: 16-21. Lee, X. and Black, T.A., 1993. Atmospheric turbulence within and above a Douglas-fir stand. Part I: Statistical properties of the velocity Field. Boundary-Layer Meteorol., 64:149-174. Liu, J., Chen, J.M., Black, T.A. and Novak, M.D., 1996. E-e modelling of turbulence air flow downwind of a model forest edge. Boundary-Layer Meteorol., 77: 21-44. Lumley, J.L. and Panofsky, H.A., 1964. The structure of atmospheric turbulence. Interscience Publ, John Wiley & Sons, New York, 239pp. Meyers, T.P. and Paw U, K.T., 1987. Modelling the plant canopy micrometeorology with higher-order closure principles. Agric. For. Meteorol., 41: 143-163. Orchansky, A.L., Lee, X. and Novak, M.D., 1994. Miniature hot wire anemometer to measure very low wind speeds. Preprints, 21st Confer. Agric. For. Meteorol., San Diego, USA, 201-202. Plate, E.J., 1971. Aerodynamic characteristics of atmospheric boundary layer. USAEC Tech. Inf. Center, Oak Ridge, TE. 190pp. Raupach, M.R., 1989. A practical Lagrangian method for relating scalar concentrations to source distribution in vegetation canopies. Q.J.R. Meteorol. Soc, 115: 609-632. Chapter 6. Turbulent statistics 169 Raupach, M.R., Finnigan, J.J. and Brunet, Y., 1989. Coherent eddies in vegetation canopies. 4th Australian Confer. Heat Mass Transfer. Christchurch, New Zealand, 75-90. Shaw, R.H. and Seginer, I., 1987. Calculation of velocity skewness in real and artificial plant canopies. Boundary-Layer Meteorol., 39: 315-332. Shaw, R.H., Silversides, R.H. and Thurtell, G.W., 1974. Some observations of turbulence and turbulent transport within and above plant canopies. Boundary-Layer Meteorol., 5: 429-449. Shaw, R.H., Tavangar, J. and Ward, D.P., 1983. Structure of Reynolds stress in a canopy layer. J. Climate Appl. Meteorol., 22: 1922-1931. Stathers, R.J., Black, T.A. and Novak, M.D., 1988. Modelling surface energy fluxes and temperatures in dry and wet bare soils. Atmos. Ocean, 26: 59-73. Stigter, C.J., 1984. Mulching as a traditional method of microclimate management. Arch. Meteorol. Geophys. Bioclim. Ser. B, 35: 147-154. Tanner, CB. and Shen, Y., 1990. Water vapour transport through a flail-chopped corn residue. Soil Sci. Soc. Am. J., 54: 945-951. Thorn, A^ S'» \97$, Momentum, maoo and heat exchange of plant communities. In: J.L. Monteith (ed.), Vegetation and the Atmosphere: Vol. 1. Principles. Academic Press, New York, 57-109. Unger, P.W. (ed.), 1994. Managing Agricultural Residues. Lewis Publishers, Boca Raton, FL, 448pp. Chapter 6. Turbulent statistics 170 Unger, P.W. and Parker, J.J., 1976. Evaporation reduction from soil with wheat, sorghum, and cotton residues. Soil Sci. Soc. Am. J., 40: 938-942. Wilson, J.D., Ward, D.P, Thurtell, G.W. and Kidd, G.E., 1982. Statistics of atmospheric turbulence within and above a corn canopy. Boundary-Layer Meteorol., 24: 495-519. Chapter 7. Sensible and latent heat fluxes 171 Chapter 7 Turbulent exchange processes within and above a straw mulch. Part II: Sensible and latent heat flux densities 7.1. Introduction An experiment to study the turbulent exchange processes of mass and energy within and above a straw mulch canopy was conducted at the University of British Columbia Plant Science Research Station, Vancouver, Canada, during July to October for three consecutive years (1992-1994). In Chapter 6, we described the statistics of the flow field within and above a 10 t ha"1 straw mulch. This chapter reports thermal and moisture regimes, sensible and latent heat flux densities, and the energy balance within and above a non-wetted and wetted 101 ha"1 horizontal straw mulch. Turbulent diffusivities within and conductance of the mulch canopy are also reported. A non-wetted mulch is dry for most of the day, but is wet during the night and early morning because of dew from the atmosphere and moisture evaporating from the soil at night (shown later). In some cases, such as just after a rainfall, or when newly harvested crop residues are dried as hay (Tuzet et al., 1993; Barr and Brown, 1995), turbulent exchange processes and the energy balance within a wetted mulch are of great interest. Therefore, we thoroughly wetted a 10 t ha"1 mulch by sprinkle irrigation, and made the same measurements as for the non-wetted mulch in the days that followed. Chapter 7. Sensible and latent heat fluxes 7.2. Methods 172 7.2.1. Calculation of sensible heat flux densities Sensible heat flux density, H, within and above the 10 t ha'1 mulch canopy was calculated using the renewal model (described fully in Chapter 4), with additional terms used to account for molecular diffusion, as follows: \-pev {-afl2l3y[(AT)31 At]U3(u% I h)2/3z + D™dT I dz}, for 0.2h < z < 3h - 2d, H ~ \-pcv {-aB2/3y[(ATf I Atf3(u% /(z-d' ))2l3z + D™dT I dz}, for z < 0.2h or > 3h - 2d, (7.1) where p and cp are the density and specific heat of air, a[5my'is a combined coefficient (calibrated to be 0.397 for all heights within and above the 10 t ha"1 mulch canopy), (AT)3 / At is measured at height, z, with sampling frequency 1/A/ = 10 Hz using fine-wire chromel/constantan thermocouples of diameter 25 um, u% is the surface friction velocity (for z < 0.2h, u% = <7W /1.25, at the measurement height), d' is an adjusted displacement height (d' = 2(h - d), for z>3h- 2d, and d' = 0 for z < 0.2h), h and d are the canopy height and displacement height, respectively, D™ is the thermal molecular diffusivity of air, and d77dz is the air temperature gradient at z. Half-hourly H was calculated continuously at z = 7.6, 9.6, 11.1, and 12.6 cm during August 16-18, 1994, and at z = 1.1, 3.3, 6.6, 9.6 cm during August 19-September 1, 1994, except during 10:00-13:00 PST, August 23, and the following night (18:00 PST, August 23 to 7:30 PST, August 24), Chapter 7. Sensible and latent heat fluxes 173 during which H was calculated continuously at 10 heights (z = 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.6, 9.6, 11.1, and 12.6 cm). Throughout the experiment, 10-min mean air temperatures at z = 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 9.6, 16.6, 21.6, and 38 cm within and above the mulch canopy were measured using a fine-wire chromel/constantan thermocouple (diameter = 75 urn for the lower six heights and 25 u\m for the upper four. Upper (in 1993) or lower-surface (in 1994) straw element temperatures were measured by placing a coarse-wire chromel/constantan thermocouple of diameter 250 urn in contact with a straw element surface using transparent tape. Measurement heights were at z = 1.1, 2.2, 3.3, 4.4, 5.5, and 6.6 cm. Besides ensuring a good contact between the surface and thermocouple, the tape also protected the thermocouple from damage. 7.2.2. Measurement of latent heat flux densities Latent heat flux density, LE, at the soil surface was measured using an improved tension-plate system (Chapter 2). This system measures first-stage evaporation and condensation to within 5 W m"2. The vertical profile of LE from the mulch elements was measured by weighing six 1.1-cm layers (cross-sectional area = 0.0139 m2) stacked in perforated acrylic containers every one to two hours. This measurement also gives the water content of each mulch layer (on mass basis, <9ml). Water vapour pressures of air at z = 1.5, 3.5, 6.6, 9.6 cm within and above the mulch canopy were measured using a humidity transmitter (Type HMM-20D, Vaisala Inc., Chapter 7. Sensible and latent heat fluxes 174 Helsinki, Finland) with a fine-wire chromel/constantan thermocouple of diameter 75 urn installed in the probe near the capacity-type sensor of the humidity transmitter. To measure humidity within a mulch canopy in the field, the probe must be: (a) shielded from direct solar radiation, rainfall, and dew fall; (b) adequate exchange between air inside the probe and that outside; and (c) small in size. The original probe is a cylinder (6 cm in length and 1.2 cm in diameter) with the sensor located in the middle of one end, and protected by a membrane filter and slotted cap. When the membrane filter is on, the 90% response time is 15 s. In a routine climate station operation, the first two requirements are met by enclosing the probe in a large shield, such as a Stevenson screen. Within a short dense mulch canopy, however, using a large shield violates the third requirement. Instead of constructing an additional shield for the probe, the slots in the upper half of the cap were filled, and the lower half of the cap and membrane filter were removed. The upper half was then painted with white, water-proof paint. In this way, all three requirements were met and the response time was likely shortened. All of these transmitters were then calibrated with a dew-point generator (LI-COR, Inc., Model LI-610) in the laboratory, to an accuracy of within 2% for relative humidity (RH) over an RH range from 15 to 95%. Values of RH below 15% were rare in our experiments, but RH values above 95% were frequently measured, and sometimes, apparent RH values above 100% (up to 108%) due to existence of water on the sensor surface were measured at night . For all RH > 100%, RH= 100% was assumed. 7.2.3. Determination of other energy components Chapter 7. Sensible and latent heat fluxes 175 Net radiation flux density, Rn, at the mulch top was measured using a net radiometer (Swissteco, Instruments, Oberriet, Switzerland, Model S-l) mounted at about 0.5 m above the ground near the center of the mulch plot. This net radiometer may have overestimated RD because of dew fall on its domes at night, but worked accurately during the day. Values of Rn within the mulch canopy were simulated using a mulch canopy radiation model (Chapter 5). Inputs to the model include solar radiation, upper and lower surface temperatures of mulch elements, and air temperature and water vapour pressure at the Stevenson screen height. The latter three variables were measured every 30 min at an auto-climate station about 100 m away. Soil surface heat flux density, Go, beneath the mulch was measured using a custom-made heat flux plate installed at a depth of 1 cm with storage changes above the plate calculated from soil temperatures measured at a depth of 0.5 cm. Soil temperatures at depths of 2 and 5 cm were also measured. Each soil temperature was measured using a 250 um chromel/constantan thermocouple fixed with epoxy resin within a 2 mm o.d. by 10 cm long stainless steel tube. Soil surface temperatures, Tsfi, were estimated using Fourier's Law from soil temperatures measured at a 0.5 cm depth ( r S ) 0 . 5 ) , and a soil heat conductance ^ s of 1.0 W m'1 C"1 (Hares and Novak, 1992): Ts0 = 0.005 x (0.75G0 + 0.25G,) / K, + Tsi (7.2) Heat storage in each 1.1-cm thick mulch layer was calculated by: forl</<6 (7.3) Chapter 7. Sensible and latent heat fluxes 176 where c and p are heat capacity and density of mulch elements (subscript ml) and of water (subscript w) (Weast, 1975), is the dry weight of mulch elements per m2 surface in the zth layer, and ATJAt is the temperature change of the zth mulch layer over time Az. 7.3. Results 7.3.1. Profiles of sensible heat flux and temperatures for a non-wetted mulch From 10:00-13:00 PST, August 23, 1994, a clear day, H was determined with the air renewal model at 10 heights within and above the 10 t ha"1 straw mulch. A typical vertical profile of H is shown in Fig. 7.1 for a half-hour period at mid-day (11:30-12:00 PST). Above the canopy, //was nearly constant with height, as expected. The fraction of sensible heat flux transported by molecular diffusion, Hm, was far smaller than that transported by turbulence (coherent structures), Hc. Near the top of the canopy, H attenuated rapidly with height, indicating the location of the main source of H. The value of H remained positive until z = 3.3 cm (or zlh = 0.5), below which it became negative due to the dominance of molecular diffusion and a positive air temperature gradient. At z = 1.1 cm, both molecular diffusion and air renewal contributed to negative values of H. The shape of the vertical profile of H within the mulch canopy is consistent with those observed in corn canopies (Shaw et al., 1974; Wilson, 1982) and forest canopies (Denmead and Bradley, 1985; Lee and Black, 1993) except for two unique features. First, unlike in the mulch canopy, H within a plant canopy decreases slowly or not at all with Chapter 7. Sensible and latent heat fluxes 111 height near the canopy top, its main source density being around zlh ~ 0.85 to 0.5 (Denmead and Bradley, 1985). Both types of profiles reflect the density distributions of sensible heat sources. The mulch canopy has a constant element area index with respect to height, so that the top mulch layer intercepts most of the solar radiation and becomes the main source of H. On the other hand, the largest leaf area of a plant canopy is usually between zlh = 0.85 to 0.5, and is the main source of H. Second, H is usually positive at all z in plant canopies during daylight hours except during low-wind periods in late afternoon Fig. 7.1. Measured vertical profdes of sensible heat flux density (H) as well as its two components due to molecular diffusion (Hm) or air renewal by coherent structures (Hc), and measured air temperature within and above a non-wetted 101 ha"1 straw mulch from 11:30-12:00 PST, August 23, 1994. Chapter 7. Sensible and latent heat fluxes 178 (Lee and Black, 1993). The lack of this feature is attributed to the high density of the mulch canopy and lower wind speeds, so that molecular diffusion becomes important, which is seldom the case for a plant canopy. In Fig. 7.1, air temperatures measured simultaneously are plotted, showing a maximum at z = 5.5 cm. Counter-gradient sensible heat fluxes thus were found at 2.2 cm < z < 5.5 cm (or 0.33 < zlh < 0.83), as frequently observed in forests (Denmead and Bradley, 1985; Amiro, 1990; Lee and Black, 1993) and agricultural canopies (Jacobs et al., 1992). Using a higher-order closure model, Meyers and Paw U (1987) simulated counter-gradient sensible heat fluxes in a soybean canopy. This mulch system is probably the shortest and densest canopy for which counter-gradient sensible heat fluxes have been reported. Diurnal variations of H are presented in Fig. 7.2. Instead of using data from August 23, 1994, where there were gaps in the data due to a change of data logger programs, August 20, 1994, a predominantly clear day, is used instead. From 6:00-18:00 PST, H > 0 at and above the mulch canopy top. H was found to be about 15% higher at 9.6 cm than at 6.6 cm. The reason for this was twofold. First, because H decreased rapidly with height near the canopy top (Fig. 7.1), a slight change in position might cause a large difference in H. Second, the value used for the mulch canopy height was an average value, and so, some straw was above the height. Consequently, the estimation of H at the canopy height did not include sensible heat fluxes from these elements which could effectively intercept solar irradiance and release large amounts of sensible heat. Therefore, the correct value of H at the canopy top should be measured at a height which Chapter 7. Sensible and latent heat fluxes 179 is slightly above the average canopy top, i.e., H at 9.6 cm should be used for energy balance analysis. Consistently positive values of H at 3.3 cm and negative values of H at 1.1 cm were found for most measurements made during the day. Positive H values were against the gradient from 9:00-14:00 PST on the day investigated (Fig. 7.3). At night, H became negative at z = 6.6 and 9.6 cm, whereas slightly positive H values were observed at z = 1.1 and 3.3 cm within the mulch (Fig. 7.2). 300 z (cm) 200 | 100 0 0 4 8 12 16 20 24 r(hPST) F i g . 7.2. D iu rna l variation of measured 3 0 - m i n sensible heat f lux density (H) at various heights w i th in and above a non-wetted 10 t ha"1 straw mulch on August 20, 1994 Chapter 7. Sensible and latent heat fluxes 180 <0 20 -1 1 r — 4.4 cm jff^. 1 1 (b) 3.3 cm If/ 2,2 cm r/i 0-(J i i 1 1 ^ 0 8 12 16 20 24 t (h PST) Fig. 7.3. Diurnal variation of (a) measured sensible heat flux density (H) as well as its two components due to molecular diffusion (Hm) or air renewal (Hc) at z = 3.3 cm, and (b) air temperature at z = 2.2, 3.3, and 4.4 cm within a non-wetted 10 t ha"1 straw mulch on August 20, 1994. Counter-gradient H occurred from 9:00-14:00 PST. Detailed profiles of air temperature (including soil temperatures) within and above the mulch on August 20, 1994, are presented in Fig. 7.4. These profiles exhibit shapes frequently observed in plant canopies (Denmead and Bradley, 1985), in which air temperatures reach a maximum at around 2/3 of the canopy height (zlh = 0.67) for most daylight hours. Detailed air temperature profiles within a mulch canopy are rare in the literature. One such measurement, however, was made by Hares and Novak (1992) within a straw mulch with similar properties to the mulch studied here. By positioning Chapter 7. Sensible and latent heat fluxes 181 thermocouples (enclosed in the stainless steel tubing described previously for soil temperature measurements) at various heights within the mulch and monitoring the surface temperature with a bolometer, these authors observed an increase of temperature with height during the day and decrease with height at night. This result was not unexpected because our measurements show that the straw element temperature differs greatly from air temperature at the top of the mulch (Fig. 7.5) and the measurement of Hares and Novak (1992) were probably more typical of element temperatures rather than air temperatures in the mulch. For four consecutive days (7:30, August 28 to 24:00, August 31, 1993), we observed that the upper-surface of mulch element temperatures (Tu) at z = 40 t Oi PST) 0:00-0:30 6:30-7:00 8:30-9:00 35 30 - o D 10 15 20 25 30 35 40 T(°Q Fig. 7.4. Vertical profiles of measured air and soil temperatures above, within, and below a non-wetted 10 t ha"1 straw mulch at various times on August 20, 1994. Chapter 7. Sensible and latent heat fluxes 182 15 Day 1 1 Day 2 1 Day 3 C h 1 Day 4 < o u o 10 c 1 \ cP °l\ S' 1 5 9 \ 1 A T 1 f A J ol c S 1 " 0 H 1 i i i 12 0 12 0 12 0 12 0 t (h PST) Fig. 7.5. Measured and calculated (Eq. 7.4) temperature differences between the mulch element upper-surface (T U ) and air (7a) at the top of a non-wetted 10 t ha"1 straw mulch (2 = 6.6 cm) for four consecutive days (7:30 PST, August 28 to 24:00 PST, August 31, 1993). 6.6 cm were up to 15 °C warmer than the air temperature (Ta) during the day and 2-3 °C cooler at night. This difference could be accounted for by using the energy balance equation for a 0.33 cm thick "elemental" mulch layer (a layer such that no mutual shading occurs among elements, as defined in Chapter 5) as follows (Campbell, 1977): pcpAR Chapter 7. Sensible and latent heat fluxes 183 where Rn is the net radiation absorbed by this layer, LE is the latent heat flux from it, AR is the residue area index of the elemental layer, and AH is the boundary layer resistance to heat transfer, given by the following for forced convection (Campbell, 1977): where de\ is the characteristic dimension of the straw (= 0.3 cm), and u is the wind speed at the measurement height. The coefficient, b, indicates the degree of turbulence, with b = 1 representing no turbulence and b = 2.5 fully turbulent conditions (Parlange et al., 1971). The shelter factor, pa, accounts for increases in resistance due to interference among elements. Field values of pd are typically between 3 and 4 within plant canopies (Thorn 1971, Stewart and Thorn 1973). Since air flow within the straw mulch was highly turbulent (Chapter 6), we chose b = 2.5. Fig. 7.5 shows the comparison between the measurements and calculated T-Ta values using Eq. (7.3) for 4 consecutive days. Regression between measurements and calculations givesp& = 3.09, which is comparable with general field values. The high regression coefficient (r2 = 0.8, n = 89) justifies our method of measuring element surface-temperatures. Inside the mulch canopy, net radiation intercepted by elemental mulch layers decreases rapidly with height (Chapter 5), and the difference attenuates correspondingly. No significant temperature differences were found below 4.4 cm (i.e., the lower 2/3 of the canopy). The same was true at all heights for the difference between mulch element lower-surface and air temperatures (not shown). As a result, mulch element upper-surface temperatures increased with height during the daytime (Fig. 7.6). At night, the large difference between V and r a decreased 1/2 (7.5) Chapter 7. Sensible and latent heat fluxes 184 to about - 3 °C at the mulch top, and both T and Ta decreased with height within the mulch. t (h PST) Fig. 7.6. Diurnal pattern of measured mulch element upper-surface temperatures, Ta, within a non-wetted 10 t ha"1 straw mulch on August 30, 1993. For clarity, Tu values at z = 2.2 and 3.3 cm (which conveniently fall between those of underlying and overlying levels) were omitted in this figure. 7.3.2. Profiles of latent heat flux and water vapour pressure for a non-wetted mulch Profiles of latent heat flux, LE, and water vapour pressure, e, were plotted in Fig. 7.7 for 11:00-12:00 PST, August 23, 1994. With over half of the LE coming from the soil (55%) and bottom 2.2-cm mulch layer (32%), the profile of LE differed significantly from that of H, indicating differences in the effective source heights for H and LE. By analogy Chapter 7. Sensible and latent heat fluxes 185 to the center-of-pressure theorem (Thorn, 1971), the effective source height, d, can be expressed as: d = J^F(z)dz_ £F(z)dz + F (7.6) where F(z) is the flux divergence or source density at height z, and Fg is the flux from the soil surface. Using data in Fig. 7.1 and Fig. 7.7, dlh was found to be 0.81 for sensible heat and 0.13 for latent heat, with the former being similar to the value for momentum (dlh = 0.85, Chapter 6). The large difference in d, between H and LE within the mulch canopy thus invalidates the use of a single value for d for heat and water vapour, which is in contrast to a plant canopy, where using a single value for d is generally accepted (Thorn, 0 20 40 60 0 1 2 3 LE (W m"2) e (kPa) Fig. 7.7. Vertical profiles of measured latent heat flux density (LE) and water vapour pressure (e) within and above a non-wetted 10 t ha"1 straw mulch from 11:30-12:00 PST, August 23, 1994. Chapter 7. Sensible and latent heat fluxes 186 1972). Another difference between the profiles of LE and H is that no counter-gradient LE was observed. Fig. 7.8 presents the diurnal variation of LE and water vapour pressure (e) on August 20, 1994. Because the evaporation rate from the mulch was not measured for this day, values of LE were approximated each half-hour by using averages (for corresponding times) from four days (August 11, 12, 17, and 23, 1994), when measurements were made for the non-wetted mulch. Times when the earliest and latest measurements were made in the four days were 8:00-18:00 PST, respectively. Values of LE between 6:00-8:00 and 18:00-21:00 PST were extrapolated according to measurements made in 1993 when times for earliest and latest measurements were 6:00 and 21:00 PST. Between 21:00-6:00 PST, no direct measurement of LE was made. Instead, we assumed each half-hour LE to equal a value which was estimated from the total amount of water accumulated overnight. During night, LE remains relatively high (10-15 W m"2), while total LE from the soil-mulch system becomes negative (because of dew fall). Thus the mulch layers act as a water vapour sink at night, with the largest sink density at the mulch top. At sunrise, the wetted mulch layer warms up and moisture evaporates at a high rate. The evaporation rate from the soil, on the other hand, falls to near zero apparently because that the magnitude of the water vapour gradient between z = 0 and 1.5 cm decreases to almost zero. Later in the morning, the situation resembles the daytime pattern shown in Fig. 7.7. At all heights throughout the day, no counter-gradient LE is observed. Chapter 7. Sensible and latent heat fluxes 187 f(hPST) Fig. 7.8. Diurnal variation of measured latent heat flux density (LE) and water vapour pressure (e) at heights within a non-wetted 10 t ha'1 straw mulch on August 20, 1994. For clarity, LE values at z = 2.2, 4.4 and 5.5 cm (which lie between those of underlying and overlying levels) were omitted in this figure. Mulch water content, 0ml, averaged over the four days indicated previously, is presented in Fig. 7.9. Note that variations in 0ml, and LE are quite large from day to day. For example, the ratio of standard deviation to mean value for w and LE from 8:00-9:00 PST was 20% and 30%, respectively. The main reason for this is the varying amounts of dew fall in the previous night, which, in turn, is a function of air temperature, wind speed, and the degree of cloudiness. Fortunately, variations of LE for the mulch layers are relatively small, except for a few hours during the morning (7:00-10:00 PST), which Chapter 7. Sensible and latent heat fluxes 188 allows the use of average values for days when LE of the mulch layers is not measured. In Fig. 7.9, #mlat the top mulch layer (i.e., z = 5.5-6.6 cm) decreases rapidly after sunrise. Within 1-2 h of daybreak, 9ml decreases to a low level and remains at this level for rest of the day. For lower mulch layers, especially the bottom layer (i.e., z = 0-1.1 cm), it takes a much longer time for 9m[ to reach a steady state. 0 . 6 0 . 0 1 1 1 1 1 1 8 1 0 1 2 1 4 1 6 1 8 f ( h P S T ) Fig. 7.9. Measured water content (on mass basis, 9M) of a 1.1 cm straw mulch layer at various heights within a non-wetted 10 t ha"1 straw mulch, averaged over four days (see text for details). For clarity, 6^ values at z = 1.1-2.2, and 3.3-4.4 cm (which fall between those of underlying and overlying levels) were omitted in this figure. 7.3.3. Turbulent diffusivity and conductance for water vapour Chapter 7. Sensible and latent he at fluxes 189 A nearly constant mulch water content (defined by variations of 6mi, < 1% in a half hour period and a mulch contribution to total evaporation < 10%) for the whole mulch canopy occurs between 15:00-17:00 PST on average for the four days (Fig. 7.9). During this period, near-field effects, which are important if there is a water vapour source or sink within the mulch, are negligible, allowing for the application of gradient-flux relationships (Raupach, 1989). Turbulent diffusivity for water vapour, Dv , within and above the mulch canopy, can then be calculated using measured evaporation rate from the soil and a water vapour pressure profile as follows: n 7 j (7;+273)Z£de L dz' K J wher R v is gas constant for water vapour. Fig. 7.10 shows the vertical profile of Dv averaged over 52 half-hour measurement periods during 1993 and 1994. The overall average wind speed at z = 57 cm for these periods was 1.66 m s-1, and Dv of each half hour was normalized by multiplying by 1.66/(5s7cm of the half hour) due to the linear dependence of Dy on wind speed (Fig. 7.11). Near the soil surface, Dv was less than 2 times the molecular diffusivity of water vapour in still air 7Jvmo (2.2 x 10"5 m2 s"1 at 20 °C). The mean values of Dy increase exponentially with height within the mulch, which is best described by: Dv = 0.000494 exp[2.6(z//7-l)], r 2 = 0.93, n = l. (7.8) At the mulch canopy top, Dv= 0.000494 m2 s*1, which is about 5% less than the diffusivity for momentum at the same height under neutral conditions (Dm (h) = 0A(h-d)u% = 0.000523 m2 s"1). The attenuation coefficient of 2.6 lies within the general range Chapter 7. Sensible and latent heat fluxes • 190 of 2.5 to 4, obtained for vegetation canopies (Lemon, 1965). To date, direct measurements of Dv within a mulch canopy have not been reported. Researchers have tended to use exponential functions, similar to Eq. (7.8), but with different attenuation coefficients, to estimate Dv values within a mulch (e.g., Thompson, 1981; Stigter et al., 1984; Tuzet et al., 1993; Bussiere and Cellier, 1994). Thompson (1981) and Tuzet et al. (1993) used an attenuation coefficient of 2.5, whereas Stigter et al. (1984) and Bussiere and Cellier (1994) used a value of about 8. Thus, the attenuation coefficient reported here may help to clear-up uncertainties faced by other researchers when similar mulch types are studied. 1.0 0.8 0.6 0.4 0.2 0.0 1 Fig. 7.10. Vertical profile of turbulent diffusivity for water vapour within and above a 10 t ha"1 straw mulch for all available 52 half-hour periods during August 28-September 1, 1993, and August 10-25, 1994. In each of these half hour periods, the mulch water content varied by < 1% and the mulch contributed to the total evaporation by < 10%. Error bars indicate one standard deviation. Chapter 7. Sensible and latent heat fluxes 191 For the same periods, mulch conductance, km\, was calculated from the integrated version of Fick's law: kml=LEx(Ta)/[7.Spcp(e(0)-e(h))]. (7.9) Due to the influence of turbulence, these km\ values are generally much larger than the still air mulch conductance, k™°, which is given by (Hares and Novak, 1992): kZ = DTifL-^)fLlh, (7.10) where / m i is the porosity (measured to be 0.95 by immersing, quickly, known mass of mulch into a known volume of water and measuring the volume change), 0ml is the volumetric water content, and / m l is the tortuosity factor for the mulch (assumed to be Fig. 7.11. Ratios of mulch conductance to conductance in still air for water vapour through a 10 t ha' straw mulch, plotted against wind speed at z = 57 cm for the same data set as Fig. 7.10. Chapter 7. Sensible and latent heat fluxes 192 0.9). Fig. 7.11 shows that km\/k™ increases with wind speed (km\/k™ = l+1.86w5 7 c m, r2 = 0.29, n = 52), and is in the range 2-7 for wind speeds in the range 0.5-3 m s"1. Similar results were found for other mulch application rates (Chen et al., 1994). Our finding is in general agreement with the values found earlier using cruder methods for a similar straw mulch (Hares and Novak, 1992), and for other types of mulch. For example, Kimball and Lemon (1971) calculated the ratio for heptane flux transferred through a 2 cm thick wheat straw mulch to be 1 + 0.58wim. The coefficient, however, changes to 0.83 for a 1.1 cm thick flail-chopped corn residue (Tanner and Shen, 1990) and about 17 for a 25 cm high herbicide-killed winter wheat mulch (Heilman et al., 1992). Converting our wind speed measurements at 57 cm to 1 m with logarithmic profile (Chapter 6), we obtain a coefficient of 1.63, which indicates that the coefficient is sensitive to mulch attributes. 7.3.4. Energy budget closure for a non-wetted mulch The sum of H, L E , Go and SH was compared to Rn measured for the half hour period (t =11.5-12, August 23, 1994) within and above the non-wetted 10 t ha"1 mulch canopy (Fig. 7.12). The profile of R„ was simulated using the mulch radiation model, except at the mulch top where measurements were available. Agreement between RD and Go+Su+LE+H is excellent, considering the fact that all terms were measured or simulated independently, and sources of error existed in every component. The large source density of H near the mulch top, as discussed previously, can be explained by the rapid attenuation of Rn into the mulch top where solar radiation was effectively absorbed. In lower parts of Chapter 7. Sensible and latent heat fluxes 193 the mulch canopy, where mulch elements are clumped, the attenuation of Rn with height is significantly slower. As a result, a relatively large Rn exists at and is absorbed by the soil surface. It follows, therefore, that source densities of H and LE for 0 < zlh < 0.5 are small, but LE and G at z = 0 are considerable. Fig. 7.12. Profiles of net irradiance (Rn measured above canopy and simulated within canopy) as well as combinations of sensible heat flux (H), latent heat flux (LE), soil heat flux Go, and heat storage in mulch elements (SH) within and above the non-wetted 10 t ha"1 straw mulch from t =11.5-12, August 23, 1994. Energy balance closure is shown diurnally for August 20, 1994 in Fig. 7.13. Since the sensible heat was measured only at 1.1, 3.3, 6.6 and 9.6 cm, Rn and G0+Sn+LE+H at 0, 1.1, 3.3, and 6.6 cm are compared for the mulch canopy. The H value at 0 cm was assumed to be the same as the H value at 1.1 cm, and good agreement was found between Chapter 7. Sensible and latent heat fluxes 194 RN and GO+SH+LE+H at all four heights. An exception occurred at night, when Go+Sn+LE+H exceeded RN, especially at lower levels. This may be because a daily average cloudiness was used in the simulation of RN. Based on the RN measured above the t (h PST) Fig. 7.13. Comparison between net irradiance Rn (lines) and G0+Su+LE+H (symbols) at z = 0, 1.1, 3.3, and 6.6 cm for a non-wetted 10 t ha"1 straw mulch on August 20, 1994. Note the difference in scale. mulch canopy, conditions appeared to be more cloudy at night than during the day, so that simulated RN values were underestimated during some periods at night. The ratio of Go+Sy+LE+H to RN during this day (6:00-18:00 PST), and mean values of the energy components are presented in Table 7.1. Agreement is within 15% at all heights, and within 5% at the mulch top. At the mulch top, H is 72% of RN, which is similar to what Chapter 7. Sensible and latent heat fluxes 195 Table 7.1. Daytime mean net irradiance (Rn), latent and sensible heat flux densities (LE and H), and heat storage in mulch (SH) and soil layers (G0) as well as the ratio (G0+SH+LE+H)/Rn for a non-wetted mulch (August 20, 1994) and a wetted 10 t ha"1 mulch (August 29-September 1, 1994) at various heights. The values of Rn and (Go+Sti+LE+H)/Rn for the wetted mulch were calculated at first by using R of fresh straw, and then corrected by increasing R by 75% and assuming a linear distribution with no increase at the canopy top (values in bracket) (cm) Flux(W m"2) 6-18, 11-18, 6-18, 6-18, 6-18, or Ratio Aug. 20 Aug. 29 Aug. 30 Aug. 31 Sept. 1 6.6 Rn 185.8 287 (287) 249 (253) 161 (158) 197(195) LE 46.3 113.6 65.5 39.3 25.2 H 133.4 151.8 154.6 98.0 149.4 GO+SH 11.3 16.3 21.6 15.8 14.7 ratio 1.03 0.98 (0.98) 0.97 (0.96) 0.95 (0.97) 0.96 (0.97) 3.3 Rn 45.1 68.4 (48.5) 65.8 (48.2) 40.7 (29.2) 44.5 (35.2) LE 33.9 19.0 36.5 22.9 19.1 H 6.5 -2.1 -1.3 -0.6 -0.7 GO+SH 11.2 18.6 21.5 15.2 14.3 ratio 1.14 0.52 (0.73) 0.86(1.18) 0.92(1.28) 0.73 (0.93) 1.1 36.4 42.3 (17.8) 48.0 (25.9) 31.3 (18.4) 39.2 (24.4) LE 30.3 -10.0 7.8 8.8 10.8 H -4.7 -4.2 -5.3 -4.0 -4.3 GO+SH 11.2 20.0 21.2 14.8 14.2 ratio 1.01 0.14(0.32) 0.49 (0.91) 0.63 (1.07) 0.53 (0.85) 0 Rn 29.4 34.4(10.1) 39.7(13.0) 25.7(8.9) 34.0(12.4) LE 27 -17.9 -5.8 -1.2 2.2 H -4.7 -4.2 -5.3 -4.0 -4.4 GO+SH 11.1 20.4 21.0 14.7 13.7 ratio 1.13 -0.05(-0.17) 0.25 (0.76) 0.37(1.06) 0.34 (0.93) Chapter 7. Sensible and latent heat fluxes 196 was observed above a standing winter-wheat mulch when mulch and soil surfaces were dry (Heilman et al., 1992). For decreasing z in the mulch, Rn consists of an increasing proportion of LE + Sn while H attenuates and eventually becomes negative. 7.3.5. Turbulent fluxes and energy balance for a wetted mulch The 10 t ha"1 straw mulch was wetted completely by sprinkler irrigation during the night of August 28, 1994. Measurements then were made from 11:00, August 29 to 18:00, September 1, 1994. Fig. 7.14 shows the variation of water content for each 1.1 cm mulch layer at various heights within the mulch canopy. At first, nearly all layers are over saturated at 6?ni ~ 400% (the saturated 0 m i was measured to be 317% in the laboratory), except at the top layer where the drying process apparently had begun before the first measurement was made. During daytime, measurements of 0m\ drop swiftly, and rise slightly at night-time, indicating significant net evaporation from mulch layers. At the end of the four days, conditions approached those of a non-wetted mulch. Correspondingly, LE values, both positive (evaporation into the atmosphere) and negative (condensation onto the soil surface) were large at the start of the 4-day measurement period (Fig. 15). Some of these large values of LE at z = 0 (near -100 W m"2) at the beginning of this measurement may have been due to water dripping from the mulch layer, as evidenced by the fact that the 6U was larger than its saturated value, although measurements were begun about two hours after the irrigation ceased. No counter-gradient LE was observed during the four days for the wetted mulch. Chapter 7. Sensible and latent heat fluxes 197 i f * bo ^ 4 ^ <3i ay Tl Day 2 I Day 3 I Day 4 12 0 z fcm) 0 - 1 . 1 2.2-3.3 4.4-5.5 - 5.5-6.6 12 0 12 t (h PST) Fig. 7.14. Measured water content (6^ 0 of a 1.1-cm layer at various heights within a wetted 10 t ha"1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The mulch was wetted completely by sprinkle irrigation during the night of August 28. For clarity, 9^ values at z = 1.1-2.2, and 3.3-4.4 cm (which lie between those of underlying and overlying levels) were omitted in this figure. Chapter 7. Sensible and latent heat fluxes 198 Fig. 7.15. Measured latent heat flux density (LE) and water vapour pressure (e) within and above a wetted 101 ha"1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The first four hourly LE values lie beyond the figure scale which has a maximum reaching 230 W m"2. The mulch was wetted completely by sprinkle irrigation throughout the night of August 28. For clarity, LE values at z = 2.2, 4.4, and 5.5 cm (which lie between those of underlying and overlying levels) were omitted in this figure. Chapter 7. Sensible and latent heat fluxes 199 No counter-gradient H was observed either during the fours days for the wetted mulch. At z - 3.3 cm, H was almost zero throughout the four-day period (Fig. 7.16), although Hc was still positive (« - Hm) during most of the daytime, but was much smaller than that of the non-wetted mulch. This is because Rn was less and LE greater at z = 3.3 cm within the wetted mulch than within the non-wetted mulch during the daytime. For larger z, Ha is expected to increase rapidly, and exceed - Hm. Therefore, counter-gradient H values could have been observed, had H been measured at a higher level, such as just below the maximum air temperature height, which was at z = 6.6 cm for the first day. The maximum air temperature height gradually decreased to z = 5.5 cm for the second day, and approached z = 4.4 cm on the fourth day, a height at which air temperature is maximum within a non-wetted mulch. The difference between H at z = 6.6 and 9.6 cm was greater for the wetted rather than the non-wetted mulch. A possible explanation for this is that wetted straw pieces that are above the average canopy height are an even more important source of H than they are for non-wetted mulches. Another possible explanation for this phenomenon was that the thermocouple at z = 6.6 cm, was pushed down somewhat during irrigation, which increased the differences of H. At z = 1.1 cm, the pattern of H was essentially the same as that for non-wetted mulches, as expected, due to the prominence of molecular diffusion. Chapter 7. Sensible and latent heat fluxes 200 Fig. 7.16. Measured sensible heat flux density (H) and air temperature (Ta) within and above a wetted 101 ha'1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The mulch was wetted completely by sprinkle irrigation throughout the night of August 28. Chapter 7. Sensible and latent heat fluxes 201 Excellent energy budget closure was found at the top of the wetted 10 t ha"1 mulch canopy during the four days (Fig. 7.17). The Rn and H values were calculated in the same way as for non-wetted mulches. During daytime hours, closure was within 5% at the mulch top (Table 7.1). However, for lower levels simulated Rn values were generally much larger than Go+Su+LE+H. Many reasons for this are possible, for example, errors in the measurement of H, LE, Go and <SH, and moisture movement in soil and among mulch 12 0 12 0 12 0 12 r(hPST) Fig. 7.17. Comparison between net irradiance Rn (lines) and G0+SH+LE+H (symbols) at z = 0, 1.1, 3.3, and 6.6 cm for a wetted 10 t ha"1 straw mulch from 11:00, August 29 to 18:00, September 1, 1994. The mulch was wetted completely by sprinkler irrigation during the night of August 28. Note the difference in scale. Chapter 7. Sensible and latent heat fluxes 202 layers in the liquid phase: Probably the most important reasons for discrepancies in closure is the break-up of residue elements, which could affect Rn mainly but also LE and H. Based on observations made by Wagner-Riddle et al. (1996), who determined that residue area index R nearly doubles in two months, we assumed that the R of our wetted straw mulch, which had been on the soil surface for about 40 days, increased by 75%. The increase in R was assumed to distribute linearly with height (with no increase at the top), because when small pieces break off they tend to fall down onto lower layers due to wind, rain, and irrigation. Using corrected values of Rn, based on the above two assumptions, the energy budget closures improved significantly at various heights within the mulch (Fig. 7.18). Except for the first day, closures at 0, 1.1, and 3.3 cm during the daytime were within 30% (Table 7.1), and the absolute value for the energy budget residue was less than 10 W m"2. Since every term was measured or simulated independently, and possessed possible sources of error, the closures are then quite good. The relatively poor closure on the first day, which had an absolute energy budget residue of less than 15 W m"2, was most likely caused by the dripping of water onto the soil surface from the residue elements, which exaggerated condensation there. Above the wetted mulch canopy, H is still the largest fraction of Rn among the energy components, despite the high water content of mulch elements. The value of H was 53% of Rn on the first day, and gradually increased to 76% on the fourth day. In contrast, H accounted for only 27% of Rn for a stubble winter wheat mulch after it was wetted (Heilman et al., 1992). The remaining 62% and 11% of the Rn was attributed to LE and Go for the wetted stubble mulch. For our wetted 10 t ha"1 straw mulch, LE Chapter 7. Sensible and latent heat fluxes 203 accounts for only 40% on the first day, and decreases to 13% by the fourth day. The G 0 value varied within the range of 7-10% during the four days, which is slightly lower than the Go for a stubble mulch (Heilman et al., 1992). This indicates that a mulch of horizontally distributed elements is more effective than a stubble mulch in terms of reducing water loss through evaporation and lowering soil temperatures after irrigation or rainfall. a o o O B 100 0 A . 3.3 cm -30 * 1 12 0 12 0 12 0 12 t (h PST) Fig. 7.18 Same as Fig 17 except that Ra values are corrected by assuming the residue area index (R) increases by 75% and is distributed linearly with no increase at the mulch top. 7.4. Conclusions Chapter 7. Sensible and latent heat fluxes 204 Sensible and latent heat flux densities, as well as the energy balance within and above a non-wetted and a wetted 101 ha"1 horizontal straw mulch were analyzed. Vertical profiles of sensible and latent heat fluxes reflect source distributions. For a non-wetted mulch canopy, the major sources of sensible heat are near the canopy top during the day. Counter-gradient fluxes of sensible heat are often observed during the day at the middle of the mulch canopy (zlh = 0.5), just below the maximum air temperature height at zlh = 0.67. The straw mulch is probably the shortest and densest canopy for which counter-gradient sensible heat fluxes have been reported. At lower levels, molecular diffusion and smaller eddies dominate, so that sensible heat fluxes are negative during the day. At night, air temperatures decrease to a minimum at the mulch top due to radiation cooling. No counter-gradient H is observed at any level during the night. The shape of the vertical profiles of latent heat flux differs greatly from that of sensible heat fluxes, its main source being at the soil surface during daytime. Displacement heights for H and LE from 11:30-12:00 PST on August 23, 1994, were calculated to be 0.81/7 and 0.13/7, respectively. Evaporation from mulch elements is relatively small except during early morning hours when the mulch is partially wet from dew fall and evaporation from the underlying soil at night. Evaporation from the soil is considerable and nearly constant, probably as a result of the nearly constant within-canopy convective air-flow associated with nearly constant vertical temperature difference. After sunrise, evaporation from soil falls to nearly zero or even negative values, because the water vapour pressure at z = 1.1 cm approaches or even exceeds that at the soil surface when the wet mulch warms. Chapter 7. Sensible and latent heat fluxes 205 Turbulent diffusivity for water vapour, calculated when the mulch water content was nearly steady, increases exponentially with height (attenuation coefficient = 2.6) from near the soil surface where it is within a factor of 2 of molecular diffusivity. For nearly steady mulch water contents, the ratio of effective to still air mulch conductance was in the range of 2-7 for wind speed ranging from 0.5-3 m s"1. Condensation was clearly and consistently observed beneath the wetted mulch during daytime hours, and the above-canopy evaporation rate was higher than that for non-wetted mulches, due to the larger contribution of LE from the mulch canopy. Despite the significant increase in LE, H was still the largest component partitioned from Rn. Air temperature reached a maximum at a higher level within the wetted mulch compared to the non-wetted mulches. No counter-gradient H or LE were observed within the wetted mulch canopy. At night, H and LE had similar patterns within wetted and non-wetted mulches. Energy budget closure within 15% was found between net radiation and the sum of all other energy components at all four heights (z = 0, 1.1, 3.3, and 6.6 cm) for the non-wetted mulch. The same was true at the top of the wetted mulch, but not at lower levels. However, after correcting the net radiation fluxes by accounting for the effects of residue element break-up, closure was improved significantly, to within 30% for all four heights, except for the first day, when dripping of water from mulch elements onto the soil may have been important. 7.5. References Chapter 7. Sensible and latent heat fluxes 206 Amiro, B.D., 1990. Comparison of turbulence statistics within three Boreal forest canopies. Boundary-Layer Meteorol., 51: 99-121. Barr, A.G. and Brown, D.M., 1995. Estimating forage yield and quality changes during field drying for hay. 2. Model of forage drying. Agric. For. Meteorol., 76:107-127. Bussiere, F. and Cellier, P., 1994. Modification of the soil temperature and water content regimes by a crop residue mulch: experiment and modeling. Agric. For. Meteorol., 68: 1-28. Chen, W.J., Novak, M.D. and Ketler, R., 1994. Turbulent vapour transfer through straw mulches using an improved tension-plate apparatus. 21st Confer. Agric. For. Meteorol., San Diego, USA, 207-210. Campbell, G.S., 1977. An introduction to environmental biophysics. Springer-Verlag, 159pp. Denmead, O.T. and Bradlay, E.F., 1985. Flux-gradient relationships in a forest canopy. In: Hutchison, B.A. and Hichs, B.B. (ed), The Forest-Atmosphere Interaction. D. Reidel Publishing Company, 421-442. Denmead, O.T., 1976. Temperate cereals. In: Monteith, J.L. (ed.), Vegetation and the Atmosphere: Volume 2. Case Studies. Academic Press, London, 1-30. Hares, M.A. and Novak, M.D., 1992. Simulation of surface energy balance and soil temperature under strip tillage: II. Field test. Soil Sci. Soc. Am. J., 56: 29-36. Chapter 7. Sensible and latent heat fluxes 207 Heilman, J.L., Mclnnes, KJ . , Gesch, R.W. and Lascano, R.J., 1992. Evaporation from ridge-tilled soil covered with herbicide-killed winter wheat. Soil Sci. Soc. Am. J. 56: 1278-1286. Jacobs, A.F.G., van Boxel, J.H. and Shaw, R.H., 1992. The dependence of canopy layer turbulence on within-canopy thermal stratification. Agric. For. Meteorol., 58: 247-256. Kimball, B.A. and Lemon, E.R., 1971. Air turbulence effects on soil gas exchange. Soil Sci. Soc. Am. Proc, 35: 16-21. Lee, X. and Black T.A., 1993. Atmospheric turbulence within and above a Douglas-fir stand. Part II. Eddy fluxes of sensible heat and water vapour. Boundary-Layer Meteorol., 64: 369-389. Lemon, E.R., 1965. Micrometeorology and the physiology of plants in their natural environment. Plant Physiology IVA, Acad. Press, N.Y., 203-227. Meyers, T.P. and Paw U, K.T., 1987. Modeling the plant canopy micrometeorology with higher-order closure principles. Agric. For. Meteorol. 41: 143-163. Parlange, J.Y., Waggoner, P.E. and Heichel, G.H., 1971. Boundary layer resistance and temperature distribution on still and flapping leaves. Plant Physiology, Lancaster, 48, 437-442. Shaw, R.H., Silversides, R.H. and Thurtell, G.W., 1974. Some observations of turbulence and turbulent transport within and above plant canopies. Boundary-Layer Meteorol., 5: 429-449. Chapter 7. Sensible and latent heat fluxes 2 0 8 Steward, J.B. and Thorn, A.S., 1973. Energy budgets in a pine forest. Q.J.R. Meteorol. Soc. 99:154-170. Stigter, C.J., Mwanpaja, A.R. and Kainkwa, R.M.R., 1984. Infrared surface and thermostor sub-surface temperature explaining the thermophysical characteristics of grass mulch. In Proceedings on the 2nd Symposium on Temperature Measurement in Industry and Science, LMEKO, Suhi (GDR), 523-531. Thorn, A.S., 1971. Momentum absorption by vegetation. Quart. J. R. Meteorol. Soc, 97: 414-428. Thorn, A.S., 1972. Momentum, mass and heat exchange of vegetation. Quart. J. R. Meteorol. Soc, 98: 124-134. Thompson, N., 1981. Modeling the field drying of hay. J. Agric. Sci. Camb., 97:241-260. Tuzet, A., Perrier, A. and Oulidaissa, A.K., 1993. A prediction model for field drying of hay using a heat balance method. Agric. For. Meteorol., 65:63-90. Wagner-Riddle, C , Gillespie, T.J. and Swanton, C.J., 1996. Rye mulch characterization for the purpose of microclimatic modeling. Agric. For. Meteorol, 78: 67-81. Weast R.C. (ed.), 1975. Handbook of chemistry and physics. CRC Press, Cleveland, OH. Wilson, J.D., Ward, D.P, Thurtell, G.W. and Kidd, G.E., 1982. Statistics of atmospheric turbulence within and above a corn canopy. Boundary-Layer Meteorol, 24: 495-519. Chapter 8. Concluding remarks 209 Chapter 8 Concluding remarks Previously, influences of turbulence on the exchange of mass and energy within a mulch were only inferred indirectly from evaporation rates beneath the mulch, which are larger than those due to molecular diffusion alone. Methods developed in this thesis (e.g., the improved tension-plate system and the new air renewal model), for the first time, allow turbulent sensible and latent heat fluxes to be measured or calculated accurately within a straw mulch. Data presented in this thesis characterize more fully the regimes of turbulence and turbulent sensible and latent heat fluxes within a 101 ha"1 straw mulch. Manually weighing a micro-lysimeter to measure evaporation under a mulch is inconvenient, time consuming, and inaccurate under mulches because of errors incurred when disturbing the mulch and exposing the micro-lysimeter to above mulch conditions, however briefly. Placing the micro-lysimeter on a buried accurate digital balance and recording the weight continuously avoids these problems, but is expensive and subject to noise caused by wind. The accuracy of the weighing lysimeter described by Grimmond et al. (1992) was about 30 W m"2, which is too large by an order of magnitude for measuring evaporation under mulches. The tension-plate system improved, in this thesis, from the original system of Arkin et al. (1974) provides a simple, inexpensive, and accurate (within 5 W m"2) method for measuring first-stage evaporation and condensation rate from bare and mulched soils. Chapter 8. Concluding remarks 210 Within a dense and short canopy, such as a straw mulch, turbulent sensible heat flux cannot be measured with standard approaches such as eddy-correlation. The new renewal model offers an effective alternative, which can calculate sensible heat fluxes within and above canopies using only the third order temperature structure function and the friction velocity. Tests of the model using eddy correlation and Bowen ratio/energy balance data from a Douglas-fir forest, a straw mulch and a bare soil show that the model performs extremely well. Furthermore, the model's only empirical coefficient was nearly identical for all three surfaces, indicating that the coefficient may be applicable to a wide range of land and water surfaces. Because it does not require a vertical velocity measurement, the renewal model is not subject to the same limitations as eddy correlation during periods of precipitation or low wind speed at night when the vertical velocity measurement becomes less accurate. As a result, the renewal model should be able to fill data gaps in eddy correlation measurements. Even when the eddy correlation method functions normally, the renewal model offers a valuable comparison by calculating fluxes independently on-line. The radiation model presented in this thesis is simple, multiple-layer model, which neglects multiple reflections between layers and calculates long-wave radiation fluxes using a view factor concept. Yet, because it incorporates three most important features of the mulch canopy (clumping between mulch elements, different temperature on lower and upper surface of a straw, and negligible transmittance of mulch element), the model can calculate net radiation and other radiative components accurately within and above the mulch canopy. Mulch structure changes (such as break-up, decomposition, and Chapter 8. Concluding remarks 211 darkening) must be taken into accounted in the simulation if the mulch has been in the field for a long period. Air flow within the mulch canopy is highly turbulent, with the longitudinal turbulence intensity varying from 0.64 to 0.91. At an occurrence frequency of about 1 Hz, determined from analyzing air temperature and wind speed time series, large-scale coherent eddies dominate the air flow. Strong daytime thermal stratification within the mulch has no effect on the air flow, but under nocturnal low-wind conditions, thermal instability may cause steady, within-canopy convective air flows. During the daytime, counter-gradient fluxes of sensible heat were calculated consistently using the new air renewal model at z = 0.5/7 within the mulch canopy. The mulch canopy is the densest and shortest canopy within which counter-gradient fluxes have ever been reported. The highest source density of sensible heat is near the top of the mulch canopy, coincident with the strongest absorption of solar radiation by the top mulch layer. Near the soil surface, sensible heat fluxes are negative (downward). During the night, sensible heat is transferred toward the mulch canopy top from both above and below. The new air renewal model developed in this thesis may also be used to infer other scalar fluxes from high-order structure functions without measuring the vertical wind component at high frequency. Vertical profiles of latent heat fluxes within the mulch differed greatly from those of sensible heat, with the highest source density being at the soil surface during most of the day, when evaporation from the air dry mulch elements is relatively small. Exceptions occurred during early morning hours when elements are wet from dew fall and Chapter 8. Concluding remarks 212 evaporation from the soil during the night. Evaporation rates from the soil, which were measured using an improved tension-plate system, are relatively high at night, reduce to near zero or even negative (e.g., condensation) at sunrise, and then increase to a peak in the afternoon. Throughout the daytime, condensation on the soil surface was measured under the wetted mulch. Turbulent diffusivity for water vapour increases exponentially with height with a coefficient « 2.6, from near the soil surface where it is close to the molecular diffusivity. As a result, water vapour conductance is typically enhanced by 2 to 7 times the molecular value, for wind speeds ranging from 0.5-3 m s"1 for the straw mulch. Diffusivities and conductances were computed from soil evaporation rates and vapour pressure profiles when the water content of the mulch canopy was stable during late afternoon, so that near-field effects were negligible. In other time periods of the day, the mulch canopy acts as either a source or a sink of water vapour so that near-field effects become important. Near-field effects are important all the time for sensible heat fluxes. Therefore, a complete simulation of mass and energy exchange within the mulch canopy must consider both far-field and near-field effects, using models such as Lagrangian type and higher-order closure schemes. The methods developed and data obtained in this thesis thus provide a basis for further investigation of mass and energy exchange within a mulch using Lagrangian models and higher-order closure schemes. Appendix. Mulch Characteristics 213 Appendix Mulch Characteristics The mulch used in this thesis' experiment was a mixture of barley straw, clover, and weeds during September 10-28, 1993, and pure barley straw otherwise. The barley straw was bright yellow during first few weeks of field application and became darkened afterwards, while the appearance of clover and weeds was dark from the beginning. A typical piece of straw was cylindrical, with a length of 30 cm and a diameter of 0.3 cm, although a large fraction of the straws was flat. The elemental reflectivity was measured to be 0.46 for the fresh straw and estimated to be 0.3 for the mixture of barley straw, clover, and weeds. Filed capacity of these straws was measured to be about 400% on the gravitational basis. Applied on the field at a rate of 2, 5, 10 and 15 t ha"1, the mulch canopy height was 1.2, 3, 6.6, and 9 cm, respectively. 

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