Measurement of heat and vapor transfer coefficients at the soil surface beneath a maize canopy using source plates

AGRICULTURAL AND FOREST METEOROLOGY

Agricultural and Forest Meteorology 75 (1995) 161-189

ELSEVIER

Measurement of heat and vapor transfer coefficients at the soil surface beneath a maize canopy using source plates T.J. Sauer*, J.M. Norman, C.B. Tanner, T.B. Wilson University

of Wisconsin-Madison,

Department of Soil Science, 1525 Observatory WI 53706, USA

Drive, Madison,

Received 26 January 1994; revision accepted 5 October 1994

Abstract

thus canopy microclimate, it is of vital importance to accurately describe heat and mass transfer rates at the soil surface. The objective of this study was to develop a technique for independent measurement of soil heat and water vapor transfer coefficients at the soil surface beneath a plant canopy. Heat and vapor source plates were installed level with the soil surface to provide areas of known and controllable temperature and/or vapor pressure. Sensible heat flux density was determined from an energy budget analysis while evaporation from wetted felt fabric on one plate’s surface was used to determine the source plate’s latent heat flux density. Temperature and vapor pressure measurements at and 10 mm above the source plate surfaces were used to calculate interfacial heat and mass transfer coefficients. Measured heat and vapor transfer coefficients (hh and h,, respectively) ranged from 2 to 30 mm s-l over wind speeds from 0.05 to 2.8 m s-’ measured 0.03 m above the plate surface. Log-profile estimates of surface transfer coefficients when the soil was bare or the canopy < 0.3 m tall, were comparable with calculated bulk soil surface and source plate transfer coefficients at moderate wind speeds but were much higher than the source plate values at wind speeds greater than approximately 1.0 m s-l.

1. Introduction The transfer

of energy

as latent

layer of air within plant canopies microclimate. Despite early and *Corresponding author at: USDA-AR& Drive, Ames, IA 5001 l-4420, USA.

and

sensible

heat

between

the soil and

is a process with important implications significant progress in understanding Midwest

Area,

National

Soil Tilth Laboratory.

016%1923/95/$09.50 0 1995 - Elsevier Science B.V. All rights reserved SSDl 0168-1923(94)02209-7

the lowest

for canopy sensible heat 2150 Pammel

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exchange and evaporation from both bare soil and dense plant canopies, knowledge of heat and vapor transfer processes at the soil surface beneath plant canopies remains deficient. Investigations at this interface are hindered by difficulty in obtaining accurate measurements of fluxes of generally small magnitude and large spatial variability. Ham and Heilman (1991) combined Bowen ratio, energy balance, and stem flow measurements to determine the sensible and latent heat flux densities from a cotton (Gossypium hirsutum L.) crop and the underlying soil separately. Resistance to heat a vapor transfer at the soil surface was determined from the appropriate flux measurements, calculated vapor pressure at the soil surface and measured surface temperature and temperature and vapor pressure profiles in the canopy air space. Resistance values at the soil surface measured on three dates were highly variable and showed a weak inverse relationship with wind speed measured above the canopy. Massman (1992) using eddy correlation and surface energy balance techniques, determined subcanopy resistance values for a semiarid shortgrass steppe of a similar magnitude as Ham and Heilman (1991). Ham and Kluitenberg (1993) studied the positional variation of the soil energy balance components and transfer coefficients beneath a wide-row soybean (Glycine max.) canopy and reported interfacial heat transfer coefficient values from 1 to 50 mm C’. Again, these values were highly variable and not well correlated with above-canopy wind speed. When data are not available to determine the desired transfer coefficients (or resistances) at exchange surfaces directly, other techniques must be employed. A common method involved combining the diffusion analogue equations (Eqs. (1) and (2)) with their corresponding log-profile heat and mass transfer equations (Eqs. (4) and (5)). The resistance forms of these equations and their momentum transfer analogue (i.e. aerodynamic resistance) have been widely applied to obtain estimates of the various resistances from analyses of wind profiles over plant canopies (Szeicz et al., 1969; Stone and Horton, 1974; Heilman and Kanemasu, 1976; Seguin and Itier, 1983; Kustas, 1990; Massman, 1992). Others (Shuttleworth and Wallace, 1985; Lascano et al., 1987) have used canopy aerodynamic resistance estimates to predict resistances at the soil surface beneath the canopy using leaf area index as a scaling factor. van Bavel and Hillel (1976) used log-profile predictions of the aerodynamic resistance at the soil surface directly as input for a model that simulates potential and actual evaporation from a bare soil surface. Examples of studies that provide independent data to corroborate estimates of soil surface resistances obtained from the log-profile analysis could not be found in the literature. In order to circumvent the difficulties imposed by spatial variability of sensible and latent heat fluxes at the soil surface beneath plant canopies, an approach using large source plates has been used to measure fluxes at this interface. The source plate technique involves replacing an area of the soil with a plate of homogeneous and controllable sensible and/or latent heat flux. Arkin et al. (1974) describe an apparatus consisting of a flat plate covered with blotter paper and a thin layer of soil to which water is supplied under a small tension. This device was used to measure first-stage evaporation in the field. Bailey et al. (1975) measured convective heat transfer from a desert surface by measuring heat transfer from ‘convection boxes’ placed at the soil

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surface. These convection boxes consisted of a thin aluminum plate surrounded by sealed air space and insulation on the bottom and sides. Schuepp (1977) used a copper plate in a similar design but with guard plates surrounding the central heat transfer plate. Field measurements were made with this design beneath several canopies and laboratory measurements were made using various surface roughness and model windbreak elements. The objectives of this study were to refine the source plate technique to measure heat and vapor exchange at the soil surface beneath a maize canopy and to characterize the measured interfacial transfer coefficients in terms of local environmental conditions.

2. Methods 2.1. Theory Heat transfer and evaporation from the soil surface to the air above are often represented as diffusion processes and may be described by H = &‘cr(To

- T,)

(1)

E = hV(MV/RTabs)(eo - e,)

(2)

for heat and water vapor, respectively, where H is the sensible heat flux density (W me2), hh is the surface or interfacial heat transfer coefficient (m s-t), p is the density of moist air (kg me3), cp is the specific heat of moist air at constant pressure (J kg-’ Y-t), To is the temperature of the surface (“C), T, is the temperature of the air at height z above the surface (“C), E is the evaporation rate (kg rnp2 s-l), h, is the surface or interfacial vapor transfer coefficient (m s-l), AI, is the molecular weight of water (kg melee’), R is the gas constant (8.31 J mol-’ K-l), Tabs is the absolute temperature (K), e. is the vapor pressure at the surface (Pa) and e, is the vapor pressure at height z (Pa). Under steady state conditions over a large, aerodynamically rough surface, the vertical profile of the horizontal wind speed is described by U, =

(u,/k){ln[(z - 4lz01 + vL>

(3)

where u, is the horizontal wind speed at height z (m s-l), u, is the friction velocity (m s-l), k is von K&man’s constant (0.40) z is the height above the surface (m), d is the displacement height (m), z. is the momentum roughness length (m), and $M is the diabatic profile correction factor for momentum. Utilizing Reynold’s analogy for the similarity between momentum transport and the transfer of scalars in the constant flux layer, analogous equations can be written for heat and mass (here water vapor) transfer, respectively T, = To - [Hl(p$u,)l{ln[(z

- d)/Zhl + @h)

e, = eo - [(ERT,b,)/(M,ku,)l(ln[(z

- d)/Gl + ‘d%)

(4) (5)

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where the subscripts h and v refer to heat and vapor. There is considerable disagreement over the relationship between the roughness lengths for momentum, heat, and vapor as the transfer of the scalars (heat and vapor) at the surface is controlled by molecular diffusion while momentum transfer also involves pressure forces (Brutsaert, 1975). Dyer and Hicks (1970) provide experimentally determined values for the diabatic correction factors where &, # & = qV. By combining Eqs. (1) and (2) with (4) and (5), respectively, and substituting Eq. (3) in for u,, the resulting equations allow the prediction of the surface transfer coefficients llh = (u,k’)/({ln[(J

- d)/~~] + tih}{ln[(z

-

4l711+ 4mI)

h, = (v,k’)/({ln((;

- (-l)/zV] + Q,>{ln[(z

-

4l4 + ?&I)

The log-profile technique requires that measurements be obtained under steadystate conditions over large, homogeneous, aerodynamically rough surfaces. Under moderately stable or unstable conditions, diabatic correction factors are necessary and may be sizable. No formulations for the correction factors are available for either strongly stable or unstable conditions. As the log-profile analysis is only valid in the constant flux layer, Eqs. (6) and (7) cannot be directly applied to the soil surface henpath “III.,ULI.

a ‘ rsnnnxr u u”“y,

ar the U” LIIU veoetatinn ,Wb”CUL’“”

EPI-XIPE a~ Y U1I ,.,., UY u ~n,,rr~ ““Ul”,,

anrllnrVI cinlr fnr heat anA x,sv-,n\t‘ U”U, .,1111.IV& ,lVUL UllU ‘uy”’

and a sink for momentum. Nonetheless, wind profile measurements may be used with Eqs. (6) and (7) to estimate the heat and vapor interfacial transfer coefficients (hi, and h,) for bare soil surfaces provided that the above requirements are met. 2.2. Field measurements All field measurements were completed during the 1990 and 1991 growing seasons at the University of Wisconsin, West Madison Agricultural Research Station near Madison, Wisconsin USA (43’8’N, 89O2O’W, 265 m above m.s.1.). The soil at the field site is classified under the USDA system as a Batavia silt loam (fine-silty, mixed, mesic, Mollic Hapludalf), with 2-6% slope. Maize (Zea muys L.) was planted in a 11.3-ha field in rows 0.76 m apart oriented in a north-south direction on 8 May 1990 and 9 May 1991 at a density of approximately 85000 plants haa’. In 1990, all instruments were installed after emergence of the maize plants and preliminary measurements were made under full canopy conditions. In 1991, installation was completed before crop emergence and comprehensive measurements were made throughout the growing season. The minimum fetches for the instrument installation was 360, 2.55, and 80 m for wind from the north, west, and south, respectively. Prevailing summertime winds at the field site are from the southwest. Alfalfa (Merlicago sativa) was grown on the adjacent fields to the west and south during both growing seasons. The topography in the vicinity of the field site is gently undulating. Tables 1 and 2 list the types of measurements made during the field experiments. The instruments along with their respective shelters and supports were positioned along a 20 m north-south transect 20 m from the eastern edge of the field. Fig. 1 is a schematic diagram of the field experimental design and layout. One heat and one

T.J. Sauer et al. / Agricultural and Forest Meteorology 75 (1995) 161-189 Table 1 Measurements

and sensors

used to describe

the local microclimate

165

of the field site

Measuremen?

Sensorb

Wind speed in and above canopy (various) Wind speed above canopy (3.7) Wind direction above canopy (3.7) Solar radiation above canopy (3.5) Net radiation above canopy (3.5) PAR’ above canopy (3.5) PAR at soil surface Canopy temperature (3.35) Air temperature above canopy (3.35) Relative humidity above canopy (3.35) Precipitation (3.35) Soil heat flux (-0.05) Soil temperature (-0.025) Soil temperature (-0.2 - 1.0)

Heat transfer anemometers Met One cup anemometer Met One wind vane LI-COR LI-ZOOS pyranometer Swissteco net radiometer LI-COR LI-190s quantum sensor LI-COR LI-191s line quantum sensor Everest Interscience series 4000 infrared thermometer Vaisala HMP 35A sensor Vaisala HMP 35A sensor Texas Electronics tipping bucket precipitation gage Radiation Energy Balance Systems heat flow transducers Campbell Scientific 107B temperature probes Thermocouples

a The positive numbers in parentheses are the height (in m) of the measurement above the soil surface while the negative numbers indicate the depth below the soil surface. b Mention of product or trade names does not consistute endorsement by the University of Wisconsin to th0 ~~0n.r;~” nf Lllr UII.,,"YI"I, "I ,ehPTP "LIIUIY. '

PAR = photosynthetically

active radiation.

vapor source plate were positioned two rows apart near the center of the transect. A 3.75-m tall instrument tower was located at the south end of the transect to support instruments used for a typical weather station, while a similar tower at the north end of the transect supported additional aerial instruments. The weather station sensors provided data on the local microclimate including solar irradiance, precipitation, wind speed and direction, air temperature and relative humidity, soil heat flux, and soil temperature (at 25 mm). The soil heat flux and soil Table 2 Measurements

and sensors used in the source plate analysis

Measurement”

Sensor

Source plate surface temperatures Source plate temperatures Source plate sheath temperatures Air temperature above source plates (0.01) Source plate power inputs ohn,ra U”Ulll ~n,,rr~ p”‘ nlotan Ifi fi<, N~pt I.UL m,i;ot;r\n I”“I‘LIl”II Y”““L Lc’o \“.“d,

Everest Interscience Agri-Therm infrared thermometer Thermocouples Thermocouples Thermocouples Campbell Scientific CR7 datalogger C&n.t0r,? 1111111 mini 1111 no+ ,Y,i;~m~t~r “..I.,LILI~” LUUl”LllrLIl Thermocouples Everest Interscience Agri-Therm infrared thermometer Middleton mini net radiometer General Eastern 1111 H dew point hygrometer Heat transfer anemometer

Soil surface temperature Soil surface temperature Net radiation above soil (0.05) Vapor pressure above wet plate (0.01) Wind speed above source plates (0.03) a The positive

numbers

in parentheses

are the height (in m) of the measurement

above the plate surface.

166

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75 (1995) 161-189

Fig. 1. Schematic of field experimental design showing heat (HSP) and vapor (VSP) source plates, weather station (WS), tower for aerial instruments (T), datalogger (CR7), power supply shelter (PS), soil net radiometer (SNR),and dewpoint hygrometer (DH).

temperature were measured using paired soil heat flow transducers and thermistors positioned 0.15 and 0.30 m from a plant row. All weather station measurements were recorded by a Campbell Scientific Inc. 21X datalogger at 60 s intervals, with 1800-s means stored for analysis. The tower at the north end of the instrument transect supported a net radiometer and infrared thermometer for above-canopy measurements. No above-canopy temperature measurements were made in 1990, however, and on 8 July 199 1 the infrared thermometer was moved to the weather station tower in order to obtain a more representative field of view. The source plate design used here is a modification of that used by Tanner and Shen (1990) to measure water vapor transfer through maize residue. Saeed et al. (1994) give a detailed description of the design, construction, and operation of the source plate system. A brief discussion of the source plate characteristics and operation follows. The plates of the source plate assemblies consisted of a 13-mm thick, 305-mm wide by 864-mm long plate of anodized aluminum. Each plate had grooves on the bottom for placement of heater windings and thermocouples that were held in place by flexible epoxy resin. The sides and bottom of the anodized aluminum plate were surrounded by 25.4 and 38.1 mm of polystyrene insulation, respectively, and placed in an aluminum pan and sealed in place with silicone sealant. Four thermocouples were affixed to the inside of the pan to measure its temperature. All thermocouple and heater winding wires were brought out to a connector strip mounted on the aluminum pan for

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connection to a datalogger or power supplies. For the vapor source plate (VSP), water was supplied from a Mariotte supply device through two holes in the center of the plate to polyester felt fabric placed on the anodized aluminum surface. The heat source plate (HSP) had an identical construction with the exception that no water supply tubing or fittings were installed and heat transfer measurements were made over the bare anodized aluminum surface. Two 0.25-m tall phenolic rods were mounted on threaded rods placed in small holes in each of the source plates to support air thermocouples, heat transfer anemometers and an inlet for a dew point hygrometer (VSP only). A shallow excavation was made in the center of an inter-row area for each source plate and the bottom of each excavation was covered with a layer of washed gravel. Aluminum frames were inserted into the excavations and the soil around the disturbed areas was shaped to correspond with the local microtopography. During measurement intervals, the source plates were installed inside the aluminum frames that were oriented parallel to the rows with their tops level with the soil surface. Between measurement periods, the source plates were raised above the soil surface and covered by a wooden shelter. During daytime measurements aluminum shades mounted on 2.45-m tall rods were positioned to block each of the plates from direct sunlight in order to ensure uniform net radiation on the plate surfaces. Another wooden shelter enclosed a Campbell Scientific Inc. CR7 datalogger that recorded all of the source plate measurements at 5-s intervals and calculated 1800-s means. For each source plate, the datalogger recorded plate temperature, air temperature above the plate surface (two thermocouples per plate), aluminum pan temperature, voltage across the heater windings (two or three per plate), wind speed above the plate surface (heat transfer anemometer), and net radiation. In addition, measurements of vapor pressure above the vapor source plate, vapor pressure above the soil surface, soil net radiation, canopy net radiation, canopy temperature, soil surface temperature (four thermocouples in parallel), soil temperature at 0.2- and 1.0-m depths, and wind speed within (two heat transfer anemometers) and above (one heat transfer anemometer) the canopy were also recorded. The heat transfer anemometers used were of the same basic design as those described by Kanemasu and Tanner (1968). All temperature measurements recorded by the CR7 datalogger were made with 0.25-mm diameter chromel/constantan thermocouples except the air temperature thermocouples that were made from 0.076-mm diameter wire and the canopy temperature that was measured with an infrared thermometer. Power supplies for the source plate heater windings and heat transfer anemometers were located in a wooden shelter adjacent to the datalogger shelter. AC power for the power supplies and infrared thermometer system was obtained from a generator located at the east boundary of the field. A quantum sensor above the canopy and a line quantum sensor at the soil surface were logged separately on a LI-COR LI- 1000 datalogger during several measurement periods beginning on 25 June 1991 to assess light penetration through the maize canopy. Canopy height was obtained by measuring the height of several plants growing near the instrument transect with a ruler during each measurement period except 10 June 199 1. Leaf area measurements were made with a ruler using four cut

168

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plants on 26 May 1991 and with a LI-COR LI-3000 Portable Leaf Area meter on six cut plants on 30 May and 5 June 199 1. A LI-COR LAI-2000 Plant Canopy Analyzer was used to estimate leaf area in 1990 and periodically after 5 June 1991. Two samples taken from the top 10 mm of soil during most measurement periods were oven dried to determine the surface soil moisture content. Volumetric moisture content was determined from the gravimetric moisture content of these samples and measured soil bulk density. The CR7 datalogger program applied a low-pass filter to the soil surface and source plate temperatures (thermocouple measurements) to dampen rapid fluctuations. The datalogger was programmed to compare the filtered soil surface and anodized plate temperatures and interrupt the heater winding circuits with a Campbell Scientific Inc. A6REL-12 relay driver when the filtered plate temperatures rose more than a preset amount above the filtered soil surface temperature. In general, 2 and 4°C offsets were used for the vapor and heat source plates, respectively. At the beginning of each experiment the anodized plate of the vapor source plate was covered with two layers of felt fabric that were wetted and allowed to come to potential equilibrium (at a small suction) with the Mariotte supply device. Evaporation from the felt was measured by recording the water level in the buret on the Mariotte supply device every 900 s. The vapor pressure above the vapor source plate surface was determined by drawing air at a rate of 0.008 L ss’ through a perforated copper tube positioned 10 mm above the felt to a chilled-mirror dew point hygrometer. An Everest Interscience Agri-Therm infrared thermometer was used to measure the temperature of the surface of each source plate and the soil surface four times per hour. The infrared thermometer was calibrated with a black body calibration source before each measurement. Tetens’ equation (Tetens, 1930) was used to calculate the saturated vapor pressure of the felt surface using the infrared thermometer measurement of surface temperature. An additional dew point hygrometer system was deployed over the soil surface during most measurement periods after 10 June 1991 to allow comparison of the vapor pressure above the soil to that above the vapor source plate. Both dew point hygrometers were calibrated with a LI-COR LI-610 Dew Point Generator. The sensible heat flux density from the heat and vapor source plates was determined by solving an energy balance H=Rn+(S-U)-G-LE

where Rn is the source plate net radiation, S is the power input through the heater windings, CJ is the heat loss from the anodized plate through the polystyrene insulation, G is the change in plate, felt, and water heat storage, and LE is the latent heat flux density (all in W mm I). Obviously, for the heat source plate, LE = 0 and G includes the aluminum plate only. A view factor correction (Eckert and Drake, 1959) was applied to the readings of the miniature net radiometers above the source plates. Power input to each of the source plate heater windings was determined from the voltage drop across the heater winding circuit measured at the connector strip. An equation for the rate of heat loss through the polystyrene insulation was obtained from a laboratory experiment where two source plates were positioned

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169

face-to-face, an equal amount of power was supplied to their heater windings, and the system was allowed to come to thermal equilibrium under an air stream while the plate and aluminum pan temperatures were recorded. From this experiment, a relation for heat loss through the insulation was found u = [0.339(T,,

- &,)]/A

(9)

where the constant 0.339 has units of W ‘C-l, r,, is the plate temperature as measured by the thermocouples in the grooves on the underside of the anodized aluminum plate (“C), T,,, is obtained from thermocouples attached to the inside of the aluminum pan (“C), and A is the area of the anodized plate surface (0.2635 m2). During field measurements, the change in source plate heat storage was calculated from the measured change in the source plate temperature (average of thermocouples and infrared thermometer readings) over the 1000 s time interval and the volumetric heat capacities for aluminum, polyester, and water. The mass of water contained in the felt fabric was determined to be 0.4 kg by weighing the difference between a vapor source plate and its dry felt fabric with water in the supply tubing just to the surface of the plate and the same system under typical operating conditions. Above-canopy sensible and latent heat flux measurements were made during the 1991 growing season on 15 July, 22 and 30 August, and 7 and 16 September using PCI~V rnrwl~tinn tm-hninluw The sensible hplt ficx rlencitv ~2s p_eas~red with 2 ~v*I~.Ic.v.I ‘v.,A”..7u’u. -u-J --“---, Campbell Scientific Inc. CA27 sonic anemometer-thermometer while two systems (LI-COR LI-6262 COz/H20 Analyzer and a Campbell Scientific Inc. KH20 krypton hygrometer) were used to determine the latent heat flux density. The Appendix describes the above-canopy flux measurement techniques in detail. Conductive heat flux at the soil surface was calculated from the average soil heat flux density measured at a depth of 0.05 m with the heat flow transducers and the soil heat flux divergence Qcrs = [Pbct&Ts/@+z

(10)

where Q, 5 is the soil heat flux divergence for the top 0.05 m of soil (W me*), Pb is the soil bulk density (Mg mP3), cbP is the specific heat capacity of the soil layer (J g-’ “Cl), Ts is the average temperature of the soil layer (“C), z is the thickness of the soil layer (0.05 m), and t is the time step (1800 s) (Fuchs and Tanner, 1968).

3. Results Reliable measurements of heat and vapor transfer from the source plates installed at the field site were obtained on 26 occasions during the 1990 and 1991 growing seasons. A summary of the measurement intervals, above-canopy wind speed, surface soil moisture content, canopy height, and leaf area index for these dates is given in Table 3. Data from 1200 to 2 100 Central Standard Time (CST) on 16 September 1991 are presented as an example dataset for the heat source plate in Table 4 and for the vapor source plate in Table 5. The soil surface was moist throughout this measurement

170 Table 3 Measurement experiments Date

T.J. Sauer et al.

intervals,

1Agricultural

and Forest Meteorology 75 (1995)

wind speed, soil moisture

Central Standard Time (CST)

Wind speed”

103OG2300 1400~1530 1200-0500 1200&2300 1000~1200 1620&0630 1200&1400 1000-2100 1030&2300 1100~2100 0700- 1200 1800-0800 0630-m 1230 1000-2300

(ms

content,

‘)

canopy

161-189

height, and leaf area index for the field

Leaf area index

Surface soil moisture content (m’ m-s)

Canopy height

0 0

0

0.06 0.12 0.30 0.45 NA 0.65 0.80 0.95 1.15 1.25 1.75 2.00 2.35 2.50 2.60 2.60 2.60 2.65 2.65 2.65 2.65 2.65

NA 0.04 0.22 0.47 NA 0.84 NA 1.60 NA 2.40 3.00 3.34 XA NA 3.79 NA NA 3.34 NA 3.02 3.00 2.46

2.25 2.25

NA 1.68

1991 5-14 5-16 5-20/21 5526 5531 66516 6-10 6613 6617 6620 6-25 6-26127 7-3 7-8 ?7!3 7-15 7723 7726127 8-l 8-19 8-22 8-30 9-7 9916

! !!x-!?OO

0.8-4.3 4.4-5.6 0.553.2 1.3-8.3 4.1-4.5 0.4-3.1 4.1-5.8 2.4-5.5 0.4-3.0 0.6-2.9 2.222.7 4.0-6.7 2.774.1 0.4-3.2 7 o-7 2.2? i.“~

lOOOG2300 0930&2300 1230&0500 1200-2300 1200-2300 0700-2100 073OG 1400 0800-2100 1030&2100

1.6- 3.5 0.553.3 0.4-2.1 0.442.2 0.4-3.5 0.443.0 1.0-2.1 0.662.9 0.554.7

0.02 NAh 0.19 0.27 0.12 0.04 NA 0.03 0.25 0.05 0.32 0.22 0.36 0.31 O.!? 0.08 0.39 0.24 0.18 0.21 0.14 0.08 0.08 0.46

1990 IO-5 10-19

1500-2400 1300-2100

3.665.2 2.6-4.1

0.37 0.51

(m)

0

a Measured 3.72 m above the soil surface. ’ NA = Not available; no measurement was taken.

period. Although the canopy was still at its maximum height, the leaf area index had decreased from a maximum of 3.79 on 23 July to 2.46. Strong westerly winds coupled with decreasing leaf area (caused by leaf senescence) resulted in relatively high wind speeds at the plate surfaces. For the heat source plate, the energy balance is dominated by the net radiation during the daylight hours. After sunset, however, the soil (and anodized plate surface) begins cooling and more power is required to keep the source plate temperature near that of the soil surface as the insulation surrounding the anodized plate prevents heat flow from the adjacent soil. The increase in power input (S) essentially replaces the conduction of soil heat (Qa) to the source plate. Throughout the experiment the source plate sensible heat flux density was in the range 15-35 W mb2. After 1630,

264.30 309.67 378.67 296.07 170.95 106.67 103.33 130.27 85.53 37.42 24.23 -0.97 -13.64 -52.62 -37.52 -28.20 NAa NA NA

grnm2)

$rn-‘)

34.20 111.47 101.86 3.83 6.30 3.84 -33.36 -23.28 ~ 17.20 -32.55 -31.37 -35.92 -39.29 -39.68 -49.79 -48.84 -53.96 -60.13 -55.75

Abovecanopy sensible heat flux,

Surface soil cond. heat flux,

a NA = Not available.

1200 1230 1300 1330 1400 1430 1500 1530 1600 1630 1700 1730 1800 1830 1900 1930 2000 2030 2100

Central standard time, CST

Table 4 Heat source plate data for 16 September

35.77 20.50 21.50 34.56 29.28 24.07 33.61 33.58 15.04 27.55 20.75 19.42 18.60 16.84 22.91 16.88 22.53 28.62 28.07

Source plate sensible heat flux, (W me2)

1991 including

22.63 17.94 3.84 0.00 0.00 0.00 0.00 5.13 2.14 18.39 23.97 32.09 38.10 41.96 48.80 48.80 52.66 61.68 67.70

SW me2)

(“w m-‘)

33.97 17.46 24.36 39.43 29.50 15.89 16.13 24.29 9.89 1.35 -6.49 -16.85 -24.46 -32.23 -39.03 -40.50 -43.59 -43.38 -36.57

Power input,

6.77 7.10 6.71 6.39 6.15 5.55 4.53 4.14 3.76 3.37 3.16 2.94 2.66 2.20 1.59 1.25 0.59 0.19 0.52

Heat loss, u (W me2)

14.06 7.79 0.00 -1.52 -5.93 -13.72 -22.02 -8.30 -6.78 -11.18 -6.44 -7.12 -7.62 -9.32 - 14.74 -9.83 - 14.06 -10.50 2.54

(“W m-‘)

Storage change,

sensible heat flux density and soil conductive

Net radiation,

above-canopy

3.97 3.96 3.39 3.91 4.26 4.29 4.04 3.39 3.31 3.23 2.99 3.13 3.04 3.05 3.16 3.49 4.27 4.38 4.03

Ta - r, (“C)

Temp. difference,

7.51 4.31 5.29 7.37 5.73 4.68 6.93 8.27 3.78 7.10 5.77 5.17 5.11 4.60 6.03 4.03 4.40 5.44 5.80

hi, (mm SK’)

Heat transfer coeff.,

0.33 0.32 0.32 0.32 0.31 0.25 0.26 0.22 0.24 0.22 0.21 0.21 0.17 0.18 0.11 0.09 0.07 0.07 0.08

yrn s-l)

0.03-m wind speed,

heat flux density at the soil surface

15.08 -56.52 -79.4 ~19.5 -84.8 -80.2 -46.7X

1800 1x30 1900 1930 2000 2030 2100

36.93 21.62 17.84 21.99 NA’ NA NA

>I.10

112.64 2 16.20 203.96 142.23 126.83 101.28 X2.66 114.94 91 21 90.78 71.97

Abovecanopy latent heat flux. LE, LI (W m-l)’

LI-6262 system hygrometer.

36.85 26.28 16.84 21.30 NA NA NA

3l.>b

122.29 125.83 122.21 11097 101.79 88.81 83.75 68.70 17.12 60.53 60.10 _^ ^^ >L.XL 44.61 47.74 35.49 33.lY 35.54 32.75 30.10

__

5.04 -6.89 15.26 6.55 5.45 15.94 14.81

4.55

-31.63 -5.17 -8.15 10.67 13.37 I .20 9.61 11.88 -2.90 13.85 6.00

plate sensible heat flux. H (W m ‘)

180.64 226.55 216.64 152.16 133.05 105.38 86.43 119.Y7 94.61 92.77 73.40 _. _,

SOlIKe

SOLIKe

plate latent heat flux, LE (W m ‘)

-14.01 -22.81 30.60 -30.31 -35.90 -35.66 -27.59

-b.LX

37.99 21.23 33.23 53.59 46.70 32.64 29.44 33.80 20.20 11.46 3.55 , ^ 55.03 52.41 62.88 51.65 5X.32 69.49 74.07

55. iu

121.05 109.26 82.43 56.91 53.01 46.41 49.15 56.31 47.13 53.10 55.66 __ _

input, s (W mm’)

POW3

0.43 0.01 -0.61 -0.99 -1.64 -2.03 I .68

U./L

9.12 I I .26 17.86 -12.01 16.94 -12.84 3.25

-X.66

64.21 II.39 -2.20 -13.9x -11.57 12.68 -15.65 I .X6 -8.17 10.26 7.81 ^ ,,

loss. c (W m?)

4.16 4.45 3.19 2.83 2.13 I .78 1.42 I .61 1.28 1.04 0.93 ^ _^

storage change, G (W rn?)

Heat

__ l.Si 1.31 I .39 I .I9 2.14 2.91 3.09 2.49

1.56 1.39 I .05 0.84 0.98 1.32 I .37 I .23 1.16 1.37 1.20

1.56 4.30 4.95

2.56

3.20 -4.13 1.10

^!./I __ ‘

-16.95 -3.09 -6.47 10.6.5 11.31 0.76 5.88 12.11 -2.08 8.46 4.16

hh (mm s-l)

Heat transfer coeff.,

and net radiation

Temp. difference, To ~ T: (“C)

sensible and latent heat flux densities

radiatmn, Rn (W m ‘)

Net

above-canopy

canopy latent heat flux, LE,Kr (W m Z)b

1991 including

Above-

’ LE,LI measured with a LI-COR h L&G measured with a Krypton ’ NA = Not available.

Ib.Lb

1/.Kl

., _,

411.5 513 563.3 513 381.8 222.8 194.3 238.6 146.3 91.6 63.78

mm’)

Abovecanopy net radiation.

1200 I230 1300 1330 1400 1430 1500 1530 1600 1630 1700

Central standard time, CST

Table 5 Vapor source plate data for 16 September

0.41 0.43 0.43 0.42 0.42 0.40 0.31

U.5L

0.93 0.82 0.19 0.72 0.70 0.65 0.62 0.54 ^ _^

1.Ol

1.oo 0.99

Vapor pressure difference, efl e. (kPa)-

6.80 7.12 6.75 6.65 6.88 6.21 6.47 5.43 6.60 5.39 6.09 _ __ 3.31 5.25 6.11 4.44 4.39 4.58 4.31 4.34

h,, (mm s-‘)

cocff,

Vapor transfer

V.24 0.19 0 20 0 12 0.10 0.09 0.09 0.10

0.36 0.36 0.36 0.35 0.34 0.29 0.29 0.26 0.28 0.25 0.25 ,, _

cums ‘)

0.03-m wind speed

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the above canopy sensible heat flux density (H,) decreased rapidly and became negative while the source plate sensible heat flux remained steady indicating that the canopy was then cooler than both the underlying soil and the air above. The net radiation, heat loss, and storage change of the vapor source plate were all similar in magnitude and trend to those of the heat source plate but the power input during the daylight hours was much greater in order to accommodate the loss of latent as well as sensible heat. The latent heat flux density was the largest term in the source plate energy balance until 1730 when the cooling soil surface and decreasing wind speed combined to reduce the evaporation rate. Dew formation on the maize leaves in the canopy was observed during the evening hours. A 20 W m-* condensation rate during the night-time hours is approximately equivalent to 0.03 mm h-l, which is a reasonable rate leading to 0.3 mm of dew formation over a 10-h night. The erratic sensible heat flux density for the vapor source plate is attributed to the temperature at which the anodized plate was operated. The datalogger program was written to maintain the filtered anodized plate temperature (thermocouples) within 2°C of the filtered soil surface temperature, whereas for the heat source plate this difference was 4°C. The offset for the heat source plate was chosen to ensure an H in excess of 10 W m-* , which was considered the minimal flux required to obtain reliable data given the measurement errors present in the energy balance relationship. The lower temperature offset for the vapor source plate was intended to ensure that the plate surface temperature was very near that of the surrounding soil. Thus, when the soil surface was moist, the saturated vapor pressure of the felt would be as near as possible to the vapor pressure at the soil surface. This strategy did, however, result in very low and irregular sensible heat flux density values for the vapor source plate. The plate surface temperatures, as measured by the Agri-Therm infrared thermometer, averaged approximately 3°C above and less than 1“C above the soil surface temperature for the heat and vapor source plates, respectively, throughout this measurement period. The interfacial heat and vapor transfer coefficients in Tables 4 and 5 are of the same magnitude and show a similar dependence on wind speed. The vapor transfer coefficients are less variable, which is expected as these values were determined from only three measurements (VSP surface temperature, vapor pressure at 10 mm, and evaporation rate) all of which had good accuracy. The calculation of the heat transfer coefficient values, on the other hand, includes substantially more measurements, some with assumptions and/or inherent uncertainty that may lead to relatively large errors in the determination of sensible heat flux densities. Thus, the heat transfer coefficient values show more variation, especially for the vapor source plate due to the reasons outlined above, the addition of the felt and water terms in the heat storage expression and the latent heat flux density to the energy balance, and the relatively small surfaceto-air temperature differences. An error analysis of a typical half-hour dataset from 0200 CST on 27 June 1991 is presented in Table 6. Manufacturer-specified inaccuracies for the various instruments and dataloggers used to collect the measurements were used throughout the analysis. While the absolute uncertainty in H for the heat and vapor source plates is comparable, the relative uncertainty is very high for the VSP (40%) due to the very low H

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hours. Reflectivity for a soil similar to the Batavia soil was obtained from Tanner et al. (1987) and used to calculate the additional energy available for sensible and latent heat at the soil surface. The day time soil fluxes were then calculated from H, = H+

{[-Y/(7 +

s)lRb(l

LE, = LE + [s/(s + y)&,(l

-

%))

(11)

- q)]

(12)

where the subscript s refers to the soil, Rb is the predicted direct beam short-wave irradiance (W mp2), Q is the short-wave reflectivity (0.14 and 0.22 for wet and dry soil surfaces, respectively), y is the thermodynamic psychrometer constant (0.067 kPa ‘C-r) and s is the slope of the saturation vapor density curve (kPa OC-‘). For sensible heat, the soil contribution during daytime hours averaged 41% of the total flux density, while at night, the above-canopy sensible heat flux density was in the opposite direction of the soil sensible heat flux (i.e. heat flowing down) while its magnitude averaged at least twice that of the soil contribution. Comparison of the above- and below-canopy latent heat fluxes was made only for 16 September 1991 when the soil surface was wet. As expected for this senescing canopy, the soil contribution was dominant indicating very little transpiration during daytime hours. By comparison, Klocke et al. (1985) and Villalobos and Fereres (1990) found the soil contribution to be 20-32% of the total crop evapotranspiration for developing and full maize canopies. At night, evaporation from the soil is 1.6 times greater than that measured above the canopy indicating that the soil is the source of vapor that forms dew within the canopy.

Table 8 Linear regression

statistics

for the surface transfer

Transfer coefficient

n

coefficient

versus wind speed regressions

of the field data

R2

Root mean square error (mm s-l)

Y intercept (mm SC’)

Slope

No or small canopy HSP heat VSPb heat VSP vapor

65 31 74

0.460 0.286 0.907

2.449 5.048 1.485

5.827 7.808 3.853

0.0339 0.0566 0.0701

Developing canopy HSP heat VSP heat VSP vapor

117 69 166

0.316 0.064 0.644

1.733 2.589 1.174

4.087 4.034 3.379

0.0872 0.0929 0.1189

FUN canopy HSP heat VSP heat VSP vapor

246 121 238

0.021 0.110 0.334

1.389 2.434 0.621

4.579 3.369 4.081

0.0259 0.1017 0.0545

a HSP = Heat source plate. b VSP = Vapor source plate.

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”

0.5

1

”

75 (199.5) 161-189

1

”

1.5 (nVsJ2 Wind Speed

2.5

3

L

VgsP VSP

o--T0

i

I 02

0.8

0.6

0.4 ‘Mnd Speed (ml@

cl x

111 x

VSP

Ll VSP

0

0.2

0.4 Wind Speed (mls)

Fig. 2

0.6

0.8

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I

F

171

1

OX 0

0.1

0.3 0.2 Wind Speed (cm/s)

0.4

0.5

Fig. 2. (Contd). Heat (HSP) and vapor source plate (VSP) heat transfer coefficients (A, C, and E) and vapor source plate (VSP) vapor transfer coefficients (B, D, and F) versus wind speed measured 0.03 m above the plate surface for the field experiments and the corresponding linear regression lines. The data are presented for intervals from 14 to 31 May 1991 (canopy <0.3 m tall, A and B), 5 June to 8 July 1991 (0.45 m to tasseling, C and D), and the remaining data when the canopy was full or beginning to senesce (E and F).

Fig. 2 presents the interfacial heat and vapor transfer coefficients for all 26 field experiments plotted versus wind speed measured 0.03m above the source plates. The data are divided into three groups: 14 to 31 May 1991 when there was no canopy present or the canopy was less than 0.3 m tall, 5 June to 8 July 1991 when the canopy was developing (0.45 m to tasseling), and all other datasets when the maize canopy was either full or beginning to exhibit leaf senescence. Note that infrared thermometer measurements were used for the source plate surface temperature for all datasets except the 14 to 3 1 May 199 1 heat source plate data. For these datasets, the plate temperature from four thermocouples in grooves on the underside of the plate was used. Calculations revealed that the low emissivity of the anodized surface (0.93) could lead to significant errors in the infrared thermometer measurement that would be maximum when no canopy was present (i.e. large cold-sky radiation). Data from laboratory experiments indicated that the difference between the thermocouple and infrared thermometer estimates of plate surface temperature were within 0.3”C of each other under a variety of conditions; thus, the heat source plate surface temperatures used for the 14 to 31 May 1991 datasets may be low by up to 0.3”C. A simple linear regression was completed on each dataset. The equations and regression statistics are given in Table 8. In general, as was noted above for the 16

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September 1991 dataset, the vapor transfer coefficient data exhibit less scatter than the heat transfer coefficient data with the greatest variation found for the vapor source plate heat transfer coefficients.

4. Discussion The surface transfer coefficient values measured in this study (2-30 mm s-l) are comparable to but more consistent than values found in the literature for a variety of canopy types and ambient conditions. Massman (1992) made surface energy balance and other micrometeorological measurements for a shortgrass steppe ecosystem in northeastern Colorado. Calculated surface transfer coefficients showed no significant correlation with friction velocity or wind speed and were relatively constant during daytime hours. Thus, the author suggested a single value of 25 mm s-l was appropriate for daytime hours. Ham and Heilman (199 1) also found that measured surface transfer coefficients were not particularly sensitive to mean wind speed in their study of energy transport in an irrigated cotton field. Mean values of transfer coefficients for midday periods during three days of this study were 1.22,3.60, and 0.63 mm ss’ when mean winds speeds measured 0.1 m above the 0.4 m tall canopy were 1.9, 3.2, and 1.6 m s-l, respectively. Both investigators noted that there were significant periods when low fluxes and/or small gradients prevented accurate determination of surface transfer coefficients. Ham and Kluitenberg (1993) studied the positional variation in the energy balance beneath a wide-row soybean canopy in Kansas and found surface transfer coefficients from 1 to SO mm s-t. The transfer coefficients were, however, highly variable and again not correlated to wind speed or position. The authors concluded that positional variation in below-canopy aerodynamic transport could not be achieved using their technique. In contrast to the above studies, surface transfer coefficients determined from source plate measurements tend to be less variable and exhibit a stronger dependence on wind speed. Bailey et al. (1975) report values of hh from 5 to 25 and 5 to 12.5 mm s-’ using 0.3 by 0.3 square heat source plates installed at two desert sites in Arizona. The transfer coefficients showed a strong correlation with wind speed that ranged from 1 to 10 m s-’ measured 0.67 or 0.4 m above the soil. Schuepp (1977) made heat transfer measurements using a copper source plate (99 by 150 mm) placed within contrasting canopies and in the laboratory with a variety of surface roughness elements and model windbreaks. The convective transfer coefficient h, was also predicted by A, = {k/V+ where above where and is

-

ln(Wzdlh

(13)

Pr is the dimensionless Prandtl number (equal to 0.72 for air), zI is the height the soil where foliage elements begin to limit eddy size (m), and S0 is the height transfer due to molecular forces approaches that due to turbulent forces (m) given by

So = v/ku,

(14)

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10

6

0

I

2

3

4

5

6

VSP Xi (mm/s)

Fig. 3. Heat transfer coefficients from duplicate heat source plates (A) and vapor transfer coefficients from duplicate vapor source plates (B) from experiments conducted on 26 July and 1 August 1991, respectively. The different symbols represent transfer coefficients obtained when the source plates were at the same temperature (<2030 and <1800) and when source plate #l was 10°C warmer than source plate #2 (>2030 and >1800).

where v is the kinematic viscosity (m2 s-l). Schuepp found good agreement between measured values and values of II, predicted by Eq. (13) and estimated the accuracy of the measurements to be from 6 to 10%. Surface heat transfer coefficients measured within a maize canopy ranged from 8.5 to 10.5 mm s-l. Spatial variability of fluxes and surface properties remains the primary obstacle to the accurate determination of energy balance components beneath plant canopies. For instance, soil evaporation measurements made with multiple minilysimeters beneath mature maize canopies have coefficients of variation from 15 to 35% (Walker, 1983 and 1984; Villalobos and Fereres, 1990). While the source plate technique enables accurate energy budget determinations, there is now concern whether the measured fluxes and transfer coefficients are spatially representative of the below-canopy environment. Although typically only a single heat and vapor source plate were used in this study, for all measurement periods, the two-source plate systems produced values of hh and h, that were similar. This is encouraging since the measurements used in determining hh and h, are nearly completely independent (the lone exception being the surface temperature measurement with the same infrared thermometer); thus, the two source plates in effect behaved as replicates. These results and the large size of the source plates as

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600

low

1200 1400 1600 1800 Central Standard Time

:: =i(

75 11995) 161-- 189

2@30

2200

B

_A

t

\\,

‘--\,

/’ -

ml

IGal

\

1200 1400 1600 1800 Central Standard Time

-1 ,

2oca

2200

Fig. 4. Vapor pressure above the soil (Soil) and vapor source plate (VW) (A) and the latent heat flux density (B) from the vapor source plate on 22 August 199 1. The arrow marks the time when the soil surrounding the vapor source plate was thoroughly wetted.

compared to those used by other workers tend to indicate that the source plates did indeed sample over a representative area. As both source plates were routinely operated at temperatures above the soil surface temperature, there was concern that enhanced free convection may occur over the plate surfaces. Two experiments were conducted to ascertain if this enhancement was taking place, the results of which are shown in Fig. 3. On each occasion, duplicate heat or vapor source plates were operated under typical conditions for several hours and then one plate’s temperature was increased 10°C above the other. This procedure was followed for two heat source plates on 26 July 1991 and for two vapor source plates on I August 1991. The two symbols on the graphs represent surface transfer coefficients determined before (~2030 and ~1800) and after (>2030 and >1800) the temperature of source plate 1 was increased. No significant effect on the transfer coefficients resulting from the 10°C increase in source plate temperature is apparent. Thus, for the field experiments, if there was enhanced heat or mass transfer due to the small elevation of the source plate temperature, the magnitude of the enhancement was too small to be detected within the typical scatter of data. Additionally, although atmospheric stability conditions near the source plate surfaces were typically unstable, no correlation was apparent between the measured transfer coefficients and atmospheric stability either within or above the canopy. Another area of concern with regard to the representativeness of the field source plate measurements is local advection. Comparisons were made between transfer

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coefficients measured with the VSP when the surrounding soil surface was wet and when the soil was dry (all other conditions being similar). In no instance was a significant difference noted, indicating that local advection was not a large source of error. Nonetheless, an experiment was completed on 22 August 1991 to test the effect of local advection. On this date the soil surface was dry ((3 = 0.14) and the wind speed was moderate (maximum 3 m s-l above the canopy) from the north. The source plates were operated in typical fashion until 1300 CST when approximately 20 1 of water were applied to the soil surrounding the vapor source plate, thoroughly wetting the soil surface within approximately 1 m of the source plate. The soil was rewet at 900-s intervals until 1400 CST and then at 3600-s intervals until 1700. At the end of the experiment (2100 CST), the samples of the wetted soil were collected and B was later measured at 0.48. Fig. 4 shows the vapor pressure measured 10 mm above the vapor source plate and 10 mm above the soil surface (non-wetted, approximately 10 m northeast of the VSP) and the source plate latent heat flux density for this experiment. The arrow marks the time when the soil was initially wetted. The vapor pressure measured over the soil was approximately 0.3 kPa lower and followed the same trend as the vapor pressure measured over the vapor source plate until 1530 CST. After 1530, the vapor pressure above the soil and vapor source plate showed fluctuations of similar scale but different trends until converging at 1800. The latent heat flux density exhibits a typical diurnal pattern aside from a sharp decrease immediately after the soil was wetted which was due to inadvertent spilling of water onto the felt surface while wetting the soil. Recovery in the evaporation rate was made by 1400, however, and the evaporation for the remainder of the period displayed a typical pattern. The vapor transfer coefficients ranged from 3.5 to 5.5 mm s-l during this experiment and decreased slightly (<0.5 mm s-l) after 1300 as compared to values obtained at the same windspeed before 1300. It was concern over local advection effects that prompted the placement of air thermocouples and the dew point hygrometer inlet at a 10 mm height. Still, it is important to know whether the inlet for the dew point hygrometer and the air thermocouples were within the plate’s internal boundary layer. The difference in temperature recorded by the two air thermocouples during periods when the wind was only from the south (150 to 210” azimuth) showed that the two thermocouples disagreed by less than 0.3”C on nearly all occasions. Further, as the thickness of the boundary layer would increase with distance downwind, the north thermocouple should have recorded a consistently lower temperature if both thermocouples were within the plate’s internal boundary layer, yet there was no indication of any such relationship. A final area of consideration with regard to the representative nature of the source plates is that of surface roughness. A rough surface has greater surface area and, under forced convective conditions, the exposed protuberances create eddies near the surface that increase mixing and, presumably, heat and mass transfer from the surface. For the Batavia soil, a z. of 6.5 * 3.6mm was obtained from wind profile measurements made during neutral conditions on 14 and 16 May 1991. However, z. beneath the canopy later in the growing season would likely be much smaller than 6.5 mm due to the smoothing effects of rainfall. The random roughness (standard error of the natural logarithm of individual surface elevations after

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Wind Speed (m/S)

0

1

2

4 3 Wind Speed (m/s)

5

6

Fig. 5. Log profile estimates of the soil surface and heat source plate (HSP) heat transfer coefficients (A) and log profile estimates of the soil surface and vapor source plate (VSP) (B) versus 0.3-m wind speed for all data from 14 to 31 May 1991.

oriented roughness has been removed) of a bare soil surface has been shown to decrease exponentially with rainfall (Zobeck and Onstad, 1987). The disparity in heat transfer between aerodynamically smooth and rough surfaces should be greatest at high wind speeds when the roughness elements enhance turbulence near the fluid/solid boundary. During much of the growing season, however, wind speed measured near the soil surface beneath the maize canopy was below 0.5 m s-l. A further complication is that not all of the roughness elements found on the soil surface have the same properties as the surrounding soil. Exposed clods would typically be drier and probably warmer or cooler than the surrounding soil surface. Thus, even when the soil surface is aerodynamically rough, it is difficult to accurately assess the effect of this roughness on heat and mass transfer processes aside from the increase in turbulent mixing at the soil surface. Although the log-profile equations have been widely employed, comparisons between log-profile estimates of h and values from other independent techniques over bare soils are lacking. Fig. 5 compares the source plate interfacial transfer coefficient data obtained when there was no canopy or the canopy was shorter than 0.3 m tall (14 to 31 May 1991) with estimated hi, and h, from Eqs. (6) and (7). The log-profile estimates of hh and h, were determined from wind speed measured 0.3 m over the soil surface using a z. of 6.5 mm. It was assumed that zh = z, = 0.2~~ (Campbell, 1977) and the displacement height was zero while diabatic profile

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32 1

Log 0

VSP

Fig. 6. Measured heat source plates (HSP) and bulk soil (Soil) heat transfer coefficients, log profile estimates (Log), and measured vapor source plate (VSP) vapor transfer coefficients versus 0.3-m wind speed for 14 May 1991.

corrections were not used because of the close proximity to the soil surface. Note that the log-profile curve would pass through the origin while regression lines for the source plate data, as shown in Table 7, have intercepts from 3.8 to 5.8 mm s-l. Nonetheless, there is fair agreement between the estimated soil transfer coefficients and the source plate values at low wind speeds but, at higher wind speeds, the log-profile predicts values that are much higher than the source plate values due to the large soil zo. Clearly the use of a 0.3m reference height is somewhat arbitrary and exchange coefficients calculated from Eqs. (6) and (7) depend on this height. A smaller reference height would result in an even larger exchange coefficient. The 0.3-m height was chosen so that similar wind speeds would be likely to occur over both surfaces. At lower heights the wind speeds over soil may be significantly less and the comparison is further complicated. Fig. 6 presents HSP hh and VSPh, data and two estimates of h for the experiment completed on 14 May 1991. The soil surface was very dry on this date (0 = 0.02) enabling the solution of the soil energy budget for H where H = Rn - G (assuming

n P

a a

04

1

0

1

2 Wind

3 Speed

4

5

(m/s)

Fig. 7. Measured desert surface heat transfer coefficients (Desert) and log profile estimates wind speed for a desert sand surface using data from Stearns (1969).

versus 0.2-m

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LE = 0, as did Ham and Kluitenberg, 1993). The H was used with thermocouple measurements of the soil surface temperature and air temperature at the temperature probe on the weather station 3.35 m above the soil surface to calculate bulk heat transfer coefficients for the soil surface. Also included is the log-profile estimate of h, over the soil surface using a 0.3-m reference height and wind speed as before. All of the data exhibit fairly wide scatter especially at low wind speeds and the log-profile estimates are again somewhat higher than the source plate values of h at high wind speeds. A similar analysis was performed on the data of Stearns (1969) from the Pampa de La Joya in Peru, the results of which are shown in Fig. 7. The sensible heat flux density was again obtained from an energy budget analysis with the assumption of no evaporation from the desert surface. In this instance, air temperature and wind speed at 0.2 m were available. This desert site consisted of bare sand and stones with a z. of 0.25 mm. The bulk surface transfer coefficients are, with one exception, somewhat smaller than the log-profile estimates but both sets of data show a similar dependence on wind speed. The desert surface transfer coefficients are also similar in magnitude to the source plate data of Fig. 6, but there is little overlap as the data from Peru were collected at higher wind speeds. Tennekes (1973) devoted an entire paper to the use of Eq. (3) in order ‘to establish guidelines for its use and to provide warnings about abuses’. Tennekes discusses controversy about the derivation of the equation, the variability of the von Karman constant (Brutsaert (1982) notes that published values range from 0.35 to 0.47) and the requirement that the wind profile be in a constant flux layer. In the present application, the primary concern is whether it is permissible to use Eqs. (6) and (7) so near a rough soil surface. It is often stated, with regard to the lower limit of the logprofile equation, simply that I >> ro. Tennekes (1973) and Brutsaert (1982) suggest lower limits of Z/ z. equal to 100 and 5, respectively. When applied to a soil surface with an aerodynamic roughness of 6.5 mm, the minimum reference height would be 650 and 32.5 mm to meet these criteria.

5. Conclusions Surface heat and mass transfer coefficients measured above heat and vapor source plates at the soil surface beneath a maize canopy during all stages of growth ranged from 2 to 30 mm SC’. The measured transfer coefficients were correlated, using linear regression, with wind speed measured 0.03 m above the source plate surfaces that varied from 0.05 to 2.8 m s-’ The range of transfer coefficient values measured were similar to those reported by others using energy balance techniques (Ham and Heilman, 1991; Massman, 1992; Ham and Kluitenberg, 1993) and source plates (Bailey et al., 1975; Schuepp, 1977). Bare soil field data from 14 May 1991 and data from Stearns (1969) for a desert sand were used to calculate bulk surface heat transfer coefficients. In general, logprofile estimates of hh were greater than the bulk transfer coefficients at high wind speeds but, since the log-profile analysis predicts an h = 0 at zero wind speed, it ultimately gives values of h lower than measured at low wind speeds. Source plate

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data at higher wind speeds for the period with no canopy or a canopy less than 0.3 m tall were also lower than log-profile estimates of h for the soil surface but there was fair agreement at lower wind speeds. The agreement at low wind speeds suggests that the source plate values are reasonable for the surrounding soil under these conditions; however, the divergence between measured and log-profile estimates at high wind speeds indicates that transfer from the smooth plates may be significantly less efficient than from a rough soil surface. The source plate method reduced the problems of spatial variability that have hampered previous efforts designed to measure transfer coefficients at the soil surface beneath plant canopies. Specific experiments were, nonetheless, necessary to determine the effect of enhanced free convection and local advection on the field measurements, the results of which showed no significant effect on the resulting transfer coefficients. Based on surface roughness considerations alone, it is expected that the source plate transfer coefficients would be lower than the rougher soil following tillage; however, beneath a canopy such as maize, the soil can become quite smooth from the effect of rain, and the wind speeds are often low within full canopies so that the source plate transfer coefticients should then be more representative of the surrounding soil. Sauer and Norman (1995) in a companion paper, expand upon the analysis presented here and report on a series of free and forced convection source plate experiments at three levels of surface roughness. Results from these experiments lead to more refined relationships for estimating heat and vapor surface transfer coefficients for soil surfaces of varying roughness and at different levels of atmospheric turbulence. These equations are then used in a comprehensive soilplant-atmosphere model to improve predictions of heat and mass transfer at the soil surface beneath a plant canopy specifically, and canopy microclimate in general.

Acknowledgments The authors wish to express appreciation to Paul Bernhard, Scott Castello, and Jinsong Zhang for their assistance with the field measurements and to Charles Stearns for providing the sensible heat transfer data for a desert site in Chile.

Appendix Various sensors were combined in an eddy correlation system to measure fluxes of sensible and latent heat, and COz above canopies of maize and soybean during the 1991 growing season. A one-dimensional sonic anemometer with fine-wire thermocouple (CA27, Campbell Scientific Inc., Logan, UT) was used to measure fluctuations of vertical velocity and air temperature. A closed-path, fast-response, infrared gas analyzer (LI-6262, LI-COR, Lincoln, NE) was used to measure fluctuations of CO2 and water vapor. To validate the latent heat flux measurement, an open-path, fast-response krypton hygrometer (KH20, Campbell Scientific Inc., Logan, UT) was also used to measure the latent heat flux in the vicinity of the gas analyzer (Tanner and Greene, 1989).

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The gas analyzer was operated in a closed-path mode, thus, air was drawn into the analyzer. A copper tube (3 m long and 4.83 mm id.) was used as a sampling line because it helped to damp out temperature fluctuations and minimize water absorption along the sampling path. The tube was clamped horizontally to the sonic anemometer with the tubing inlet close to the thermocouple. A filter (SS-4FW-2, NUPRO, Badger Valve and Fitting Co., Wauwatosa, WI) was installed at the inlet of the analyzer to remove particulate matter. A vane pump (Cole-Parmer Instrument Co., Chicago, IL) sucked air through the sample cell of the analyzer. A 2 1 ballast was placed between the pump and the outlet of the analyzer to dampen high frequency fluctuations in the airstream. Pressure and temperature sensors were installed at the outlet of the LI6262 sampling cell. The pressure measurement is required to correct gas concentration measurements because the large flow rate results in an absolute pressure in the analyzer sample cell of 9070 kPa where atmospheric pressure is 9800 kPa. This pressure reading was calibrated to the flow rate and used to monitor the system flow. Ambient air was moved through the sampling line at a flow rate of 0.167 1 s-‘. The tubing inlet, the sonic anemometer, and the krypton hygrometer were mounted 1.5 m above the canopy and oriented into the prevailing wind. A single mast was used for all sensors. The LI-6262 analyzer was calibrated with a standard gas supply at the beginning of each series of measurements. The response of the gas analyzer was slower than the sonic and the krypton hygrometer because of the damping in the inlet tube. In addition, the signal from the analyzer lagged behind the sonic, krypton and temperature sensors because of the time required to bring air from the tubing inlet into the analyzer. In a careful laboratory test, the delay in sampling the air to the

4cml

soybean

A A

0

100

200

300

canopy.

doy224 doy226 doy223

4M)

500

LI-6262: LE (W/m’) Fig. Al. Comparison of latent heat flux density (LE) measured above canopies closed- and open-path sensors in conjunction with a 1-D sonic anemometer.

of maize and soybean using

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analyzer was estimated to be 0.45 s for a flow rate of 0.167 1 s-‘. This was done by placing a fine-wire thermocouple at the inlet of the copper sampling tube, blowing a rapid puff of exhaled breath near the end of the inlet tube, and recording the CO*, water vapor, and temperature signals 50 times per second while the system was sampling air. The time delay between the fast response thermocouple and the LI6262 COZ, and water vapor responses determined the delay time. Using the total volume (0.071 1) of the system and this delay time, we estimated the flow rate of the system. This flow rate determination agreed with a precision flow meter to within about 5%. Relative to the analyzer, the sonic anemometer and krypton hygrometer were assumed to have nearly instantaneous responses. A datalogger (21X, Campbell Scientific Inc., Logan, UT) recorded all the measurements at a frequency of 10 Hz. The fluxes of sensible and latent heat, and COZ were proportional to the covariances of the vertical velocity fluctuations and the respective fluctuations of temperature, water vapor, and COZ. These calculations were done on-line. To correct for the delay of the gas analyzer, the vertical velocity fluctuation was lagged for 0.5 s, corresponding to the estimated delay, and then used to compute the covariances involving water vapor and CO2 fluctuations from the analyzer. The instantaneous vertical velocity was used to calculate the covariance involving temperature fluctuations, and that involving the water vapor from the krypton hygrometer. The data were averaged over 1200 s and the equivalent sensible and latent heat, and CO2 fluxes calculated. Density fluctuations in the atmosphere can lead to flux loss when sensible and latent heat, and CO2 fluxes are measured simultaneously with either a closed-path or open-path sensor. However, flux correction factors have been derived for these effects (Webb et al., 1980). Sampling air through an intake tube eliminates the need to correct fluxes for effects of temperature fluctuations because temperature fluctuations are damped out. Thus, off-line correction factors for density effects and oxygen absorption were only applied to latent heat flux measurements involving the krypton hygrometer. Oxygen interferes with latent heat fluxes because it absorbs radiation in the wave bands that overlap those of water vapor and corrections were applied to account for this. On the other hand, a sampling tube attenuates air fluctuations, which also leads to flux loss. Tube attenuation correction factors derived by Suyker and Verma (1993) using a model by Massman (199 1) were applied off-line to the raw latent heat flux involving the analyzer. Flux densities of latent heat measured using closed-path and open-path sensors are compared in Fig. Al, The differences in raw fluxes measured with the two sensors were only a few percent and in spite of all the adjustments, a good linear correlation (r* = 0.98) was obtained for the flux measurements.

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