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Atmósfera 19(2), 49-82 (2006)
Characteristics of the surface layer above a row crop
in the presence of local advection
P. I. FIGUEROLA
Departamento de Ciencias de la Atmósfera y los Océanos,
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,
Ciudad Universitaria 1428, Buenos Aires, Argentina
Corresponding autor: P. I. Figuerola; e-mail: figuerol@at.fcen.uba.ar
P. B. BERLINER
Blaustein Institute for Desert Research, Ben-Gurion University of the Negev,
Sede Boqer Campus, Israel
Received September 8, 2004; accepted December 6, 2005
RESUMEN
En algunas regiones áridas los campos cultivados no son contiguos y están rodeados por grandes áreas de
suelo desnudo. Durante el verano y la estación sin lluvia, la radiación solar es mayor la temperatura del suelo
durante el día en las áreas desnudas y secas es mucho más alta que la del aire. El calor sensible generado
sobre estas zonas puede ser advectado hacia los campos irrigados. Los cultivos son usualmente plantados
en hileras y son irrigados por sistema de goteo, no mojando totalmente la superficie del suelo. El suelo
desnudo y seco entre las hileras del cultivo alcanza altas temperaturas y lleva a una convección dentro del
cultivo entre las hileras. La advección desde el área seca de los alrededores y la actividad convectiva dentro
del cultivo entre el suelo desnudo afecta la capa arriba del cultivo. Se estudió la capa de superficie arriba de
un cultivo irrigado de tomate plantado en el desierto del Negev, Israel. El cultivo fue plantado en hileras,
irrigado por goteo y la distancia entre bordes entre dos filas adyacentes era de 0.36 m al momento de realizar
las mediciones. Los gradientes de temperatura y presión de vapor de agua fueron medidos a varias alturas
arriba de la cobertura vegetal con un sistema de Bowen. El residuo de la ecuación de balance de energía fue
usado como criterio para determinar la capa de equilibrio. Durante la mañana predominaron condiciones
inestables y la capa interna de equilibrio estuvo entre Z/h ~ 1.9 a 2.4. En algunas circunstancias, a las últimas
horas de la mañana, el suelo desnudo entre las hileras alcanza temperaturas extremas altas y baja velocidad
del viento siendo identificadas situaciones de convección libre. Durante estas horas, el residuo para las
alturas Z/h ~ 1.5 y 2.4 fue significativamente diferente de cero y fue evidente una extrema variabilidad para las
capas Z/h = 3.2. La advección local ocurre después del mediodía, resultando en un aumento de la estabilidad
en la capa más alta que se propagó hacia abajo. La capa de equilibrio estuvo entre Z/h ~1.5 a 2.4. Los residuos
fueron significativamente diferentes de cero para las capas más altas Z/h ~ 2.7 a 3.2 durante este periodo. Los
resultados indican que la profundidad y ubicación de la capa interna de equilibrio, arriba del campo irrigado
rodeado por áreas desérticas, responde a la velocidad del viento y la temperatura del suelo entre las hileras del
86
P. I. Figuerola and P. B. Berliner
cultivo. Para algunos intervalos, el cálculo de los flujos usando la aproximación de flujos gradientes no fue
posible.
ABSTRACT
In some arid land, the irrigated fields are not contiguous and are surrounded by large patches of bare land.
During the summer time and rainless season, the solar radiation flux is high and the surface temperature
during daylight in the dry bare areas, is much higher than that of the air. The sensible heat generated over
these areas may be advected to the irrigated fields. The crops are usually planted in rows and the irrigation
systems used (trickle) do not wet the whole surface, the dry bare soil between the rows may develop high soil
surface temperatures and lead to convective activity inside the canopy above the bare soil. Advection from
the surrounding fields and convective activity inside the canopy affect the layer above the crop. We studied
the surface layer above an irrigated tomato field planted in Israel´s Negev desert. The crop was planted in
rows, trickle irrigated and the distance between the outer edges of two adjacent rows was 0.36 m at the time
of measurement. The gradients in temperature and water vapor pressure were obtained at various heights
above the canopy using a bowen ratio machine. The residual in the energy balance equation was used as a
criterion to determine the equilibrium layer. During the morning, unstable conditions prevail, and the equilibrium
layer was between z/h ~ 1.9 to 2.4. In some particular circumstances, in the late morning, the bare soil between
the rows reached extremely high temperatures and during conditions with low wind speeds free convection
was identified. During these hours the ‘‘residuals’’ of the energy budget to the heights Z/h = 1.5 and 2.4 were
significantly different from zero and an extremely large variability was evident for the Z/h = 3.2 layer. Local
advection took place during the afternoon resulting in an increase in the stability of the uppermost measured
layer and propagated slowly downwards. The equilibrium layer was between Z/h ~ 1.5 to 2.4. The residuals
were significantly different from zero for the uppermost layers Z/h = 2.7 and 3.2 during these periods. Our
findings suggest that the depth and location of the internal equilibrium layer above trickle irrigated row crop
fields surrounded by dry bare areas, vary in response to wind speed and the temperature of the soil in
between the rows of the crop. For some time intervals, the computation of fluxes using the conventional flux-
gradient approach measurements was not possible.
Keywords: Advection, row crop, convection.
1. Introduction
Evaporation of water is a key element in the regional water balance of semi-arid regions and its
quantification is necessary in order to manage successfully the limited water resources of these
areas. A convenient and well-established approach to achieve this goal is to estimate the flux
density of latent heat within the surface layer that lies above the vegetated area (Monteith and
Unsworth, 1990).
The spatial discontinuity is very pronounced in arid and semi-arid regions, where locally the
crops are surrounded by dry land. When an air mass moves from a surface to one with different
characteristics, the lower boundary conditions change abruptly and it must adjust to the new set of
boundary conditions. Downwind of the new roughness, an internal boundary layer develops growing
in height with downwind distance, whose properties have been affected by the new surface. The
adjustment is not immediate throughout thickness of the air layer. Bradley (1968) and Mulhearn
(1977), describing the downwind velocity profiles within the internal boundary layer, suggested that
it might be described through a modified logarithmic law. Far downwind of the roughness change,
87
Characteristics of the surface layer above a row crop
a new equilibrium may be visualized so that the stress everywhere is constant. The region where
has been achieved a new equilibrium with the new surface is often called the equilibrium layer and
the logarithmic laws can be applied. This layer is the lowest region, about the lowest 10% of the
internal boundary layer; it is supported as far as the roughness change (Kaimal and Finnigan, 1994).
Local advection is the situation in which the growing internal boundary layer is no deeper than
the upstream surface layer, and shows the development of a deepening inversion layer in an existing
unstable lapse profile, referred as an advective inversion. It is the classical agrometeorological
circumstance of airflow from hot dry to cool irrigated pasture (Dyer and Crawford, 1965).
In our case of row crops that do not completely cover the soil, the lack of surface homogeneity
introduces a complicating factor. Vorticular flow patterns appear when
λ
/h >> 1, where l is row
spacing and h is crop height (Perrier et al., 1972). The roughness sublayer is the region at the
bottom of the internal boundary layer where the presence of the canopy impinges directly on the
character of the turbulence. Further problems in applying the semi-logarithmic profile laws and
their diabatic extensions could be encountered.
In arid and semi-arid areas, two factors increase the complexity of the soil-plant-atmosphere
system: the influence of local advection and the high temperatures of the bare soil between the
rows of the crop. The transport of energy in the horizontal plane is classified as being either regional
or local. The former case describes situations in which the transport of sensible heat energy is the
result of warm dry air masses on a synoptic scale or mesoscale (Prueger et al., 1996). The latter
describes the local flow between two adjacent fields. An example of local advection is an irrigated
field crop bordered by a large area of dry fallow land. This is a common feature of arid and semi-
arid regions, as irrigated areas frequently occupy small patches of land that are surrounded by large
bare areas. In this case, the horizontal advection of sensible heat increases the evaporation of
water from the irrigated areas. Lee et al. (2004) describe the characteristic differences between
local and regional advection.
High temperatures of the soil surface, the second complicating factor mentioned above, are the
result of the fact that row crops in arid areas are usually watered using trickle irrigation, which
results in the localized wetting along the rows of the crop. The bare areas in between the rows of
the crop are dry and due to the high solar radiation, typical of these areas, the soil surface temperature
may reach very high values and generate plumes of hot air. These plumes may therefore enhance
the strong horizontal lack of homogeneity due to the structure of the crop.
Consequently, local advection would result in the lowering of the upper boundary of the internal
boundary layer and its equilibrium layer, while the incomplete cover and the associated plumes from
the bottom would lead to an increase in the height of the lower boundary. A description is presented
in Figure 1.
The three most common micrometeorological methods used to estimate actual evapotranspiration
above a crop are based on the Bowen ratio, the aerodynamic equation, and the Penman-Monteith
equation (Brutsaert, 1982). The application of these methods requires horizontal advection to be
negligible when compared to the magnitude of the vertical fluxes. In this case, the closure of the
88
P. I. Figuerola and P. B. Berliner
energy balance equation for an imaginary plane located above the canopy must be satisfied. The
aerodynamic method has to be applied (Rana and Katerji, 2000) at heights that are larger compared
to the roughness length and smaller compared to the boundary layer depth. To perform the routine
estimation of fluxes, much care must be taken to analyze local advection under arid conditions
(Prueger et al., 1996) and in plot without enough fetch. In mixed plant communities, hilly terrains
and small plots these techniques cannot be used (Rana and Katerji, 2000).
The height where the energy closure is calculated may vary because it depends on the distance
to the border of the field, humidity conditions of the soil, plant density and height, and also, the
energetic and dynamic conditions of the flow field. An experiment was undertaken in order to
estimate the height interval above a row crop over which fluxes could be computed using the
conventional micrometeorological methods in the presence of advection, therefore the crop
evapotranspiration can be estimated being of particular importance in arid zones.
2. Materials and methods
2.1 The area: general features
The Negev is located on the northern border of the planetary desert and is a continuation of the
Egyptian desert. The rainfall near the coast is 100-150 mm and drops sharply towards the south.
Prevailing pressure systems and their interaction with local land features establish the wind regime
of any given place. Except for its extreme south, a land and sea breeze system affects most of the
Negev. During the summer months, a semi-permanent low-pressure trough extends from the Persian
Gulf to the northeastern Mediterranean, causing a general northwesterly flow over the entire country,
modified by the sea breeze. During the summer the sea-land breeze produces a daytime westerly-
northwesterly component over the northern and western Negev, becoming easterly southeasterly
at night (Zangvil et al., 1991).
Kibbutz Mashabei-Sade, on whose fields the trial was carried out, is located about 60 km from
the Mediterranean coast and 50 km south of the city of Beer-Sheva (32 °N, 34
°E), in the south of
Israel. Data obtained from available records at a meteorological station at Mashash (5 km from the
Fig. 1. The scheme: (1) the
surface layer, (2) the
internal boundary layer,
(3) the equilibrium layer,
(4) the roughness layer
and (5) the thermal
internal boundary layer
under local advection
condition.
89
Characteristics of the surface layer above a row crop
experimental field), indicate that during the summer, wind directions at 10 m high are mainly from
the north-northwest between 8:00h until 22:00h, becoming easterly during the night. The wind
speeds are low during the morning and higher in the afternoon.
Field trial was carried out between 8 and 14 September 1999 on a commercial tomato field (330
m × 220 m) at Kibbutz Mashabei-Sade. The field was surrounded on the west and south by fallow
fields, on the north by a field planted with jojoba, and on the east by an olive grove. The distance
between rows was 2 m. In Table 1, the average distance between the outer edges of two adjacent
canopy rows is presented, as well as the average height of the crop. The crop was trickle irrigated
with brackish water (EC = 6 dSm
−1
) every three days.
2.2. Data acquisition
The Bowen ratio machine was designed with a distance of 0.5 m between psychrometers, thus
spanning a total height interval of 1.5 m. The machine was installed at various heights by shifting it
on a pole, and the height was regularly changed throughout the measuring period (Table 1). The
lowest measuring height was 0.8 m, 0.2 m above the canopy.
Profiles of horizontal wind speed were measured using four three-cup anemometers (014A
Med-One) set at the same measuring heights as the psychrometers in the Bowen ratio system. The
outputs of all meteorological sensors were recorded with a Campbell CR23X data logger.
A four-level Bowen machine with six-aspirated thermocouple psychrometers was used for
above-canopy measurements (three on each side). The positions of adjacent psychrometers were
interchanged every five minutes during the 30 min. The data were stored every four minutes plus
one-minute rest, obtaining four levels of measurement. A representation of the Bowen ratio machine
is showed in Figure 2.
Copper-constant thermocouples were used as temperature sensors. The thermocouples (0.5
mm) were with a low frequency response and it was necessary to shield them. The psychrometers
Table 1. General information about the days of measurements. z
i
are levels of measurement.
Observed period 12:00 11:00 10:00 10:00 10:00 10:00
to 18:30 h to 18:30 h to 18:30 h to 18:00 h to 19:00 h to 18:30 h
Height 0.61 m
Row-gap width 0.36 m
Irrigation No No Yes No No Yes
z
1
1.5 m 1.5 m 0.8 m 0.8 m 1.1 m 1.1 m
z
2
2.0 m 2.0 m 1.3 m 1.3 m 1.6 m 1.6 m
z
3
2.5 m 2.5 m 1.8 m 1.8 m 2.1 m 2.1 m
z
4
3.0 m 3.0 m 2.3 m 2.3 m 2.6 m 2.6 m
Days 251 252 254 255 256 257
90
P. I. Figuerola and P. B. Berliner
were lined with polyurethane boards and covered by aluminum foil, both on the inside and on the
outside. Wind speed in the psychrometer duct close to the sensors was estimated at 4 ms
−1
. Sensors
from adjacent heights were wired differentially and measured differentially with a CR23X datalogger.
Particular attention was paid to the proper functioning of the wet bulb. The wick was wetted using
a Mariotte bottle located inside the psychrometer, downwind of the sensors, thus virtually eliminating
the dangers of radiative heating of the water reservoir. The water supply system functioned
satisfactorily even during events with very high temperatures and unusually low relative humidity
(35 °C and 25% respectively). The paired thermocouples were tested in the lab by measuring
temperature differences when placed in a well-stirred water bath. Average differences in the order
of 0.05
°C were registered. Pairs of psychrometers were tested in the lab and in the field. In both
cases, the intakes of the two psychrometers were placed in one box with a hole in the distal end.
The Bowen machine and the anemometers were tested at Wadi Mashash Experimental Farm at 10
km from the Institute. The experimental field soil is sandy loam and completely bared, the place is
wide open without obstacles or trees near, only the lab is there. The Bowen machine was installed
outside in the prevailing wind direction (N – NW). The pair of psychrometers was placed at the
same level at each height (Fig. 2). Typical differences, ranging from 0.02 to 0.2 °C for dry and wet
bulbs, respectively, were registered and could only be the result of slight construction differences.
The anemometers were calibrated relative to each other by setting them up at the same height in
the open field.
Canopy temperatures and the row-gap soil temperatures were measured with an infrared thermo-
meter, IRT (Telatemp Model AG42) and each measurement was taken on the crop (T
ic
) and on the
bare soil surface (T
is
). The IRT was held at 45° from the horizontal and aimed at the same prede-
termined points throughout the trial. Three readings were taken at each point and the average used.
Z
1
Z
2
Z
3
Z
4
0.5 m
0.61 m
0.36m
advection
convection
Fig. 2. The schematic figure of Bowen
ratio machine is shown. The system was
mounted on a foot with the possibility
to change the height. The six
psychrometers are shown, three on each
side of the machine and the measuring
position interchanges every 5 minutes.
91
Characteristics of the surface layer above a row crop
Net radiation was measured at 2 m above the canopy (Q−7, Campbell Scientific) and soil heat
flux was measured with two-heat flux plates (HFT-3, Campbell Scientific) buried at a depth of 2
cm in the soil, one midway between the rows and the other under the vegetation. The copper-
constant thermocouples were placed one under the canopy and the bare soil, at a depth of a few
millimeters (0.012m). Global radiation was available from routine data measured with an Eppley
precision pyranometer at the Blaustein Institute for Desert Research (Ben-Gurion University of
the Negev) located at 5 km.
2.2.1 Data
Measurements were carried out on the following days: 251 (8/9), 252 (9/9), 254 (11/9), 255 (12/9),
256 (13/9) and 257 (14/9). The crop was irrigated every third day, on days 254 and 257, irrigation
started at 14:00 h. Typical diurnal changes of temperature profiles above the canopy are slightly
unstable during the morning, are almost isothermal at noon, and show a weak inversion thereafter.
The predominant wind direction was from the NW and N. Wind gusts from the W or NE were
observed usually before midday, when the average wind speed was low. After 13:00 h, the wind
speed increased and generally blew across the rows from the NW with enough fetch. The daily
maximum temperature and the minimum daily relative humidity were between 30 to 35 °C and 30
to 40% respectively; as measured at the weather station located nearby. The soil surface temperature
measured by infrared thermometer may reach 55 °C at noon.
2.3 Micrometeorology parameters
Stability conditions are defined using the gradient Richardson Number (Ri) (Thom, 1975):
where,
θ
i
,
θ
j
and u
i
, u
j
are respectively, the potential temperature (K) and wind speed (ms
−1
);
measured at heights z
i
and z
j
(m); g is the acceleration due to gravity (ms
−2
) and
θ
is the average
temperature within the height interval (K). While different criteria have been suggested for defining
neutral stability, we adopted Thom´s (1975) criterion of |Ri| ≤ 0.01. The Richardson number was
estimated from the data measured at the highest and lowest levels (i = 4; j = 1, see Table I) and the
computed Ri are presented in Figure 3a. The common feature is one of unstable conditions before
noon and stable conditions in the afternoon. High wind speeds occur during the afternoon as result
of the breeze, Figure 3b.
Several arguments have been put forward to explain the anomaly in flux-gradient relationships
in the roughness sublayer, in terms of wake diffusion, horizontal inhomogeneity, vertical location
of sources and sinks. It has also been argued that these anomalies could vanish by adjusting the
zero-plane displacement height (d) (Hicks et. al., 1979). Garratt (1979) and Raupach (1979)
rejected this argument.
2
()( )
()
ij i j
i
ij
gz z
R
uu
θθ
θ
−−
=
−
(1)
92
P. I. Figuerola and P. B. Berliner
-0.10
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
10:00
14:00
18:00
12:00
16:00
10:00
14:00
18:00
12:00
16:00
10:00
14:00
18:00
12:00
16:00
Richardson number
(
251
)
(
252
)
(
254
)
(
255
)
(256 ) (257 )
(a)
Fig. 3. (a) The Richardson numbers
for each day were estimated from the
data measured at the highest and
lowest levels, according to Table 1.
(b) Wind speed observed at z high of
days: 251(z =1.5 m), 252 (z =.5 m), 254
(z =1.3 m), 255 (z = 1.3 m), 256 (z =1.6
m) and 257 (z = 1.6 m).
We obtained the zero-plane displacement height (d) and the roughness length (z
o
) using Robinson’s
(1962) approach. The approach employs a minimum of four levels of wind measurements to
mathematically solve for d and z
o
, using the accepted logarithmic wind profile under neutral condition.
The sum of the squares of errors to be minimized:
()
()
2
1
0
*
/ln
∑
=
⎥
⎦
⎤
⎢
⎣
⎡
−−=
n
i
ii
m
zdz
k
u
uE
(2)
11:00
16:00
19:00
12:00
15:00
13:00
10:00
17:00
14:00
10:00
18:00
17:00
14:00
11:00
18:00
12:00
15:00
16:00
13:00
19:00
Time of day
Time of day
93
Characteristics of the surface layer above a row crop
where the subscript i stands for the i-th level of wind speed. The equation is differentiated with
respect to u
*
, d and z
o
and equated to zero. This expression is essentially a linear function of d that
can be solved numerically by simple bisection to within ± 1 mm of the solution.
The Robinson’s (1968) approach was used by Kustas et al. (1989) who compared the sensible
heat flux calculated using the flux-gradient theory and sonic anemometer, finding that z
o
and d will
differ depending on whether the flow is generally across or along the rows. Schween et al. (1997)
obtain d with this approach finding that friction velocity u
*
(calculated from flux-gradient theory) fit
the measured values very well. However, the sensible heat flux is estimated too low.
We analyzed only neutral conditions (Ri < 0.015) and the cases for which the average wind speed
was below 1.5 ms
−1
were excluded. Results are presented in Table 2. The wind data led only to few
values for d and z
o
. Seeing the table, in the highest layer the Ri values were > 0.015 except one case
where the d value was 0.380 m, agreeing well with the average d value (= 0.383 m ± 0.05 m).
The ratio of both quantities to the height of the obstacles, h,was z
0
/h ≈ 0.033 and d/h ≈ 0.63
when the canopy height was 0.61 m, this latter compares well with the ratio suggested by
Thom (1975). From summary of Raupach et al. (1991) with a roughness density, λ, approxi-
mately 0.7 (Hebbar et al., 2004) z
o
/h and d/h should be about 0.10 and 0.67, respectively. The
lower z
o
/h = 0.03 observed instead of 0.10 could be due to the winds blow along the rows. We will
show later the error analysis to friction velocity and the sensible heat flux in relation to d. In
advance, we can say that the friction velocity error is no affected for d.
Elliot (1958) proposed an empirical formula for the internal boundary layer,
δ
i
:
δ
i
/z
02
= A
1
(x/z
02
)
0.8
where z
02
is the roughness length after roughness change, x the distance from the border, fetch, and
A
1
is a constant of proportionality and has a weak dependence on the strength of the roughness
change: A
1
=0.75 + 0.03 M, where M = ln(z
01
)/ln(z
02
) and z
01
is before roughness change. In
agreement with Monteith and Unsworth (1990) we used the equation (3) with M = 0 as the minimum
depth (M is negative in smooth-rough change).
(3)
Table 2. Ri( j ) is the Richardson number in each layer, j. Ri layer is the Richardson
number of the total layer. d is displacement high. z
0
is the roughness length in meters.
Day Hour Ri (1) Ri (2) Ri (3) Ri layer d(m) z
0
(m)
254 14:00 0.005 0.007 0.020 0.008 0.418 0.0178
255 15:00 0.002 0.008 0.010 0.005 0.380 0.0175
255 15:30 0.004 0.008 0.027 0.007 0.311 0.0286
255 18:00 0.006 0.014 0.024 0.011 0.422 0.0168
Mean values = 0.383 0.0202
94
P. I. Figuerola and P. B. Berliner
Based on wind tunnel evidence the flux of momentum is constant in the lowest 10 −15 % of the
turbulent boundary layer (Bradley, 1968), the logarithmic wind profile would be expected to extend to a
height
δ
i
´ = 0.01;
δ
i
often called the internal equilibrium layer (IEL). Jegede and Foken (1999) have
demonstrated in his study that the expression:
δ
i
´ = 4.5x
0.5
can safely be used to determine the height of
the internal equilibrium layer that is free of the influence of overlying the internal boundary layer. For our
experiment it is
δ
i
´ = 4.5 m with x = 230 m. We have not enough data at a higher altitude to confirm this.
The internal boundary layer depth was computed according to equation (3) being x the fetch
equal to 230 m when the wind direction is from WNW and to 318 m when it is from NW (M = 0).
The resulting boundary layer depth,
δ
´
i
is between 26.6 m to 34.5 m, then the internal equilibrium
layer, d
i
’, is 2.6 m and 3.4 m from WNW and NW direction respectively.
The review achieved by Kaimal and Finnigan (1994) of the experiments where the approach to
local equilibrium, or more directly, the validity of the flux-gradient connection can be compared with
fetch, suggests that eddy diffusivities should be used with the greatest caution at fetch x < 10 d
i
.
3. Methodology and results
3.1. Profiles
We define the gradients of temperature and vapor pressure as:
(4)
(
)
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
−
=
∂
∂
+
+
dz
dz
Z
z
i
i
j
ii
1
1
ln
ς
ς
ς
where
ζ
i
is the value of the relevant entity (temperature or vapor pressure) on adjacent levels and
Z
j
the mean geometric height: (Z
j
= √(z
i + 1
− d) (z
i
− d)) of the corresponding levels i(= 1, 2, 3). This
gradient is first suggested by Panofsky (1965) and used by Paulson (1970).
3.1.1. The temperature profiles
In Figure 4 the temperature gradients at various heights (expressed as Z
j
/h, with h the crop height)
for days 251, 254 and 255 are presented and the levels of measurements are detailed in Table 1. For
example, on day 251, the lowest level was at 1.5 m and the highest at 3.0 m. Graphs for the
remaining three days were similar.
A typical example of the behaviour of the gradients is presented in Figure 4. The sign of the
temperature gradient changes close to midday. The gradients were largest in the lowest layers and
exhibited less change in the highest layers. The sign first changed in the highest layer, one hour
thereafter in the intermediate layer (Z
j
/h = 1.9), and two hours later in the lowest one. A similar
behaviour was observed when the Bowen ratio machine was installed at different heights. The
inversion temperature gradient in the afternoon was observed constant at the top (Fig. 4, Z
j
/h = 3.9).
95
Characteristics of the surface layer above a row crop
The development of an inversion layer is referred as an advective inversion, representing the
circumstance of airflow blow from hot dry area to cool irrigated pasture (Dyer and Crawford, 1965).
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
o
C/m
Fig. 4. The temperature gradient with z
j
/h: at 1.0 (day 255) (- -
°
- -), at 1.9 (day 255) (- -
∗
- -),
at 2.7 (day 254) (-
°
-) and at 3.9 (day 251) (-
•
-)
Systematic measurements were not observed upwind, but data from a meteorology station
outside showed that the air upwind temperature was usually higher (~2 °C) than downwind and the
temperature of the bare sandy soil can reach to 60
°C at noon. In some level above the boundary
layer, the stable (inversion) temperature profile above the wet surface (downwind) lost connection
with the surface, and it should follow with unstable temperature profile upwind.
Our results agree with Kroon and Bink (1996). They investigated the turbulent fluctuations in
the internal boundary layer which forms in the wake of a dry to wet surface transition. They
defined three periods with different thermal stability regimes: (1) morning with an unstable
stratification up and downstream of the transition, (2) afternoon, when downstream of the transition
the stratification changes from unstable to stable while upstream the conditions remain unstable, (3)
evening with stable stratification upstream and downstream.
3.1.2. The vapor pressure profiles
The vapor pressure gradient above an actively transpiring crop should diminish with height and this
was observed everyday. Day 255 is presented as an example in Figure 5a (Z
j
/h = 1, 1.9 and 2.7).
When the tower was placed higher, for example, on day 252 (Fig. 5b), the gradient at Z
j
/h = 3 was
larger than at Z
j
/h = 2.2. This occurred after 14:00 h and it could be due to the influx of hot dry air.
Temperature gradient
Time of day
96
P. I. Figuerola and P. B. Berliner
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
Vapour pressure gradient
(a)
mb m
-1
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
Vapour pressure gradient
(b)
mb m
-1
Fig. 5. The vapor pressure
gradient with z
j
/h: a) day 255: at
1.0 (
°
), at 1.9 (-
•
-) and 2.7 ( - -
∗
- - );
b) day 252: at 2.2 (o), at 3.0 (-•-)
and 3.9 ( - -
∗
- - ).
In Figure 6, the relative humidity is presented for days 252 at z = 1.5 m (Z/h = 1.8) and 257 at
1.1m (Z/h = 1.2). In each case, there is a ‘‘plateau’’ in the relative humidity from 12:00 until 16:00
h (day 252) or 17:00 h (day 257) due to irrigation. A minimum relative humidity close to 30% (14:00 h)
was measured at the meteorological station outside the field and this increased monotonically up to
80-90% at night. The ‘‘plateau’’ could not be observed.
Prueger et al. (1996) measured temperature and humidity profiles in a study around a well-
watered alfalfa field surrounded by arid surfaces. Downwind the edge, they had shown that the
profiles describe an inversion temperature and humidity decrease with height, the same case shown
by us. Using eddy correlation, they found a negative heat sensible flux and a positive heat latent flux
with height values (~ 500 W m
−2
). Stull (1988) says that under these conditions (negative heat
sensible flux, positive heat latent flux and positive net radiation) an exceptional case of the oasis
effect, due to the excess of evaporation from a well-irrigated surface, ocurrs. Summarizing, in our
case, the wind speed is stronger during the afternoon, developing an inversion of temperature and
a strong vapour pressure gradient over the irrigated tomato field.
Time of day
Time of day
97
Characteristics of the surface layer above a row crop
0.3
0.4
0.5
0.6
0.7
0.8
0
.
9
10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
H
r
Fig. 6. Relative humidity for days: 252 at z = 1.5 m (
*
) (z − d/h = 1.8)
and 257 at z = 1.1 m (
°
) (z − d/h = 1.2)
3.2. The convective activity
Jacobs et al. (1994) showed that a decoupling between above −and within−canopy processes
develops under conditions of low speed winds at night. Moreover, inside of the canopy, the relatively
warm floor generates free convection cells. This argument can extend to those daylight hours
during which low wind speed, high radiation prevail (late morning and midday) and high temperatures
in the bare soil between the rows crop occurs, resulting in strongly unstable conditions inside the
canopy. We observed that the temperature differences between the non-covered soil surface (T
is
)
and the air temperature measured at the lowest level above the canopy (T
is
−
T
a
) are of the same
order of magnitude as the differences between the former and the covered soil surface temperature,
T
sc
(under the plants), T
h
= (T
is
−
T
sc
). This fact supports the view that convective activity could
take place during the previously defined time intervals.
Monteith and Unsworth (1990) use the ratio of the Grashof (Gr) to the Reynolds (Re) numbers
(C
0
=Gr/Re
2
) to identify the ranges of convection. The pure forced convection and pure free
convection regimes occur when C
0
< 0.1 and C
0
> 16 respectively, and mixed convection occurs
when 16 < C
0
< 0.1.
Raupach (1979), Jacobs et al. (1994) and Zelger et al. (1997) suggested that for the computation
of Re within a canopy, the friction velocity u
*
derived from above canopy wind speed profiles be a
more convenient choice instead of the wind speed within the canopy. If the distribution of sources
Time of day
99
Characteristics of the surface layer above a row crop
R
Ns
=
ε
a
σ
T
a
4
−
ε
s
σ
T
s
4
+ (1
− α
)R
g
where T
s
is the soil surface temperature (as measured with an infrared thermometer),
ε
s
the emissivity
of the soil (= 0.99),
ε
a
emissivity of air equal to 1.24(
ε
a
/T
a
)
1/7
(Brutsaert, 1982) where T
a
and
ε
a
are
the temperature and the water vapor pressure of air observed at the upper level,
α
is the albedo
(estimated from spot measurements as 0.3), and R
g
the global radiation. The R
Ns
computed by (9)
slightly underestimates the actual flux density as long wave radiation emitted from the canopy, and
short wave radiation scattered downwards by the canopy were not considered. The computed
values of w
*
are therefore slight underestimates as well. The value R
N
is different at R
Ns
because
this latter has in consideration the bare soil temperature between the rows only.
Fig. 7. Daily evolution of the coefficient
convective, C
0
(Eq. 5). The dashed line
in the top is C
0
= 16 and in the bottom is
C
0
= 0.1, for days 254 (
•
), 255 (
°
), 256 (∆)
and 257 ( × ).
(9)
Low wind speeds at canopy height (u(h) < 1 ms
−1
) and w
*
> u
*
, are necessary conditions during
nighttime for free convection to persist (Jacobs et al., 1994). During daytime these conditions will
not be usually met, but a significant decrease of the horizontal wind velocity leads to a strongly
reduced u
*
,which coupled with larger values for the free convection scaling velocity w
*
could result
in conditions under which free convection could persist (Stull, 1988).
Figure 8 shows the values of w
*
and u
*
between 10:00 to 17:30 h. Values of w
*
>> u
*
occurred
at 12:00 h, 13:30 h and 14:00 h during periods during which extremely high soil surface temperature
(T
is
) were measured (43.6 °C, 52.7 °C and 53.9 °C, respectively). The cases for which w
*
< u
*
coincide with values of C
0
less than 16 indicated that mixed or forced convection conditions prevailed.
Data of day 257, between 11:00 and 13:00 h were lost due to the stack of anemometer when low
wind speeds occurred. The error
δ
u
*
is about 0.13 ms
−1
and
δ
w
*
is approximately 0.02 ms
−1
, being
obtained from error propagation method (3.4).
C
0
, convective coef.
Time of day
100
P. I. Figuerola and P. B. Berliner
Fig. 8. The speed friction velocity,
(
°
) u
*
(estimated for the lowest
layer) and the free convection scale,
(•) w
*
, for days 254, 255 at Z
j
/h = 1.0
and days 256 and 257 at Z
j
/h = 1.5
is shown.
For values of u
*
< 0.16 ms
−1
free convection conditions were found. Zelger et al. (1997) reported
a similar value (0.2 ms
−1
).
From our data (w´ T´)
0
>> (w´ T´)
1
, this latter was calculated above the canopy by flux-
gradient method, (equation 12). The relation found is: ( w´ T´)
0
= 2.6 ( w´ T´)
1
+ 0.2 ms
−1
K, with
a determination coefficient r
2
= 0.73. An amount of the heat flux originated at the floor (w´ T´)
0
,
of the canopy is transformed into sensible heat (Jacobs et al., 1994). To calculate the correction
factor, g, of the profiles in the roughness sublayer, we should know how much of the heat flux
originated from bare soil will arrive to the canopy top. But the characterization of the within-
canopy flow is very complex (Jacobs et al., 1994), and the value’s g and the roughness layer
depth are not possible to estimate from this information. These can be deduced from the residual
of the energy balance.
3.3. Residual of the energy balance
The roughness sublayer is defined as the region below the surface layer in which the Monin-
Obukhov (MO) similarity theory no longer applies. This definition emphasizes that the flux-gradient
relationship in the roughness sublayer is different from that predicted by the MO theory.
We had computed the latent and sensible heat fluxes by means of the aerodynamic method
(flux-gradient relationship) using the measurements of the surface boundary layer, and the
energy balance equation results:
(H
aj
+ E
aj
) − (R
N
− G) = g (Z
j
/h)
(10)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10:00
11:30
13:00
14:30
16:00
17:30
10:00
11:30
13:00
14:30
16:00
17:30
10:00
11:30
13:00
14:30
16:00
17:30
10:00
11:30
13:00
14:30
16:00
17:30
w
*
and u
*
(m s
-1
)
Time of day
101
Characteristics of the surface layer above a row crop
where R
N
is the net radiation; H
aj
and E
aj
are the sensible and latent heat fluxes, for the layers Z
j
(with
j = 1, 2, 3). g(Z
j
/h) is the residual of the energy balance equation for each layer j. G is the heat soil flux
at surface, computed as weighted average of the percentage of tomato and bare soil (j = 1, 2). G
j
= G
0.02m, j
+S
j
where G
0.02m, j
is the heat soil flux at 0.02 m in the position j and S
j
is the change in heat storage above
each heat flux plates (Mayocchi and Bristow, 1995). From the idea suggested by Cellier and Brunet
(1992), the residual g(Z
j
/h) has an evolution with the height in the roughness sublayer, and it is equal to
zero in the inertial sublayer, finding the equilibrium layer. The closure of the balance equation is an
important test to value the measurement of the fluxes. If g(Z
j
/h) 0 , it is due to the departure of the
fluxes from the MO theory and an additional source or sink of energy is present.
The fluxes of sensible and latent heat were calculated in the three layers between adjacent pairs
of measurements levels, by the aerodynamic method, using:
E
aj
= −
ρ
L
v
u
*j
q
*j
H
aj
= −
ρ
C
p
u
*j
T
*j
where
ρ
is the air density, L
v
is the latent heat of vaporization, C
p
is the specific heat and j is the
layer, defined by the mean geometrical heights, Z
j
; and u
*
, T
*j
and q
*j
are scaling parameters for
wind speed, temperature and specific humidity, respectively, defined by (Businger et al., 1971;
Dyer, 1974; Kaimal and Finnigan, 1994):
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
+
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
+
⎟
⎠
⎞
⎜
⎝
⎛
−
+
=
j
L
d
i
z
f
j
L
d
i
z
f
d
i
z
d
i
z
i
F
i
Fk
j
F
ψψ
1
1
ln
1
*
(11)
(12)
where F is the variable (u, T or q) and i is the height of measurements adjacent; and
ψ
m
,
ψ
h
and
ψ
v
are, respectively, the stability correction functions for momentum, temperature and specific humidity,
of Paulson (1970) and Dyer (1974); based on the measurement of two levels, k is the von Karman
constant (= 0.40), so that:
ψ
m
((z
−
d)/L) = 2ln[(1 − x
2
)] + ln[(1+ x
2
)/2] − 2 arctan (x) +
π
/2
ψ
h
((z
−
d)/L) =
ψ
v
((z
−
d)/L) = ln[(1+ x
2
)/2]
where: x = (1
−
16(z
−
d)/L)
1/4
with (z − d)/L < 0
ψ
m
((z
−
d)/L) =
ψ
h
((z − d)/L] +
ψ
v
((z − d)/L) = − 5((z − d)/L) with 0 < (z
−
d)/L < 1
(15)
(16)
(14)
(13)
≠
102
P. I. Figuerola and P. B. Berliner
The Monin-Obukhov length, L, was obtained using the gradient Richardson number of each
layer, j (Kaimal and Finnigan, 1994; Dyer and Hicks, 1970):
L
j
= Z
j
/Ri, with Ri
j
< 0
L
j
= Z
j
(1 - 5Ri
j
)/Ri
j
with Ri
j
> 0
The residual of the energy balance (g(Z
j
/h)) can be plotted against any parameter we choose
(for example, the canopy or soil temperature) in order to ascertain the relationship between them.
Daamen et al. (1999) used a similar procedure to study the influence of a shelter and Cellier and
Brunet (1992) to locate the inertial sublayer.
The residual in energy balance g(Z
j
/h) plotted against the temperature difference (T
h
) is between
the bare soil surface temperature midway between the rows (T
is
) and the soil surface temperature
under the plants (T
sc
); the rationale being that the horizontal temperature is linked to convective
activity within the canopy and thus it explains the lack of balance in the lowest layer of the internal
boundary layer. The relation between the residual, g(Z
j
/h), and T
h
, is presented in Figure 9, for two
relative heights (Z
j
/h = 1 and 1.5). The g(Z
j
/h) obtained from equation (10) is not dependent of T
h
but from Figure 9 we can see that it is connected with T
h
. The value of the residual was close to
zero when T
h
was close to zero, which happened during the afternoon (after 15:30 h). The largest
residuals were computed when the temperature (T
h
) difference exceeded 20 °C.
(17)
(18)
Fig. 9 The residual, g(Z
j
/h), in the
energy balance vs. the horizontal
inhomogeneity of the surface tempe-
rature, T
h
= T
is
− T
sc
. Days 254, 255: g(Z
j
/
h) at Z
j
/h = 1.0 (
°
) and days 256 and
257: g(Z
j
/h) at Z
j
/h = 1.5 ( • ).
The relative magnitude of w
*
to that of the friction velocity allows us to recognize the cases for
which the sensible heat generated at the bare soil could reach the layers above the canopy. We
[watt m
−2
]
Horizontal inhomogeneity
103
Characteristics of the surface layer above a row crop
0
0.5
1
1.5
2
2.5
3
3.5
-500 -400 -300 -200 -100 0 100 200 300 400 500
H
a
+E
a
-(R
N
-G)
Z
j
/h
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-500 -400 -300 -200 -100 0 100 200 300 400 500
H
a
+E
a
-(R
N
-G)
Zj/h
Fig. 10. The residual in the energy
balance, g(Z
j
/h), calculated as
(H
aj
+ E
aj
) − (R
N
−
G), in function
with relative layer (Z
j
/h) without
the cases of free convection.
(The average residual in the
energy balance in each layer is
presented: from morning until
midday (10:00 to 15:00 h). The bar
represents the standard devia-
tion.
Fig. 11. Idem Fig. 9, but during
the afternoon (15:30 to 19:00 h).
excluded these cases, and the vertical variation in g(Z
j
/h) for the remaining ones is presented in
Figures 10 and 11, for unstable and stable cases, respectively.
Mahrt (2000) defined the thermal blending height for unstable conditions as directly proportional
to the surface heat flux and inversely proportional to the wind speed. Results presented in Table 3
indicate that during unstable conditions the average residuals are not statistically different from
zero for Z
j
/h = 1.9 to 2.4. These results are consistent with those of Kaimal and Finnigan (1994)
and Cellier and Brunet (1992) that reported that when unstable conditions prevailed the roughness
sub-layer extended until about twice the canopy height.
104
P. I. Figuerola and P. B. Berliner
Table 3. Data corresponding to the cases where free convection did not occur. It shows the application of
t´student, t
1 − α/2
, each layer Z
j
/h, with α level of significance. *The null hypothesis (mean residual balance=0)
is accepted at the 5% level of significance, and
+
at the 2.5% level of significance. N is the amount of data.
Mean residual balance Z
j
/h Standard deviation t´student N
[W m
−2
] [W m
−2
]
Midday (10:00 to 15:00 h)
−170.83 1.0 67.51 −11.32 20
−166.32 1.5 82.81 −4.92 6
−55.80 1.9
+
103.76 −2.41 20
−15.01 2.4* 140.33 −0.26 6
−223.28 2.7 168.01 −5.94 20
−294.25 3.2 88.92 −8.11 6
Afternoon (15:30 to 19:00 h)
−53.19 1.0 37.66 −5.09 13
−11.08 1.5* 61.70 −0.70 15
−12.17 1.9* 57.94 −0.76 13
43.53 2.4
*
118.56 1.42 15
−111.31 2.7 73.25 −5.48 13
−86.50 3.2 56.83 −5.90 15
During the period when stable conditions prevailed (afternoon) the average residuals are not
statistically different from zero for Z
j
/h = 1.5 to 2.4. This lowering of the lower boundary may be
due to the combination of high wind speeds and a decrease in convective activity. The latter is a
result of the fact that the canopy casts a shadow on the bare soil surface between the rows, thus
decreasing the horizontal differences in soil surface temperatures. The inhomogeneity of the canopy
seems to decrease due to both effects. Cellier and Brunet (1992) deduced the correction factor
γ
of the universal functions (derivate above smooth surfaces) where
γ
is applied in the roughness
sublayer. The
γ
for the sensible and latent heat flux result both equal to
γ
h,v
(Z/Z
*
) = Z
*
/Z where Z
*
is the roughness layer depth. Taking the inter-row spacing
δ
= 0.36 m, we obtain Z
*
/
δ
= 3.2 and 2.5
for unstable and advection conditions.
In Figure 12 the vertical variation of the residuals is presented for the cases for which the
conditions that could lead to free convection inside of the canopy were observed [(u
*
−
w
*
) < − 0.02
and C
0
> 16]. These values were day 256 between 12:00 h until 14:30 h and day 257 at 10:00 and
10:30 h. At the lowest levels, the residuals were significantly different from zero (Fig. 12), negative
values for the lowest level, and positive ones for the intermediate one. The uppermost layer showed
an extremely large variability. Extremely unstable conditions (Ri < − 0.05) prevailed during these
periods at the lowest level above the crop. The strong unstable condition can help the thermals
105
Characteristics of the surface layer above a row crop
emanating from the surface to reach the heights of measurements. This could be an explanation for
the lack of balance in the energy equation. These results suggest that for this particular canopy and
environmental condition (high soil surface temperature and relatively low wind speed) fluxes of
sensible and latent heat could not be computed using the conventional flux-gradient relationships.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-500 -400 -300 -200 -100 0 100 200 300 400 500
H
a
+E
a
- (R
N
-G) [watt m
-2
]
Z
j
/h
Fig. 12. The residual in the energy
balance, g(Z
j
/h), calculated as
(H
aj
+ E
aj
) − (R
N
− G), in function
with relative layer (Z
j
/h), only the
hours with free convection inside
the canopy (w
*
> u
*
) are showed.
()
()
0
0
1
N
b
R
G
H
β
β
−
=
+
(19)
The residuals of the two uppermost layers are significantly less than zero for both, stable and
unstable conditions. This could be due to insufficient fetch during the early morning (unstable
conditions, Fig. 10) but not in the afternoon during which the wind blew from the NW. During this
period, the lack of balance can only be ascribed to advection. The influence of advection can be
estimated by the horizontal heat transport and is compared with the (vertical) sensible heat flux
(H
a3
). The horizontal heat transport approximates to ~ T
a3
· u
3
where the sub index 3 is the highest
level of air temperature and wind speed observed. It is compared in Figure 13 with H
a3
, observing
that when H
a3
is negative a linear relation with horizontal transport exists, and there is a poor
relation when H
a3
is positive. For that reason, when H
a3
< 0, the sensible heat flux has a component
of horizontal heat transport, being an advection situation.
Finally, using the Bowen ratio (ßo) it is possible to compute the sensible (H
b
) and latent (E
b
)
heat fluxes as:
()
()
0
1
N
b
R
G
E
β
−
=
+
(20)
106
P. I. Figuerola and P. B. Berliner
where
β
0
=
γ
(T
i
− T
i − 1
)/(
ε
i
−
ε
i − 1
) and
γ
(mbar °C
−1
) is the psychrometric constant. Blad and
Rosenberg (1974) concluded that when –2.5 < Ri < 0.025, the relation between the turbulent
transfer coefficients for heat and water vapour, k
h
/k
v
, is close to 1 and the error in the Bowen
estimation is < 10%. The Richardson numbers (Ri) for the layer Z/h = 1.9 do not exceed 0.02.
0
20
40
60
80
100
120
140
160
180
200
-100 -50 0 50 100 150
H
a3
(W m
-2
)
T
a3
. u
3
(
o
C m s
-1
)
Fig. 13. An approximation of horizontal
advection at the highest level ~ T
a3
· u
3
(T
a3
and u
3
are the air temperature and
wind speed) is compared with the heat
sensible flux (H
a3
). The sub index 3
represents the levels Z
j
/h = 2.8 (o) (days
254 and 255) and Z
j
/h = 3.3 ( • ) (days
256 and 257).
-200
-100
0
100
200
300
400
500
600
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
hours
Flux (W m
-2
)
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Bowen ratio
Fig. 14. Computed fluxes for day 255.
The sensible heat flux H
b
(grossed line),
and the latent heat flux, E
b
(dotted line),
were computed from the Bowen ratio
(
β
0
) at Z
j
/h = 1.9 (o), and the available
energy, R
N
−
G (thinned line) is pre-
sented.
Horizontal advection
Heat sensible flux
109
Characteristics of the surface layer above a row crop
The K
d
u*
is the same equation (A3) (Fig. 15), near the canopy top in the extreme case results
K
d
u*
~ 1, and
δ
d/d = 0.13, then
δ
u
*
/u
*
due to d is not so big. It is about 0.13 in unstable cases.
The K
∆
u
coefficient of the equation (24) is defined by the equation (C2) with (C3) and (C4) for
the unstable and stable cases, respectively. In addition, the K
∆
T
coefficient of the equation (25) is
defined by the equation (D2) with (D3) and (D4). K
∆
u
and K
∆
T
are shown in Figure 16 as function
of the stability parameter, Z/L. The highest unstable condition results in K
∆
u
~ 0.5 and K
∆
T
~ 1.5. In
neutral stability (− 0.01 ≤ Z/L ≤ 0.01), K
∆
u
and K
∆
T
are about 1. Neutral stability is more probable
to occur occurs near of the canopy top, and the unstable conditions increase with height although
high instability can occur in free convection near the canopy top. If strong stable conditions prevail,
K
∆
u
increase and K
∆
T
decrease.
The largest
∆
u and
∆
T value’s are near the canopy, as result the relative errors 2
δ
u/
∆
u and
2
δ
T/
∆
T are small, increasing with height. According to equations (24) and (25)
δ
Ha/Ha are big
when
∆
T or
∆
u are so small as two times the instrumental error.
∆
T is small (< 2
δ
T) at noon when
change of sign occurs, or
∆
u is small when free convection takes place.
In the afternoon, stability conditions between 0 < Z/L < 0.01 prevail on the lower layer (Z/h <
2.4) and
∆
T and
∆
u are big and
δ
Ha/Ha < 1. The same way we can say that the error of latent
heat flux depends of error 2
δ
q/
∆
q, being significant after 17:00 h.
The application of flux-profile relationships have lower error at Z/h < 2.4 than at Z/h > 2.4 when
∆
z is 0.5 m. Inversely, the error due to d is big at the lower high, but in our case the former error
was more important that this latter.
Fig. 16. The K
∆
u
( • ) and K
∆
T
(
°
)
coefficients with stability parameter,
(Z
−
d)/L, are shown.
K
∆
u
or K
∆
T
110
P. I. Figuerola and P. B. Berliner
()
u
u
K
u
u
u
u
∆
∆
=
⎟
⎟
⎠
⎞
∆
∆
δδ
*
*
(28)
0123456
δu
*
/u
*
(m s
-1
)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0123456
δ
u
*
/u
*
(m s
-1
)
Z/h
Fig. 17. The relative
error of friction
velocity,
δ
u
*
/u
*
, in
relation with
∆
u is
shown, being (
°
) the
stable and ( • ) the
unstable cases.
The same as equation (27), but with relation to ∆u, results in:
According to equation (28), du
*
/u
*
is < 1 (Fig. 17) when Z/h < 2.4, except in free convection
cases (see Z/h = 1.5). We calculate du
*
~ 0.7 ms
−1
if Z/h < 2.4 and dT
*
~ 0.6
o
C are the greatest
values observed.
4. Conclusions
The study was carried out in an irrigated field planted with tomato, which was surronded by large tracts
of dry, bare soil. The crop was planted in rows and irrigated by trickle irrigation. The effects of these
features on the surface boundary layer above the crop were researched on a number of selected days.
The gradients in temperature and water vapor pressure were obtained at various heights above the
canopy using a Bowen ratio machine. This area is influenced by the sea breeze. The maximum temperature
difference between the sea and desert land is about midday (maximum radiation), which generates a
strong wind component. The hot air arrives on a cooler crop and the temperature gradient of the highest
layer changes of sign at midday, and later in the lowest layer. The layer Z/h = 3 receives the entrance of
dry air from the desert area and the evapotranspiration induces a strong cooling in the bottom.
The fluxes of sensible and latent heat for several heights were computed applying the aerodynamic
method. The residual in the energy balance equation was used as a criterion to determine the
internal equilibrium layer.
111
Characteristics of the surface layer above a row crop
d
d
d
H
H
d
H
h
aj
ajaj
aj
δ
δ
||
∂
∂
=
d
d
K
d
d
K
d
d
K
d
d
d
T
T
d
d
u
u
d
H
H
T
d
u
dd
j
j
j
jaj
ja
δδδδ
δ
**
*
*
*
*
+==
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∂
∂
+
∂
∂
=⇒
(A1)
Mixed convection conditions occurred from morning to midday (u
*
> w
*
) inside the canopy and
weak unstable conditions above it. The closure of balance energy equation is between Z/h ~ 1.9 to
2.4. The enclosure for Z/h < 1.9 was associated with inhomogeneous temperature in the soil of the
canopy. The temperature differences between soil under the plants and bare soil between rows can
arrive to 20
o
C. During the late morning in short periods, the bare soil between the rows reached
extremely high temperatures and low wind speeds occurred above the canopy (u
*
< 0.16 ms
−1
) and
thus free convection inside were the dominant transport regime (w
*
> u
*
) during some hours. Z/h =
1.5 and 2.4 were different from zero and an extremely large variability was evident for the Z/h =
3.2 layer, no finding the equilibrium layer. Strongly advective conditions prevailed during the afternoon,
manifested as an increase in the stability of the uppermost measured layer, and propagated slowly
downwards. The closure of balance energy equation for the stable conditions above the canopy
was between Z/h ~ 1.5 to 2.4. The lowering of the equilibrium boundary for stable conditions was
ascribed to the high wind speed and the fact that horizontal gradients in the soil surface temperature
were small due to canopy shading, prevailing mixed and forced convection inside the canopy. In these
cases, the inhomogeneity canopy did not have influence at the height 1.5 h. The residuals were significantly
different from zero for the uppermost layers (Z/h = 2.7 and 3.2) during these periods.
Our findings suggest that the location of the equilibrium layer above fields surrounded by dry
bare areas and in which row crops are trickle irrigated, vary in response to wind speed and the
temperature of the soil between the rows of the crop, and that for some time intervals the estimation
of fluxes may not be possible.
Acknowledgements
P. Figuerola received during her visit at the Jacob Blaustein Institute of the Ben Gurion University
of the Negev a fellowship from the FOMEC (University of Buenos Aires, Argentina) and from the
CONICET (National Council for Science and Technology, Argentina). This study was as well
partly supported by GLOWA-JR.
Annex A
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∂
∂
=
d
u
u
d
K
j
j
u
d
*
*
*
(A2)
114
P. I. Figuerola and P. B. Berliner
()
() ()
u
u
K
u
u
u
u
u
u
H
H
u
j
j
u
aj
aj
∆
∆
=
∆
∆
∆∂
∂
∆
=
⎟
⎟
⎠
⎞
∆
∆
δδ
δ
||
*
*
(C1)
()
()
()()
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−−
−
−
−=
⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
⇒
+
+
+
3
1
1
1
512
5
dzdz
zz
Ri
Ri
d
ii
ii
j
j
i
h
ψ
(B4)
() ()
()
()
()
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
+
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
−
∆
−
∆
=
∆∂
∂
⇒
+ i
m
i
m
j
J
j
uuuk
u
u
u
u
u
ψψ
1
2
*
*
*
()
()
()
()
() ()
u
u
K
u
u
uuk
u
H
H
u
i
m
i
m
j
u
aj
aj
∆
∆
=
∆
∆
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
+
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
−−=
⎟
⎟
⎠
⎞
∴
∆
+
∆
δδψψ
δ
1
*
1
(C2)
()
()
()
()
()
()
()
()
()
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
∂
−∂
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−∂
∂
⎥
⎦
⎤
⎢
⎣
⎡
∂
∂
=
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
+
+
+
+
+
u
Ri
R
Ldz
Ldz
x
xu
j
j
ji
ji
i
i
m
i
m
/
/
1
1
1
1
1
ψψ
()
()
()
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎭
⎬
⎫
⎩
⎨
⎧
∆
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
−−
⎭
⎬
⎫
⎩
⎨
⎧
+
−
+
+
=
⎥
⎦
⎤
⎢
⎣
⎡
∆∂
∂
⇒
+
−
+
+
+
+
+
u
Ri
dz
dz
L
dz
x
x
xu
j
i
i
j
i
i
i
i
i
m
21614
1
12
1
2
2
1
1
4
3
1
2
1
1
1
1
ψ
(C3)
The stable case: y
m
= y
h
= y
v
\ y
h
(z
i + 1
− d/L
j
) = -5(z
i + 1
− d/L
j
) and Z
j
/L
j
= Ri
j
(1 − 5Ri
j
)
Annex C
with F = u (wind speed) equation 13, and ∆u = u
i+1
− u
i
The unstable case:
115
Characteristics of the surface layer above a row crop
()
()
()
()
()
1
j
j
mm
jj
i
R
i
L
uLRiu
ψψ
+
⎡⎤
⎡⎤ ⎡⎤
∂
⎡⎤
∂
∂∂
=⋅ ⋅
⎢⎥
⎢⎥ ⎢⎥
⎢⎥
∂∆ ∂ ∂ ∂∆
⎢⎥ ⎢⎥
⎢⎥
⎣⎦
⎣⎦ ⎣⎦
⎣⎦
()
()
()
()
()
1
1
22
1
5
2
ii
i
j
m
jj
i
zdzd
zd
R
i
uu
LRi
ψ
+
+
+
⎡⎤
−−
⎡⎤
⎡⎤
−
∂
⎡⎤
⎢⎥
⇒ =⋅− ⋅−
⎢⎥
⎢⎥
⎢⎥
∂∆ ∆
⎢⎥
⎣⎦
⎢⎥
⎢⎥
⎣⎦
⎣⎦
⎣⎦
()
() ()
*
*
aj
T
aj
T
TT
H
TT
K
H
TTT T
δδ
δ
∆
∆
⎞
∆∆
∆∂
==
⎟
∂∆ ∆ ∆
⎠
(C4)
()
()
()
()
() ()
*
1
¨
1
aj
hh
T
aj
T
ii
TT
H
T
K
H
kT T T T
δ
ψψ
∆
∆
+
⎡⎤
⎧⎫
⎛⎞
⎡⎤⎡⎤
⎞
∂∆ ∂∆
∂∂
⎪⎪
⎢⎥
⎜⎟
=− + =
⎟
⎨⎢ ⎥ ⎢ ⎥⎬
⎢⎥
⎜⎟
∂∆ ∂∆ ∆ ∆
⎢⎥⎢⎥
⎠
⎪⎪⎣⎦⎣⎦
⎢⎥⎝⎠
⎩⎭
⎣⎦
()
()
()
()
()
()
()
()
()
1
1
1
1
1
/
/
ij
j
i
hh
ij
ij
i
zdL
R
i
x
Tx R T
zdL
ψψ
+
+
+
+
+
⎡⎤⎡⎤
∂−
⎡⎤ ⎡⎤
∂⎡⎤
∂
∂∂
⎢⎥⎢⎥
=
⎢⎥ ⎢⎥
⎢⎥
∂∆ ∂ ∂ ∂∆
∂−
⎢⎥⎢⎥
⎢⎥ ⎢⎥
⎣⎦
⎣⎦ ⎣⎦
⎣⎦⎣⎦
()
()
3
1/2
4
111
2
1
1
4
41 16
1
iii
j
h
ji
i
i
xzdzd
R
i
TLzdT
x
ψ
−
+++
+
+
⎡⎤
⎡⎤
⎡⎤
⎡⎤
⎛⎞
−−
⎛⎞
∂
⎡⎤
⎢⎥
⎢⎥
⇒ =−−
⎢⎥⎜ ⎟⎢⎥
⎜⎟
⎢⎥
⎢⎥
∂∆ − ∆
+
⎢⎥
⎣⎦
⎢⎥⎢⎥
⎝⎠
⎝⎠
⎣⎦
⎣⎦
⎣⎦
⎢⎥
⎣⎦
(D2)
(D3)
()
()
()
()
()
1
j
j
mm
jj
i
R
i
L
TLRT
ψψ
+
⎡⎤
⎡⎤ ⎡⎤
∂
⎡⎤
∂
∂∂
=
⎢⎥
⎢⎥ ⎢⎥
⎢⎥
∂∆ ∂ ∂ ∂∆
⎢⎥ ⎢⎥
⎢⎥
⎣⎦
⎣⎦ ⎣⎦
⎣⎦
(D1)
The same to x
i
= (1 - 16(z
i
- d)/L
j
)
1/4
The stable case:
Annex D
To F = T (temperature) equation 13, and ∆T = T
i + 1
− T
i
result:
The unstable case:
The stable case:
ψ
m
=
ψ
h
=
ψ
v
and
()
()
()
()
()
1
1
22
1
5
ii
i
j
m
jj
i
zdzd
zd
R
i
TT
LR
ψ
+
+
+
⎡⎤
−−
⎡⎤
⎡⎤
−
∂
⎡⎤
⎢⎥
⇒ =⋅− ⋅
⎢⎥
⎢⎥
⎢⎥
∂∆ ∆
⎢⎥
⎣⎦
⎢⎥
⎢⎥
⎣⎦
⎣⎦
⎣⎦
(D4)
116
P. I. Figuerola and P. B. Berliner
Acknowledgements
P. Figuerola received during her visit at the Jacob Blaustein Institute of the Ben Gurion University
of the Negev a fellowship from the FOMEC (University of Buenos Aires, Argentina) and from the
CONICET (National Council for Science and Technology, Argentina). This study was as well
partly supported by GLOWA-JR.
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