USDA T-STAR
Measuring the Energy Balance of a Sugar Cane
(Sacharum officinarum) Plot in Southwest Puerto Rico
Victor Hugo Ramirez Builes1 and Eric W. Harmen2
1Agronomy and Soils Dept., 2Agricultural and Biosystems Engineering Dept., University of Puerto Rico – Mayaguez Campus
Introduction
The
vertical
measurements
of
temperature (temp) and relative
humidity (RH) were carried out at six
levels above the ground within the crop
at 0.1 m, 0.5 m, 1.0 m and 1.5 m and
above the crop at 2.0 m and 2.5 m.
Every fifteen minutes the temp/RH
sensor measurements were taken
during a one minute period at each
vertical position.
During the one
minute interval the data logger saved
six readings. Additionally, net radiation,
wind speed, wind direction, soil heat
flux, soil moisture, and soil temperature
were saved to the CR10X data logger
850
1000
1150
1300
1450
1600
1750
-0.50
-0.75
-1.00
Time
1.20
600.00
1.00
0.80
400.00
0.60
300.00
0.40
200.00
Temperature at different heights. Only a slight variation was observed
in the vertical temperature distribution (Figure 1). This result was
expected since vertical temperature gradients tend to be small under
irrigated conditions. This is due to the fact that most of the solar
radiation is dissipated by the evaporation of water and not by sensible
heat transfer. Harmsen et al. (2004) observed similar results for grass
between 10 cm and 200 cm heights in a study conducted at Rio Piedras
Puerto Rico. Although a temperature gradient for the day (based on
average daily temperature values) existed (figure 2), the overall range
Canopy
in temperature was less than 1 degree centigrade.
height
28.25
28.20
28.15
28.10
28.05
28.00
27.95
27.90
27.85
27.80
27.75
27.70
1645
1615
1545
1515
1445
1415
1345
1315
1245
1215
1145
1115
1045
945
915
0.00
845
0.00
815
0.20
745
100.00
ET (mmh-1)
(8)
700.00
500.00
Results and Discussion
Time
Rn
ET-BR
Figure 7. Relation between net radiation and ET by Bowen-ratio
methodology in sugar cane crop (S. officinarum)
The Energy Balance. Figure 8 shows the components of the energy
balance on February 1, 2005 in the sugar cane crop. Generally, net
radiation was the largest component followed by the latent heat flux. In
those cases where the LE was greater than Rn, this may represent
measurement error since evapotranspiration would not be expected to
exceed the net radiation component.
800.00
600.00
400.00
200
250
300
Heigth (cm)
200.00
1745
1715
1645
1615
1545
1515
1445
1415
1345
1315
1245
1215
1145
1115
1045
745
0.00
945
150
915
100
845
50
815
0
-200.00
Time
Figure 1. Air temperature variation at six heights Figure 2. Average temperature variation
with height
-400.00
Rn
Relative Humidity at different heights. Differences were observed in
the relative humidity at each height (figure 4). Figure 5 shows the
vertical distribution of RH based on daily average values. It is clear from
Figure 5 that the vertical RH gradient was not linear.
LE
G
H
Figure 8. Energy balance to cane crop (S. officinarum)
Conclusions
-0.0327
y = 53.937x
R2 = 0.9155
51.00
100.00
50.00
90.00
80.00
49.00
R.H (%)
R.H(%)
70.00
60.00
50.00
40.00
48.00
47.00
46.00
30.00
20.00
45.00
10.00
44.00
1745
1715
1645
1615
1545
1515
1445
1415
1345
1315
1245
1215
1145
1115
1045
1015
945
915
845
815
745
0.00
Energy balance and Evapotranspiration.
0
50
100
150
200
250
Figure 3. Measured RH in cane crop
50
100
150
200
250
300
Heigth (Cm)
Data were presented from an energy balance study conducted in a sugar
cane crop at Lajas, PR on February 1, 2005. The temperature gradient
in the cane crop was small, whereas the relative humidity gradient was
relatively large, which is expected under irrigated conditions. The trends
in vertical distribution of temperature and relative humidity with height
were nonlinear.
However, assuming linearity in the vertical relative
humidity distribution would be sufficiently accurate and would allow
collecting data within and above the crop at only two vertical positions.
Currently an automated device is being developed to obtained
measurements in this manner.
Figure 5. Comport of RH with height
References
The energy balance equations can be expressed as:
(1)
Rn is net radiation, LE is laten-heat flux, H is sensible-heat flux,
and G is soil-heat flux. The units of each term in equation 1 are
Wm-2.
The net radiation (Rn), is defined as the sum of all incoming
shortwave solar radiation and incoming long wave sky radiation
minus the sum of reflected solar radiation and emitted long wave
radiation (Tomilson, 1994). In this studied net radiation was
measured at 2 meter above the ground surface.
The temperature and relative humidity gradient. Early in the day
temperature differences between 2 m and 0.1 m above the ground were
positive, but later became negative except for a short period in the
afternoon. The temperature differences varied between -0.648ºC and
0.942ºC (figure 4). Relative humidity differences between the two
heights varied between 0.895% to -12.618% (figure 5). This result
indicates that the relative humidity during the day was higher within crop
canopy, partly because the crop was being irrigated on the day of the
experiment.
0.800
( Rn  G)
LE 
(1   )
0.648
0.600
0.400
0.200
0.000
-0.200
700
850 1000 1150 1300 1450 1600 1750 1900
-0.400
-0.600
-0.800
-0.942
-1.000
R.H(%)
Temperature ºC
The latent-heat flux (LE) is the product of the evapotranspiration
and the latent-heat of evaporation (λ), which is defined as the
amount of energy required to convert 1 gram of liquid water to
vapor at constant temperature and pressure:
(3)
2
0.895
0
-2700 850 1000 1150 1300 1450 1600 1750 1900
-4
-6
-8
-10
-12
-12.618
-14
Time
-1.200
Time
Where ß is the Bowen ratio.
The soil-heat flux (G) is defined as the amount of energy moving
through the soil at the ground surface, caused by a temperature
gradient (Tomilson, 1994). this was measured using two soil heat
flux plates at 8 cm, and soil moisture and temperature sensors
(Campbell Scientific, Inc. 1998).
 FX 1  FX 2 
G
S
2


-0.25
Rn (Wm -2)
 LE 
ET  
(86.4)
  
10
(4)
0.00
Figure 6. Bowen-ratio (ß) ton the cane crop (S. officinarum)
The ET by the Bowen-ratio method was calculated employing the latentheat flux in watts per square meter, and converting to the rate of water
loss in millimeter per day (Tomilson, 1996):
Time
Rn= LE+H+G
0.25
The sensible-heat flux (H) is the product of the Bowen-ratio and latentheat flux:
H  LE
(7)
Materials and Methods
The study was conducted at the UPR Agricultural Experimental
Station at Lajas, located in the southwest of Puerto Rico. The cane
crop, planted in June 2004, had attained a height of 1.5 meter on
the day of the experiment (Feb. 1, 2005). The cane was watered
using drip irrigation.
0.50
Bowen (H/LE)
where γ is the psychometric constant; ∆T is the difference in air
temperature at the two heights (◦C); and ∆e is the difference in vapor
pressure at two heights (kPa).
0.75
Wm
a) To measure the vertical temperature and relative humidity
distribution inside and outside the sugar cane crop.
b). Calculate the energy balance components and the
evapotranspiration by the Bowen-ratio method.
(6)
1.00
-2
Objectives
T
 
e
Temperature (C)
Performing an energy balance of a crop canopy is a way to
determine how much of the net radiation (Rn) is converted to
sensible heat (H), evapotranspiration (ET) or latent heat (λE), soil
heat flux (G), and other processes like photosynthesis and
Respiration. Net radiation is the primary climatic factor controlling
the ET, when the water is not limited, especially in subhumid and
humid climates.
An energy balance study was conducted in a sugar cane
(Sacharum officinarum) plot on February 1, 2005, at the University
of Puerto Rico Experiment Station at Lajas, PR. The sugar cane
was planted in July of 2004 and had attained a height of 1.5 m.
The following climate parameters were measured: air temperature,
air relative humidity (RH), wind speed, wind direction, net radiation,
soil moisture, soil heat flux and soil temperature. Additionally, RH
and temperature were measured at 0.1 m, 0.5 m, 1.0 m, 1.5 m, 2.0
m and 2.5 m above the ground every 15-minutes using a single
RH/temperature sensor.
The results indicate that there was only a small vertical
temperature gradient and consequently the sensible heat transfer
(H) was negligible.
In the case of RH, a significant vertical
gradient existed between 0.1 m and 2 m. Although the vertical RH
gradient was found to vary nonlinearly, an assumption of linearity
could be made with little error. This finding is important because
we have begun development of an automated device for obtaining
the RH at two vertical positions above the ground every 2 minutes.
This poster also presents the estimates of variation of Rn, ET and
G throughout the day.
The Bowen-ratio (ß) was estimated employing the temperature and
humid at two levels (10 cm and 2.0 m) every 15 minutes, and using the
equation (Merva, 1974):
 Ts 
S
d b C s  WC w 

 t 
(5)
S is soil heat storage (Wm-2), ∆T is the time interval between
measurement (sec), in this study measured were made each 15
minutes (900 sec), d is depth to the soil-heat-flux plates (0.08 m), ρb
is bulk density of dry soil (1300 kgm-3), Cs is specific heat of dry soil
(840 J/Kg◦C), W is water content of the soil (kg the water/ Kg the
soil), Cw is specific heat of water (4,190 J/Kg◦C),
and FX1 and FX2 are soil heat flux measurements (Wm-2).
Figures 4 Air temperature differences
between 0.1 and 2 m (T2 - T0.1).
Figure 5 Relative humidity
differences between 0.1 and 2
m. (T2 - T0.1).
The Bowen-Ratio. Values of the Bowen-ratio (ß) during the morning
were negative and positive during the afternoon, except for a short
period (figure 6). Negative values of the Bowen-ratio has the effect of
increasing the latent heat flux (or evapotranspiration) (see equation 3).
Positive values of the Bowen-ratio, on the other hand, have the effect of
decreasing the latent heat flux. Figure 9 shows the evapotranspiration
estimated from equations 3, 5 and 8, along with net radiation. Note the
strong correlation between net radiation and evapotranspiration (r2 =
0.84)
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Acknowledgments
This material is based on research with financial support
from NOAA-CREST, NASA-EPSCoR (NCC5-595), NASA-URC,
UPRM-TCESS and USDA TSTAR100.