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Determination of Grass Evapotranspiration Rates and Crop Coefficients Using Eddy Covariance Method in Eastern North Dakota


Abstract and Figures

Accurate evapotranspiration (ET) estimation is essential to crop water management and irrigation scheduling. As a major agricultural area, North Dakota lacks studies on crop ET measurement for major crops. In this study, an eddy covariance system (EC) and two sets of soil moisture sensors were installed to measure cool season grass ET and estimate the crop coefficient (Kc) in eastern North Dakota from January 2011 to December 2013. The residual energy balance and Bowen ratio method were used to calculate the latent heat flux (LE) and ET values. Priestly-Taylor method also was used to estimate the missing values. Daily and monthly variability in fluxes and ET were quantitatively analyzed. For the study period, the soil moisture content for grass root zone has been continuously monitored and the relation between flux data, weather data, and soil moisture content were illustrated. The results showed that the growing season ET during 2011–2013 ranged from 560 mm to 773 mm from April to October, with the highest ET in July. The annual difference in ET was related to differences in weather and soil moisture conditions. The Kc for grass was developed as a ratio of actual ET measured by the EC, and the reference ET using ASCE-EWRI ET reference method. Seasonally, the highest ET and Kc were observed in July and April, respectively. The average Kc values for 2011, 2012 and 2013 were 0.97, 0.65 and 0.85, respectively. Therefore, 0.8 is recommended Kc value based on cool season grass as a reference crop for the study area during the growing season.
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Determination of Grass Evapotranspiration Rates and Crop Coefficients Using Eddy
Covariance Method in Eastern North Dakota
Ali Rashid Niaghi1 and Xinhua Jia2
1Dept. of Agricultural and Biosystems Engineering, North Dakota State Univ., 208 Morrill
Hall, P.O. BOX 58108-6050, Fargo, ND. E-mail:
2Dept. of Agricultural and Biosystems Engineering, North Dakota State Univ., 205 Morrill
Hall, P.O. BOX 58108-6050, Fargo, ND. E-mail:
Accurate evapotranspiration (ET) estimation is essential to crop water management and
irrigation scheduling. As a major agricultural area, North Dakota lacks studies on crop ET
measurement for major crops. In this study, an eddy covariance system (EC) and two sets of soil
moisture sensors were installed to measure cool season grass ET and estimate the crop
coefficient (Kc) in eastern North Dakota from January 2011 to December 2013. The residual
energy balance and Bowen ratio method were used to calculate the latent heat flux (LE) and ET
values. Priestly-Taylor method also was used to estimate the missing values. Daily and monthly
variability in fluxes and ET were quantitatively analyzed. For the study period, the soil moisture
content for grass root zone has been continuously monitored and the relation between flux data,
weather data, and soil moisture content were illustrated. The results showed that the growing
season ET during 2011–2013 ranged from 560 mm to 773 mm from April to October, with the
highest ET in July. The annual difference in ET was related to differences in weather and soil
moisture conditions. The Kc for grass was developed as a ratio of actual ET measured by the
EC, and the reference ET using ASCE-EWRI ET reference method. Seasonally, the highest ET
and Kc were observed in July and April, respectively. The average Kc values for 2011, 2012 and
2013 were 0.97, 0.65 and 0.85, respectively. Therefore, 0.8 is recommended Kc value based on
cool season grass as a reference crop for the study area during the growing season.
Evapotranspiration (ET) is the main component of terrestrial energy and water balance
(Bastiaanssen 2000, Thoreson et al. 2009), and transfers a huge amount of water and energy in
the form of latent heat from bare soil (evaporation) and vegetation (transpiration) into the
atmosphere (Anderson et al. 2012). For efficient water resources management, having an
information about ET values is essential. Imprecise estimation of ET can lead to inefficient use
of water, increase the potential for surface and ground water pollution, and reduce crop yield for
the grower.
There are several methods to directly measure the daily actual ET of crops. The Eddy
Covariance (EC) (Tanner and Greene 1989), lysimeters (Allen and Fisher 1990; Howell et al,
1995) and Bowen Ratio (Payero et al. 2003; Irmak et al. 2014) methods are widely used to
measure the actual ET. The EC method is one of the recent techniques that has several distinct
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advantages (Baldocchi et al. 2001) but takes considerably more effort to maintain, process, and
quality assures results for long-term measurements ( Papale et al. 2006). Considerable research
efforts were done to develop accurate procedures to estimate actual ET from weather data (Allen
et al. 1998). However, EC systems are becoming widely used in ET measurement due to easy
setup, lower cost of sensors, and the ability to co-measure latent heat flux (λE), sensible heat flux
(H) and CO2 fluxes, depending on the equipment configuration. This technique has been widely
accepted as the most accurate method to estimate flux values, and has been used successfully to
directly measure actual ET around the world (Li et al. 2008; Castellvi 2008; Zhou et al. 2014),
the United States (Sumner 2001; Jia et al. 2007, 2009; Castellvi and Snyder 2010), and North
Dakota (Rijal et al. 2012).
The EC concept is based on the statistical covariance (correlation) between vertical fluxes
of vapor or sensible heat within upward or downward legs of turbulent eddies (Allen et al. 2011).
This needs a high-speed measurement of temperature, wind speed, and vapor pressure. Tanner
(1988) and Tanner et al. (1993) described the preliminary usage of EC system. Since then, many
developments in instrumentation have been made and now EC method is widely used
(Baldocchi, 2003, Allen et al. 2011). EC method provides more spatial coalition and less site
disconnection and allowing comparative temporal resolution in comparison with lysimeter
(Sumner 2001). However, the number of studies on ET using the EC system are few in ND
To quantify crop ET, grass reference ET adjusted with crop coefficient (Kc) is becoming
a more useful method to obtain crop ET in different crop development stages and various climate
conditions (Niaghi et al. 2013; Irmak and Irmak, 2008). Kc can reflect the coupled effect of
environment on crop factors, such as leaf area, plant height, the rate of crop development, soil
and weather conditions (Irmak, 2008). Therefore, grass Kc is one of the sources to obtain the
actual crop water requirement based on reference ET. The most dominant reference ET method
for ND was the Jensen-Haise (JH) method to obtain Kc value for different crops based on its
simplicity. Because of high wind speeds in ND, using the JH method gave inaccurate results as it
ignores the wind function. Also, Kc values in windy periods estimated from the JH method were
different from that of standard alfalfa reference ET method, which is widely accepted as a
standard method to calculate the grass or alfalfa reference ET.
Since there is no new grass Kc values developed in 40 years in ND, in this study we used
the actual measured ET with EC system to develop grass Kc for the growing season based on
alfalfa- reference ET method. The overall object of this study was to improve our knowledge on
grass water requirements specifically by: (1) estimating the actual ET from the EC system, (2)
evaluating the ET values for each year using soil moisture data, and (3) developing the grass
crop coefficients during the 2011-2014 study period.
Study Area and Climate Dataset
The experiment was conducted at the North Dakota Agricultural Weather Network (NDAWN)
research center in Cass county (46° 53' 49.2'' N and 96° 48' 43.2'' W), located near North Dakota
State University. Field data were collected in 2011-2014 on a grass site, while data in 2011-2013
growing season was used in this paper. The site is located at a sub-humid temperature climate
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zone with a mean temperature 15oC, average precipitation of 500 mm, average wind speed of 3.5
m/s during the growing season (NDAWN, 2017). Average groundwater table was very shallow,
and during the early season, it was near the surface. According to the lab tests, the soil had a
heavy clay loam texture, with a mean bulk density of 1.43 g/cm3, mean volumetric water content
at field capacity of 0.41 cm3/cm3 and mean volumetric water content at the wilting point of 0.27
cm3/cm3 at the 0-30 cm layers. The study site was covered by cool season grass and mowed
frequently to keep the grass to below 12 cm tall for research.
Field Measurements
In 2011, the EC system (Campbell Scientific, Inc., Logan, Utah) was installed to measure
the actual ET on the grass site. The EC system was mounted on a tripod above the ground and
has been in operation since January 2011 until December 2014. Instrumentation used in this
study and the variables measured are listed in Table 2.
The energy balance and primary meteorological variables were measured using the EC
system during the study period. Data from the sensors were stored using a CR3000 data logger
(Campbell Scientific, Inc., Logan, Utah). The data sampling frequency was 10 Hz (10 times a
second) following the general approach of Beringer et al. (2007) for wind speed, temperature
and humidity, and ET calculated from latent heat flux (Campbell and Norman, 1998). All data
was stored as 30-min averages.
The EC system is independent of the soil surface condition comparing to point
measurements by a lysimeter. It has a fetch distance approximately 100 times of the sensor
height above the crop canopy. The height of the instrument above the crop defined the fetch
distance for the instrument. In the study area, the EC was installed at 1.5 m above the soil
surface, facing the prevailing wind from the northwest direction (Campbell and Norman 1998).
The south and west side of the weather station were agricultural fields, while there are several
scattered buildings located 100 m north of the EC system, and a large building is located at 120
m east of the EC system.
Soil moisture, temperature, and salinity measurements were measured near the EC
system using the Hydra Probe II sensors (Stevens Water Monitoring Systems Inc., Portland, OR)
at seven depths (5, 15, 30, 45, 60, 75, 90 cm). Also, the rainfall was measured using an
automated tipping bucket and a manual rain gage. Due to shallow root depth of cool season
grass, near soil surface sensors (5, 15 and 30 cm) were chosen for studying the soil water status,
and average soil moisture content was used.
Table 1. Instrument of Complete Eddy Covariance Weather Station at NDAWN grass site, North
Dakota in 2011-2013.
CSI CSAT3 3D Sonic Anemometer
Turbulent fluctuations of horizontal and vertical wind
CSI KH20 Krypton Hygrometer
Rapid fluctuations in atmospheric water vapor
Texas Elec. TE525WS Tipping Bucket
REBS Q7.1 Net Radiometer
Net radiation
Vaisala HMP45C Temp/RH Sensor
Air temperature and relative humidity
HFP01SC Soil Heat Flux Plates (2)
Heat flux
TCAV Averaging Soil Thermocouple Probes (2)
Soil temperature
CS616 Water Content Reflectometer (2)
Volumetric water content
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Energy Balance and Evapotranspiration Calculation
The EC system was used to measure cool season grass ET at the NDAWN site. This
system considered different components of energy balance and making use of the complex
mathematical process to obtain data. A CSAT3 sonic anemometer was used to estimate H
through the use of 3D sonic anemometer measurements along with virtual air temperature.
Therefore, the H values were measured by EC system from the covariance between the vertical
wind speeds and air temperature. Also, KH20 hygrometer measured vapor density and when
used in conjunction with the CSAT3 sonic anemometer, it was used to estimate latent heat flux
(LE) (Sumner 2001). The data recorded at 10 Hz frequency was averaged in every half hour (Jia
et al. 2009; Rijal et al. 2012). As following (Jia et al. 2007, 2009; Rijal et al. 2012), the H and LE
were calculated:
   (1)
where H is sensible hit flux, ρ is the density of air; Cp is the specific heat, and T' is the
fluctuation of air temperature.
  
where ' is the fluctuation of water vapor density, w' is the fluctuation of vertical wind
speed, and λ is the latent heat of vaporization. The overbar represents the average of the period
and primes indicate the deviation from the mean values during the averaging period.
In this paper, because of vapor on the KH20 hygrometer lens and its sensitivity to
moisture, early morning and evening time values were excluded from the calculation.
Furthermore, the daytime which has a positive net radiation value was used for ET estimation.
The LE predicted in every half hour was corrected for temperature-included fluctuations in air
density (Webb et al. 1980). To account for the difference between virtual and actual air
temperature, the sensible heat flux was also corrected. Furthermore, both sensible and latent heat
flux were corrected for the error attributable to the natural wind coordinate system (Baldocchi et
al. 1988), and the average vertical wind speed was forced to zero. The Bowen Ratio method was
used to close the energy balance for each 30-minute period (Twine et al. 2000). According to this
method, the EC system measures the Bowen ratio correctly and overcomes the underestimation
of the LE flux measured by the EC system (Sumner 2001; Twine et al. 2000).
The modified Priestley-Taylor method was used to fill the missing LE values (Priestley
and Taylor, 1972). This method required empirical coefficient () in the general equation in
which it is determined from the available LE, H, Rn, G and temperature data by using Eq. (3).
The calculated monthly values during the growing season were used to estimate the missing 30-
min LE in that month instead of a constant value (1.26) by Priestly and Taylor (1972).
  
 (3)
where is PT constant, LE is latent heat flux in W/m2, Rn is solar radiation in W/m2, G is
soil heat flux in W/m2, is slope of the saturation vapor pressure curve in Pa/°C and is
psychometrics constant in Pa/°C.
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Due to problems in sensors in 2011, H value was missing whole study period. The
missing H was directly calculated using eq. (1) with no other adjustments.
The vertical energy balance at the soil or water surface or at the effective surface of a
crop is the sum of H to or from the air and soil (or water), LE, Rn and other miscellaneous fluxes
(Allen et al, 2016). Therefore, Rn and soil heat flux (G) were also measured to help add closure
to the energy balance through the use of the following relation:
LE = RnG H (4)
G was estimated with the use of soil heat flux plates and thermocouples. The soil heat
flux plates were located at 0.08 m depth (Allen et al. 2016) to make sure that the sensor is
located below the zone of soil water vaporization. Because of the strong thermal gradients near
the soil surface during the late morning and early evening, two temperature depths at 0.02 and
0.06 m were installed to correct the measurement and decrease impacts of spatial variation. The
measurement by the plate was corrected to the ground surface by measuring soil temperature at
two depths in the soil layer above the plate and averaged to decrease impacts of spatial variation
as follow:
G = G plate + Cs (ΔT/Δt)Z plate (5)
where G plate (MJ m-2 d-1) is the measurement by the soil heat flux plate at depth Z plate (m)
beneath the soil surface, ΔT (°C) is average soil temperature over the time, Δt (d). Generally, Cs
is the heat capacity in J/oC and is calculated using the soil water content to account for the effect
of variation in water content over time by using Eq. 6:
      (6)
where is bulk density, which was measured as 1.43 g/cm3 for the soil in study site,
is heat capacity of dry mineral soil (840 J/Kg°C), is soil moisture content in cm3/cm3, is
density the of water (1000 Kg/m3), and is heat capacity of water (4,910 J/Kg°C).
In 2011 and some days in other years during the study period, because soil heat flux
sensors malfunctioned, the total soil heat flux was estimated by using the Allen et al. (2016)
recommendation for grass:
G= 0.1 Rn (7)
Development of Crop Coefficients
The crop coefficient for cool season grass was estimated as the ratio of actual ET values
calculated from the energy balance measured by EC system and daily ETo values calculated from
the standardized ASCE-PM reference ET method for grass by using the data from NDAWN
weather station (Allen et al., 2005). The daily value of Kc is calculated and an average of half-
monthly value was used to show the variation of Kc during the study period.
To calculate the Kc, the days with less than twelve measured (with 30-min average)
points were neglected. Also, due to the heavy rainfall on some days of the study period, the
measured ETc was not in a range, and this is related to the eddy covariance system weakness
during the rainfall occurrence. Therefore, the average calculated Kc and reference grass
evapotranspiration are used to estimate the missing ETc.
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Average air and soil temperature, wind speed, incoming solar radiation and precipitation amount
obtained from the NDAWN station are listed monthly for each year in Table 1.
Table 1. Average daily or monthly weather conditions (average air temperature = Tavg, soil
temperature = Tsoil, wind speed = Uavg, and incoming solar radiation = Rs) for each month during
the growing season (2011-2013) at NDAWN site.
The highest monthly precipitation totals typically occurred in May and June. For the
study period, May and June 2013 had the highest precipitation, 141 and 200 mm, respectively. In
all study years, 2013 had a relatively wet spring in contrast with 2012, which was a dry year.
During 2011 and 2013, there were several large precipitation events, while the highest
accumulated precipitation amount was 47 mm and 177 mm on June 1, 2011, and June 5, 2013,
respectively. The annual precipitation rate changed among the years, 457 mm in 2011, 243 mm
in 2012 and 640 mm in 2013. The average rainfall amount based on the NDAWN record is about
450 mm which indicates that 2012 received less than half and 2013 received more than half of
the average rainfall, respectively.
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The highest daily incoming solar radiation was observed in June and July in which the
highest precipitation occurred. Also, the highest air and soil temperature occurred in July and
August during the growing season. The highest wind speed values were from April to May.
Figure 1. Soil water content and rainfall events during the growing season for the study area.
The average soil water content for three years of study in the top 30 cm root zone was
shown in Figure 1. As shown in Figure 1, for the study period, except 2012, the normal
interaction was observed between rainfall, growing season and soil water content. However,
2011 was a drought year according to the weather data, and the field was under severe water
stress. This also affected the energy balance parameters.
Figure 1 shows the timing and magnitude of daily rainfall events during the three years of
the experiment. Rainfall events during the 2011 growing season were more frequent and had
sometimes larger magnitude during the high demand period of growing season. However, during
2012, the maximum amount of rainfall occurred in a day was 25.4 mm in late May. During the
2013 growing season, regarding the weather station data shown in figure 1, the magnitude of the
rainfall events in some days was around two times of 2011. However, as mentioned, the
frequency of rainfall was not as many as 2011 and most of the precipitation occurred in late May
and June. During the high water demand period of the crop between July and September, a very
tiny magnitude of rainfall was observed and this caused reduced soil water content close to
permanent wilting (PWP). In comparison with all study years, 2011 had a good soil moisture
content in the most stage of the growing season, and the rainfall events were more frequent than
others. The total available water for the crop was in the acceptable range and no stress occurred
in term of water scarcity to the crop. In 2012, the soil water content curve shows that from July
to the end of the growing season, soil moisture was under the permanent wilting point, meaning
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that there was not any water in the soil for uptake by plant roots. The study area has a heavy clay
soil. During the dry period, the soil had a very high rate of expansion. Because of cracking at the
soil surface, especially the top layer of the soil, the sensors were forced to have a connection
with air, and this caused to measure the wrong value of soil moisture content during the dry
period. Although there was not enough water to overcome the plant requirement, the total
available water from the deeper soil layer was enough to provide water to the plant and prevent it
from death. In 2013, during the high demand of water from July to August, there was not
sufficient rainfall, so the soil water content was reduced. However, like 2012, because of the soil
cracking, the sensors malfunctioned and did not read soil moisture correctly. This was also fixed
after soil received some rainfall events.
Energy Fluxes
After applying the corrections, daily daytime latent heat flux and sensible heat flux values
were obtained for the three years of the study period for cool season grass in the NDAWN site
(Fig. 3). Figure 2 shows the daily average daytime energy Rn, LE, H and G for the study period.
Figure 2. Energy balance flux for the growing season of cool grass for study period
All energy balance parameters showed high day to day variability, mainly due to changes
in weather variation, and available soil water content. The daily Rn energy reaching the canopy
represented between 15 and 537 W/m2, with an average 254 W/m2, H was ranging between -36
and 305 W/m2, and G represented the smallest energy component, ranging between -22 and 60
W/m2. The LE values showed similar cycle to Rn, higher in summer and lower in the winter. This
pattern showed the relationship of evapotranspiration with net available energy. This cycle was
also presented in Jia et al. (2009). However, LE values were low at the beginning of the growing
season, in which most of the received energy was converted to sensible heat flux instead of latent
heat flux or ET.
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The lowest value for H was observed in 2013, which had a high amount of rainfall and
sufficient available water for evaporation and transpiration. On the other hand, the largest H
value observed in 2012 due to the less rainfall and high wind, which convert most part of the
received energy to sensible heat flux. High H values in 2012 indicating that there is greater heat
energy transfer and the large temperature difference between the surface and the air exists. H was
mostly positive during the growing season of cool grass, however, it was sometimes negative.
According to figure 2, the amount of H sometimes exceeded LE, and this mostly occurred during
a dry and windy day. Exceeding the H from LE was also shown in Nebraska, in a study by
Payero and Irmak (2013). This trend, however, changed reversely after rainfall events. In 2012,
the amount of rainfall was around half of the other years, causing a dry year. Because of water
restriction in 2012, most of the energy occurred in the term of H, and there was not enough water
either in soil or surface to convert energy for evaporation and increase the LE value. During the
time when H was negative, LE was close to exceeding Rn, which represents the presence of the
advection phenomenon that moved from surrounding areas by horizontal movement of wind.
This is also supported by Payero and Irmak (2013) for Nebraska. Although heavy rainfall
occurred on some days, high transpiration and the evaporation rate were the main reason for the
LE excess. LE became so close to Rn some days as shown in 2013 which had several heavy
rainfalls and was known as a wet year.
Highest LE and lowest LE was shown in 2013 and 2012, respectively. Overall, the LE
values were greater than the H values during the active growing season from the late-April to
October, illustrating a large fraction of available energy was used for evapotranspiration. During
the same period, ET ranged from 0.02 to 7.92 mm/d with an average of 3.34 mm/d. The highest
ET occurred in July during the study period.
On a monthly basis, the highest ET was observed between May and June. However,
during 2013, the highest ET occurred during April-May, and the Lowest ET was observed at the
end of the growing season in October. However, there was accumulative ET difference between
the study years. The main reason for this difference were weather conditions. As shown in figure
2, the energy balance trend illustrated 2012 as a dry year. The difference between Rn and LE
were high in comparison with other years, this proved that there wasn’t enough energy to convert
to the ET. Also, the H was high in 2012 because of dry soil and high amount of sensible heat.
Advection phenomenon during the dry year can also cause the high H during the growing season.
On the other hand, for 2013 as a wet year, most parts of the Rn were converted to LE and thus,
increased the ET. During 2013, several heavy rainfalls occurred and most of the time, the field
had a good soil moisture condition for high evaporation and transpiration and increased the rate
of ET.
Table 2 summarized the average monthly daytime energy balance fluxes and calculated
ET values. The Rn values were highest in July and lowest in October, thus, LE values were the
highest in July and the lowest in October. The crops in 2011 and 2012 had the highest and lowest
cumulative ET during the growing season, respectively. Distribution of rainfall magnitude in
2011 during the crop high water requirement from May to August was similar in each month.
Due to the same distribution of rainfall during 2011 in each month, the ET rate was higher,
which helped the crop to receive sufficient water for active growth. The average rate of H was
especially close to each other and most net radiation was converted to LE or ET. Also, the soil
heat flux showed that the rate of stored energy in the soil during the growing season was nearly
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In 2013, despite heavy rainfall during the growing season, ET rate was lower than 2011.
This was caused by the difference in rainfall distribution among the months. According to table
2, the lowest precipitation occurred in July and August and there was not sufficient water to
increase the rate of ET. Beyond the difference in climate condition during the three years of
study, the highest cumulative monthly ET was measured in July. The daily trend of actual ET for
three years of study from January to December by the EC measurements is shown in figure 3.
The daily ET graph showed that the highest ET range was in 2011, while the lowest ET was in
2012. In 2013, there was an average ET trend in which located between 2011 and 2013.
Table 2. Daily average fluxes (net radiation, Rn; soil heat flux, G; sensible heat flux, H; and
latent heat flux, LE) and total evapotranspiration (ET) and rainfall amount for each month during
the 2011-2013 growing season at the experimental site.
No. of
Figure 3. Daily actual evapotranspiration rates (ETc) for 2011, 2012 and 2013 growing seasons.
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Crop Coefficient
Daily crop coefficient for cool season grass is calculated as the ratio of actual ET and
reference ET (Allen et al. 1998). The ASCE-EWRI (2005) reference ET method is used to derive
the amount of reference evapotranspiration for each day. To obtain an acceptable result, the days
with minimum twelve data point of 30-min measured data are selected. among the study period,
Table 3 summarizes the monthly cumulative precipitation (obtained from NDAWN site), actual
monthly ET measured by Eddy Covariance, average ETc for a month, and Kc values by month.
Also, the average of fifteen days’ Kc for cool season grass is derived from all measured data are
plotted in figure 4. For comparison, the average Kc curve of three years is plotted in the same
figure (Fig. 4).
The highest Kc estimated for 2011. The trend continued to reduce by end of the growing
season and cold weather condition. This pattern coupled with the regional climate conditions
which had high rainfall events and wind speed during April and May, and the highest solar
radiation in June and July. The calculated Kc values are characterized by a rapid increase when
the wetting event occurred. While rainfall occurred or irrigation was applied, wetting events tend
to increase the potential ET. On the other hand, rainfall events tend to decrease the transpiration
component (Payero and Irmak 2013). Therefore, both are influenced the calculated Kc values.
The impact of crop stress on Kc can be seen in 2012 data. In 2012, the calculated Kc values in the
growing season were much lower than the recommended value as 0.8 by NDAWN which is
indicative of crop stress. The available water was not able to keep up with the water demand of
the crop. Also, due to insufficient available water for crop during the growing season and severe
soil moisture condition as shown in figure 1, the calculated Kc values were lower than average.
In 2011, frequent rainfall events occurred for each month which increased the measured ET, and
thus, calculated Kc values. This is noticeable during the initial growing period due to the large
soil evaporation resulting from a wet soil surface. Because of the frequent rainfall events during
2011, the estimated Kc values were considerably larger than average Kc for the growing season.
In 2013, we had several rainfall events in which occurred 12 days, 9 days and 5 days of May,
June, and July, respectively. Due to the rainfall events, the potential ET decreased and therefore,
caused to decreased the Kc values regarding high available water to the crop. As soon as
increasing the potential for evapotranspiration in late June by reducing the rainfall events, the
ETc increased and caused to increase the crop coefficient.
The results are in agreement with Li et al.’s (2008) finding, the period which has the
highest crop ET also has the highest total available energy to increase ET and then Kc values.
The average Kc values for 2011, 2012 and 2013 were 0.97, 0.65 and 0.85, respectively. The
variation in observed Kc for different years corresponded to different weather conditions and
rainfall amounts. Also, the frequency and timing of the rainfall are the effective parameters on
crop coefficients which are previously supported by Stewart et al. (1969). The recommended Kc
is shown in Table 4. The average recommended Kc for cool season grass based on ASCE-EWRI
grass reference evapotranspiration is 0.82.
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Figure 4. Average bi-monthly calculated crop coefficient based on a daily ratio of eddy
covariance measured evapotranspiration and grass reference evapotranspiration.
A three-year study was conducted in the eastern part of North Dakota to measure cool season
grass evapotranspiration rates using an eddy correlation system. Meteorological data necessary to
calculate reference ET were also measured at the same site. In this study, we measured the daily
actual ET and other energy balance components of cool season grass and studied the daily and
seasonal behavior of grass crop coefficient (Kc) and evaluate the impact of climate conditions
and weather variables like wind and rainfall on actual ET and Kc. While doing this, we found a
considerable difference in weather conditions among the three study years that affected crop ET
and Kc.
The daily measurements of energy fluxes, including Rn, G, H and LE were also
presented. The results showed that H is mostly positive during the growing season especially
during the early and late portion of the growing season. As a conclusion, 2011 as a normal year
showed an acceptable trend either in energy flux or Kc. Furthermore, the ratio and distribution of
energy flux illustrated the condition of each year clearly. Due to the high potential of either
weather condition or water availability, cumulative ETc for the year was higher than normal.
Also, the calculated Kc showed the higher value in comparison with recommended value for the
study area. 2011 as a normal year and 2012 as a dry year showed a highest and lowest LE and
ET, respectively. Although 2013 had more rainfall events and highest accumulative precipitation
among the study years, it showed the average ETc and Kc for the study period. We can conclude
that the wetting distribution had a huge effect on either energy balance exchange and crop water
requirement. In addition, we found considerable differences in Bowen ratio during the dry and
wet year and this can affect not only crop water usage but also crop coefficient and any water
management decision.
According to the obtained results, rainfall events distribution among the growing season
also plays an important role in either total and actual ET rate or Kc values. Besides, net radiation
as a source of energy for ET was another effective parameter on actual ET rate. In 2011,
although the total rainfall was less than 2013, the distribution of rainfall and high net radiation
caused to increase the ET and Kc.
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Table 3. Summarized monthly measured crop ET by eddy covariance, average monthly ETc, and
crop coefficient (Kc) for cool season grass during growing season 2011, 2012, and 2013.
We presented the calculated Kc for the three years of study. Each year had different
climate conditions and this can be obvious in calculated Kc. Therefore, we recommended using
0.82 as an average Kc based on grass reference ET with respect to the available soil moisture and
rainfall events for irrigation scheduling. Considering the soil surface conditions especially after
heavy rainfall and the long dry period is important to define any malfunction of either the soil
moisture sensors or eddy covariance data quality.
ETc by EC
Avg. ETc
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... Actual evapotranspiration (ET a ) can be estimated through direct ET a measurement using eddy covariance (EC) ( Niaghi et al., 2017;Tanner and Greene, 1989), lysimeters (Allen and Fisher, 1990;Howell et al., 1995;Niaghi et al., 2015), and the Bowen ratio (Irmak et al., 2014;Payero et al., 2003). Among these methods, the EC system has become widely used in ET a measurement due to its more precise and accurate sensors and its ability to quantify energy balance components separately. ...
... used overseas ( Li et al., 2008;Zhou et al., 2014) and in the United States (Castellví and Snyder, 2010;Jia et al., 2009;Sumner, 2001), including North Dakota ( Niaghi et al., 2017;Rijal et al., 2012). The concept of EC is to measure the statistical covariance (correlation) between the vertical vapor or sensible heat fluxes within upward or downward legs of turbulent eddies. ...
... The standardized reference evapotranspiration (ET o ) method by the American Society of Civil Engineers-Environmental and Water Resources Institute (ASCE-EWRI) (Allen et al., 2005) has been shown to provide an accurate estimation for grass as a reference crop. The ASCE-EWRI method has been widely accepted worldwide (Anapalli et al., 2018;Jia et al., 2013;Majnooni-Heris et al., 2013;Niaghi et al., 2017) but has not been tested in North Dakota. The ratio between the ET a and the ET o may provide insights to guide the water management of irrigated turfgrass in northern cool climates and during drought periods when measured ET a values are not available. ...
Full-text available
Turfgrass actual evapotranspiration (ET) measurements are critical for water management and irrigation scheduling. With no historical ET measurements in eastern North Dakota, turfgrass ET rates were measured with the residual method using eddy covariance instrumentation and two arrays of soil moisture sensors on unirrigated turfgrass under natural conditions in the 2011, 2012, and 2013 growing seasons. An on-site weather station provided weather data to calculate the standardized grass-based reference evapotranspiration (ET) (). The daily ET/ET ratios were screened using the criteria of soil moisture ≥50% of available water for the top 30 cm of the root zone, rain amounts ≤10 mm, and a recovering period after drought. The screened monthly average ET/ET ratios for the unirrigated turfgrass were 1.03, 0.98, 0.94, 0.90, 0.82, and 1.18 from May to October. The mean ET/ET ratio for the entire growing seasons was 0.96, implying that the American Society of Civil Engineering–Environmental and Water Resource Institute ET method was valid for guiding the turfgrass ET calculation even in unirrigated and cold climate conditions. Because this is the first reported study on ET measurement of a turfgrass site, the limited data can provide a baseline on water management for turfgrass under various weather conditions in this region. The results indicated that a monthly refinement of ET/ET values might be required to maintain the landscape turfgrass quality more precisely in terms of water management.
... In reality, the Earth's surface flux varies at different time scales. For the communities of hydrology, meteorology, and agriculture, the spatial and temporal continuous ET is more useful in practice [7]. Therefore, a fundamental problem in using remote sensing to estimate ET in local and regional scales is the extending of instantaneous latent heat flux to daily, monthly, or even yearly ET. ...
... It can be seen that assuming the EF selfpreservation is not a valid hypothesis, since EF depicts a concave-up shape with a straight decrease in early morning and a sharp increase in the late afternoon. Because an increase in EF mainly results from an increase in incoming solar radiation and a decrease in atmospheric humidity, Hoedjes parameterizes the diurnal shape of EF as a function of incoming solar radiation and atmospheric humidity (see Equation (15)) [7]. On the contrary, the SEBAL EF parameterization is the only function of vapor pressure deficit (see Equation (14)), and for this reason, the Hoedjes parameterization approximates the observed EF diurnal variation in a better way than SEBAL. ...
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Extending instantaneous latent heat flux to daily, monthly, or even yearly evapotranspiration (ET) is a fundamental issue in using remote sensing to estimate ET at local and regional scales. In this study, the extending parameterizations of the surface energy balance of a mid-latitude grassland with shallow water table (SWT) at diurnal and seasonal time scales are examined based on data measured by the eddy covariance system and automated weather station from Wageningen University from June 2014 to October 2018. The results show that the ratio of turbulent heat flux to available surface energy (often called budget closure rate) ranges between 0.86 and 0.93 for warm times (March to October), and between 0.59 and 0.77 for cold times (November to February the following year). The parameterization models used to approximate the surface albedo and evaporative fraction (EF) are also evaluated. Although obvious variation under clear skies during daytime are observed, the constant EF and albedo method provided an acceptable estimation of the daily scale ET with an underestimation of about 6–8% for the grassland with SWT and parameterization of diurnal correction shows little improvement in both the bias and RMSE. The progression of daily ET shows a seasonal cycle, which follows the variation of the net radiation flux. These results will be helpful for estimating ET at daily and long temporal scales based on satellite remote sensing.
... The results are shown in Table 1. Details about the EC system, associated meteorological measurements, soil water and water table depth monitoring, and data processing were previously described by Niaghi et al. [23,26]. The EC was installed in the middle of the field with fetch over 150 m in all directions. ...
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As an important component of the water budget, quantifying actual crop evapotranspiration (ET) will enable better planning, management, and allocation of the water resources. However, accurate ET measurement has always been a challenging task in agricultural water management. In the upper Midwest, where subsurface drainage is a common practice due to the shallow ground water depth and heavy clayey soil, ET measurement using traditional ground-based methods is more difficult. In this study, ET was measured using the eddy covariance (EC), Bowen ratio-energy balance (BREB), and soil water balance (SWB) methods during the 2018 corn growing season, and the results of the three methods were compared. To close the energy balance for the EC system, the residual method was used. For the SWB method, capillary rise was included in the ET estimation and was calculated using the measured soil water potential. The change of soil water content for ET estimation using the SWB method was calculated in four different ways, including daily average, 24:00–2:00 average, 24:00–4:00 average, and 4:00 measurement. Through the growing season, six observation periods (OPs) with no rainfall or minimal rainfall events were selected for comparisons among the three methods. The estimated latent heat flux (LE) by the EC system using the residual method showed a 29% overestimation compared to LE determined by the BREB system for the entire growing season. After excluding data taken in May and October, LE determined by the EC system was only 10% higher, indicating that the main difference between the two systems occurred during the early and late of the growing season. By considering all six OPs, a 6%–22% LE difference between the EC and the BREB systems was observed. Except during the early growing and late harvest seasons, both systems agreed well in LE estimation. The SWB method using the average soil water contents between 24:00 and 2:00 time period to calculate the daily capillary rise produced the best statistical fit when compared to the ET estimated by the BREB, with a root-mean-square error of 1.15. Therefore, measuring ET using the capillary rise from a shallow water table between 24:00 and 2:00 could improve the performance of the SWB methodology for ET measurement.
... Some of the most used methods are ground-based, such as soil water balance and lysimeter (Djaman and Irmak, 2013;Niaghi et al., 2015). Others are above ground methods, including eddy covariance ( Niaghi and Jia, 2017;Niaghi et al., 2019;Shi et al., 2008), surface renewal ( Rosa and Tanny, 2015), Bowen ratio energy balance ( Shi et al., 2008;Uddin et al., 2013), and remote sensing technology (Nagler et al., 2005;Niaghi, 2014). Since ET a is an important component of water balance and hydrologic studies, considerable research efforts have attempted to estimate the ET a from weather data (Allen et al., 1998). ...
Over the past 20 years, marketplace demand for corn has prompted many farmers in the Red River Valley (RRV) of the north to include more corn in their crop rotations. With a very flat topography and heavy clayey soils, the RRV can have shallow water tables in the spring and fall but can be dry in the summer. Due to these field conditions, some farmers have installed subsurface drainage (SD) systems with structures for controlled drainage (CD, manage the water table in a field) and subirrigation (SI, add water to the field via the SD system) to improve corn production. In a CD + SI field, an eddy covariance system was used to measure and quantify energy flux components along with soil moisture content (SWC) and water table depth (WTD) measurements during four corn growing seasons in 2012, 2013, 2016 and 2017. The results show that the average SWC in 2012 was significantly different from the other three years. The SWC and WTD in 2016 were more stable compared to the other years. The CD practice had a positive effect during a wet year in 2013, which resulted in 26.7% higher yield than the county average. During the dry growing season of 2017, the use of subirrigation resulted in 6.6% higher yield than the county average. The corn evapotranspiration totals (ETa) were 468, 476, 551, and 537 mm for 2012, 2013, 2016, and 2017 growing seasons, respectively. The average crop coefficients were 0.49, 0.73, 0.88, 0.86, and 0.69 for the initial, development, tasseling, reproductive, and maturity stages, respectively. They were calculated from the daily ETa, values only from days with more than 45% of total available water in the root zone, and the ASCE-EWRI standardized grass-based reference evapotranspiration. This study showed that the SD along with the CD + SI system can be used for optimal water management of field corn during both wet and dry years.
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Accurate evapotranspiration estimates are needed to determine the crop water requirements for the purpose of irrigation scheduling. Numerous methods have been developed for evapotranspiration estimation out ofwhich some techniques have been developed partly in response to availability of data. The Penman-Monteith equation standardized by the Food and Agriculture Organization (FAO56-PM) is accepted as a standard method to estimate ETo. Therefore, the other methods are evaluated by FAO56-PM method results. Nine methods in three groups, which are temperature based methods (Thornthwaite (TH), Hargreaves (HA) and Blaney-Criddle (BC)), solar based method (Priestley-Taylor (PT), Makkink (MA) , Rs (Ir- Rs) and Rn (Ir- Rn) based methods), and combined methods (Penman (PE) and Penman-FAO24 (PE24)), were used to evaluate with FAO56-PM method to choose the best method for using in research and projects. Performance analysis for the estimatedvalues using climatic data for 7 years (Jan 2003 – Dec 2009) and validation of methods using 2 years climatic data (Jan 2010-Dec 2011) were made. The root mean square error (RMSE) was calculated on a monthly basis. The estimated values by the mentioned methods were all correlated with FAO56-PM having RMSE values were 67.89, 49.45, 36.22, 61.35, 63.98, 58.28, 58.26, 5.48, 23.19 mm/month, respectively. The difference among the nine ETo methods before calibration showed a wide range of variation across the research period about 712 mm/yr. As a result of using the calibrated constant values in the equations, all nine methods are able to estimate monthly values perfectly. The RMSE of methods after validation were 37.16, 21.50,16.67, 27.82, 17.50, 17.70, 32.15, 2.62, 3.70 mm/month, respectively. Investigation shows the closer slope to 1 and intercept to 0 for PE method. However, the worst amounts of slope, intercept, R2 and RMSE before calibration were belong to MA, BC, IR-Rn and TH, respectively. The best output after calibration was belong to the BC method without considering the combined methods, and the TH method had worst results. Although these revised methods increase the accuracy of estimates, FAO56-PM method is preferred if it is applicable due to the complexity of its input parameters. KEYWORDS: Reference evapotranspiration, temperature, radiation, FAO56-PM
The discipline of environmental biophysics relates to the study of energy and mass exchange between living organisms and their environment. The study of environmental biophysics probably began earlier than that of any other science, since knowledge of organism-environment interaction provided a key to survival and progress. Systematic study of the science and recording of experimental results, however, goes back only a few hundred years. Recognition of environmental biophysics as a discipline has occurred just within the past few decades.
The Bowen ratio energy balance (BREB) method of indirect measurement of latent and sensible heat fluxes and other major components of the surface energy balance is accepted as one of the robust approaches in the fields of agricultural engineering, micrometeorology, water resources research, hydrology, and related disciplines. The adoption of this technology in quantification of surface energy fluxes in practical applications is mainly attributed to the method's performance and robustness in measurement of such fluxes for various agro-ecosystem surfaces in different climates. The method determines the Bowen ratio (β) by means of measured gradients of atmospheric temperature and air moisture content (actual water vapor pressure) and applies β in the energy balance equation to solve for the latent and sensible heat flux. The main assumption in the Bowen ratio theory is that the energy transfer coefficients for latent heat (KV ) and sensible heat fluxes (KH ) are equal. This assumption is made because all energy scalars are carried by the same eddies, therefore, these scalars are associated at the same boundary layer of the evaporating surface. A basic criterion of this method is that the air temperature and water vapor pressure are measured (above an evaporating surface) at such heights that the horizontal gradient of air temperature and water vapor pressure can be neglected. The equality (or similarity) assumption (KV = KH) has been proven to be valid for a range of field and vegetation surfaces in various climates. However, the assumption has also been proven invalid for some heterogeneous vegetation surfaces. Nevertheless, successful application of the BREB method to measure surface energy fluxes has been reported for many different types of terrestrial surfaces, including agricultural fields, grasslands, forestry, lakes, wetlands, ocean, etc. This article reviews the history; the main scientific, theoretical, and technical principles; the operational characteristics; and some of the advances in instrumentation of the BREB method. Some studies utilizing the BREB method are also presented. © 2014 American Society of Agricultural and Biological Engineers
The magnitude of the of the Webb et al. (1980) density corrections on water vapor fluxes due to the flux of sensible heat is examined in terms of the Bowen ratio. The correction due to latent heat is proportional only to the mole fraction of water vapor and is 5 times smaller than that for the sensible heat. The temperature regime within the path of the krypton hygrometer was measured to determine its effect in the Webb et al. (1980) corrections and the krypton O2 absorption corrections. The results of this experiment are inconclusive, but confirm the need for additional measurements. Two methods for determining water vapor from krypton hygrometer measurements are reexamined. An approximate method endorsed by the manufacturer and having errors of less than 3 percent for fluctuation smaller than 2 gm-3 is shown to underestimate the vapor flux by 14% under specific conditions of light winds and irrigated surfaces in arid regions (K. Kunkel, 1992, personal communication).
For a variety of reasons, the measurement of latent heat flux using the Bowen ratio method can sometimes result in erroneous data. This study provides guidelines for detecting erroneous Bowen ratio data and illustrates the application of these guidelines by comparing Bowen ratio and lysimeter data collected over grass and alfalfa in southern Idaho. Errors in net radiation were detected by comparing measured with theoretical values. However, it was found that good theoretical procedures to validate soil heat flux data are lacking. Only empirical equations mainly used for remote sensing applications to obtain estimates close to noontime are available. Extremely inaccurate latent heat fluxes were easily filtered out by rejecting data when the calculated Bowen ratio (β) values were close to -1. A simplified procedure was proposed to reject fluxes with the wrong sign, and three different equations were used successfully to detect the occurrence of condensation inside the type of measurement system used in the study. Guidelines to assure adequate fetch are provided. Fetch did not affect the measured fluxes in this study, which may have been due to the similarity in surface properties between the crops under study and those in the surrounding fields.
A field experiment was conducted during the 2009 and 2010 growing seasons to determine the effect of subsurface drainage (SSD) on evapotranspiration (ET) and crop coefficients (K-c) for a farm field in the Red River Valley of North Dakota. The total area of the field was 44 ha, half of which had subsurface drainage installed in the fall of 2002 at an approximate depth of 1.1m and a spacing of 18.3m. Corn (Zea mays) was planted in 2009 and soybean (Glycine max) in 2010. Evapotranspiration rates were measured in both the SSD and surface drained [or undrained (UD)] by using the eddy covariance (EC) method. The changes in water table and soil moisture content were monitored continuously in both fields. The K-c for corn and soybean was developed by using the ET measured by the EC system, and the reference ET was estimated by using the American Society of Civil Engineers Environmental and Water Resources Institute alfalfa reference method. As expected, the use of SSD affected the ET in a seasonal pattern and the ETwas crop dependent. Seasonally, higher ETwas observed during spring and fall in the UD field attributable to shallower water table and higher soil moisture content. In the summer, a higher ETwas found in the SSD field. The higher ET in the UD field in spring and fall, which was 109 and 191 mm in 2009 and 2010, compared with 105 and 176 mm in 2009 and 2010 in the SSD field, did not offset the higher ET in the SSD field in the summer, which was 310 and 351 mm in 2009 and 2010, compared with 249 and 324 mm in 2009 and 2010 in the UD field. For July and August, the ET in the SSD field was 31% greater in 2009 for corn and 14% greater in 2010 for soybean than that in the UD crop fields. For the entire growing season, the ET in the SSD field was 16% higher in 2009 and 7% higher in 2010 compared with the UD field. During the peak growing season (July), the K-c was greater in the SSD field, with peak values of 0.70 for corn and 0.76 for soybean, but in the UD field, the peak K-c values were only 0.54 for corn and 0.65 for soybean. DOI: 10.1061/(ASCE)IR.1943-4774.0000508. (C) 2012 American Society of Civil Engineers.
Evapotranspiration represents the main consumptive use of water in agricultural production and its magnitude is important for irrigation water management. Since water shortages are increasing in many areas, there is a pressing need to improve irrigation water management, for which farmers need reliable information and tools to make better irrigation decisions. There is a lack of knowledge about the water use and irrigation requirements of crops grown in different environments, especially of new crop hybrids. The overall objective of this study was to improve our understanding of the water requirements of soybean. Specific objectives were to: (1) measure and document the daily crop evapotranspiration (ETc) and other energy fluxes, (2) document the daily and seasonal behavior of crop coefficients (Kc), and (3) evaluate the impact of weather variables on alfalfa-reference (ETr) and grass-reference (ETo) evapotranspiration. Here we report results of direct ETc measurements using an eddy covariance system obtained from soybean fields at North Platte, Nebraska, during 2002, 2003, and 2005. We found considerable differences in weather conditions among seasons that affected the accumulation of growing degree days, crop development pattern, crop ETc and Kc. We found that ETr values were on average 32.3% greater than ETo, which is important when choosing Kc values for calculating crop ETc. We also found that vapor pressure deficit (VPD) explained 90 and 92% of the variability in ETo and ETr, respectively. We presented daily measurements of energy fluxes and Kc values and found that measured Kc values were quite variable and often deviated considerably from the average Kc curves given in FAO-56 due to wetting events (rain and irrigation) and crop stress. Therefore, we recommend using the dual Kc method, rather than the single Kc method, for irrigation scheduling. In addition, we found considerable differences in crop maturity among years and suggested that acceleration in maturity could be due to crop stress, especially during the reproductive period. We raised the need for accurate methods to quantify the effect of stress on crop maturity and its impact on Kc.