論文., December 2012, Vol. 122, 15 ‒ 21

Original
Paper
15

Evaluation of energy-balance-based evapotranspiration in a
grass ﬁeld
Kosuke NOBORIO1, Kazuyoshi ONO2, Junpei MANO2, Takumi MIURA2, Naoya SATTA3,
Kiyoshi KOGA3 and Yoshiaki MUKAIDA2

Abstract : The proper estimates of evapotranspiration（ET）are critical for better animal manure and/or water management practices in farmlands. Micrometeorological methods,, the Bowen ratio method andthe eddy covariance method, to estimate ET havebeen popularly used. Those methods, however, require
specially‒designed instruments or the multiple numbers of instruments. Estimates of ET based on the energy balance at the canopy surface, on the other hand,need only routine weather data that were easily available. Evapotranspiration estimated by the energy balance method along with routinely‒obtained weather
data was evaluated by comparing with estimates of
ET by the Bowen ratio method. Weather data,
shortwave irradiance, （W m‒2），air temperature, a（K），relative humidity, and wind speed, required forthe energy balance method were measured in a reedcanarygrass ﬁeld located near Morioka in north‒eastern Japan. A Bowen ratio system was installed alongside in the same grass ﬁeld. An energy balance on a
grass canopy is expressed as a function of canopy surface temperature, （K）．Using the Newton‒Raphson
method, the energy balance equation was numericallysolved for, to obtain an evapotranspiration rate,（kg m‒2 s‒1）．Values of net irradiance, （W m‒2）andlatent heat flux,（W m‒2），were overly estimatedwith the energy balance method when
> 500W m‒2.
‒2
For
< 500W m , however, n,, and sensible heat
flux, （W m‒2），estimated with the energy balancemethod agreed well with those estimated with theBowen ratio method. Daily ETs between July 1 and28, 2003 were calculated by accumulating
betweensunrise and sunset. The daily ET values obtained by
the two methods agreed very well with the correlation
coefficient, = 0. 96（ < 0. 001）．The energy balancemethod to estimate daily ET could be promising.
Keywords : Evapotranspiration, Bowen ratio method,
Energy balance method, Atmospheric emissivity, Cropheight1. Introduction
Surface‒ and/or ground‒water pollution with animal
wastes is prohibited by the law in Japan. The proper
management of dairy cattle manure for applying to an
agricultural grass ﬁeld, which is popular in the areas
with large livestock industry, is very critical for the
livestock industry. Prior to the application of dairy cattle manure, soil water content in the field must be
known to minimize surface runoﬀ and/or deep percolation. The proper estimation of soil water content depends on how well evapotranspiration（ET）is predicted or measured. Measuring ET is usually made bymeans of lysimeter, soil water balance, energy balance,and eddy covariance methods. Some methods require
speciﬁcally‒designed equipments whereas others justuse routine weather data. From the practical view offarmers, the latter methods would be appreciated.
Penman（1948）would be the ﬁrst to develop a model
to estimate ET using meteorological data. Penman smodel is modiﬁed into various models, and so‒called thePenman‒Monteith model has been very popular and extensively evaluated by many researchers（Kustas et al . ,1996；Howell and Evett, 2004；Gong et al . , 2006）．In
Penman s procedure, evaporating surface temperature
is not required because he assumed a linear relationship between saturated vapor density and air temperature over a narrow range of 10K（Monteith and Unsworth, 2008）．With the improvement of digitalcomputing power, however, numerical iteration procedures, which are able to solve a full energy balance
equation on an evaporating surface, are readily available to estimate ET with few assumptions（Van Baveland Lascano, 1987）．Van Bavel and Lascano（1987）
model predicts ET and the profile of water content

1School of Agriculture, Meiji University, Kawasaki, Kanagawa
214 ‒ 8571, Japan. Corresponding author : K. NOBORIO, E-mail：noboriok@isc.meiji.ac.jp
2
Formerly Faculty of Agriculture, Iwate University, Morioka,
Iwate 212 ‒ 8750, Japan
3
Faculty of Agriculture, Iwate University, Morioka, Iwate 212 ‒
8750, Japan
2010 年 11 月 25 日受稿，2012 年 9 月 29 日受理
土壌の物理性 122 号，15 ‒ 21（2012）

and temperature in soil. Since their model deals withwater and heat transport in soil, data for root distribution are required.
We tested a sort of a submodel, estimating ET using
weather data, of Van Bavel and Lascano（1987）or ofan extended model of Van Bavel and Hillel（1976）．
The model that we tested used numerical iteration,

土壌の物理性 第 122 号（2012）16

with no soil and root parameters nor any assumptions

where

such as Penman（1948）made, to estimate canopy tem-

cient for solar radiation deﬁned as a ratio of potential

is the total atmospheric transmission coeﬃ. The potential

perature and then eventually ET. Testing this kind of

to measured shortwave irradiance,

submodel will provide with the feasibility of a simple‒

shortwave irradiance is a function of the solar constantyet‒fully‒theoretical ET model. Evaluation of the mod-（≈1367 W m‒2）and the locations of the sun and an ob-

el proposed was made by comparing ET estimatedserver. See Campbell（1985）for a detailed calculation

with that measured with the Bowen ratio method.

procedure for the potential shortwave irradiance.
The latent heat ﬂux,

2. Materials and Methods（ ），is expressed as a func-（Van Bavel and Hilell, 1976）as：tion of2. 1 An energy balance at a canopy surface（ ）＝

An energy balance equation, （ ），at a bare soil

ρ（ ）−ρ（ ）[5]surface is expressed as a function of surface temperature,（, Van Bavel and Hillel, 1976）as：（ ）＝ （ ）+

（

）+ （

）+ （

）＝ 0

[1]

where

is the latent heat（J kg‒1）of vaporization ofwater,

is the evapotranspiration rate（kg m‒2 s‒1），

ρ（ ）is the water vapor density（kg m‒3）at the canopy surface, and

where

（

‒2

）is the net irradiance（W m ）， （is the latent heat flux（W m‒2）， （heat ﬂux（W m‒2），and （is the aerodynamic resistance（s‒1）

m ）for water vapor transport. The latent heat, （J）is the sensiblekg‒1），of vaporization of water is derived from the data

）is the soil heat ﬂux（Wof Monteith and Unworth（2008）as：m‒2）that could be measured with a heat flux plate.
= 2. 201 × 106 − 2369. 2（

Fluxes away from the surface are expressed as nega-− 273. 15）[6]tive, and are those toward the surface as positive. We
assumed that Eq. [1] was also true at the canopy sur-whereface in a grass ﬁeld where the soil surface was fully

the evaporating surface,ρ（in Eq.

covered with reed canarygrass. In this case,[1] indicates the canopy surface temperature（K）．
Net irradiance,（），was assumed to be sat-uration at the canopy temperature,, because the hu-

midity of stomatal cavities is always near unity（Camp-），is expressed as the sum of

incoming and outgoing shortwave and longwave irra-

bell, 1985）．Saturation water vapor density,ρ（kg m‒3），
is estimated（Campbell, 1985）as：,（No-

diances as a function of surface temperature,borio et al , 1996a）as：（

exp 31. 3716− 6014. 79 −0. 00792495
εεσ 4 −εσ 4（ ）＝（1−α）[2]

where α is the albedo of the canopy surface, whichis thewas measured with pyronometers in our case,incoming shortwave irradiance（W m‒2），ε andεa are
the emissivities of the canopy surface and the atmosphere, respectively,

is temperature（K）．Water vapor density atais air temperatures（K），and

ρ＝）0. 001． [7]Water vapor density of air, ρa（a），is then calculated

as the product of ρ and the relative humidity,

, of

air.
The sensible heat flux, （ ）, is expressed as a
（Van Bavel and Hilell, 1976）as：function of‒8

σ is the Stephan‒Boltzmann constant（ = 5. 67 x 10 Wm‒2 K‒4）．The canopy surface emissivity, ε , was cho-

−

（ ）＝

sen as 0. 97 according to Campbell（1977）．The atmo-[8]

spheric emissivity, εa , is calculated（Campbell, 1985）
as：

where

is the volumetric heat capacity of air（≈1200

J m‒3 K‒1），
εa ＝（1−0. 84

1/7a（850. 0ρ ）+ 0. 84
）

[3]

a

is air temperatures（K），and

aerodynamic resistance（s m ）for heat transport. The
andaerodynamic resistances,‒3

where ρa is the water vapor density（kg m ）of air.
The fraction of cloud cover,, is estimated（Campbell,

is the‒1, are assumed to beequal at the canopy surface and are described（Campbell, 1977）as：

1985）as：＝ 2. 33 − 3. 33

[4]

＝ ＝

1n［
（＋ − ）/ ］1n［
（ ＋
2

− ）
/ ］

[9]

論文：Evaluation of energy-balance-based evapotranspiration in a grass ﬁeld
whereis the Karman s constant（≈0.4）， is the17（Campbell, 1977）as

height（m）above the ground where the temperature
and wind speed are measured,is the zero plane dis-placement（m）for the surface,is the mean windspeed（m s‒1）at the height （m），and

and

β＝

＝

（
a

− 2）

1

[16]

（ρ1−ρ2）arethe roughness lengths（m）for heat and momentum,

where the subscripts 1 and 2 indicate values of therespectively. For typical plant surfaces, the following

variables at heights

empirical relationships with the plant height, （m），

be

are used（Campbell, 1985）as：=and, and it was assumed toas mentioned in Eq. [9].

2. 3 Measurement
Experiments were conducted in July 2003 in north-＝ 0. 77[10]

ern Honshu, Japan（39 o48＝ 0. 13[11]

mental plot raising reed canarygrass（＝ 0. 2.

[12]

N, 141 o05

E）．An experi-）was managed by a farmer with routine workin a usual manner. The area of the experimental plot,

Since the energy balance equation, Eq. [1], is ex-

sloped with about 5. 5 degrees from the northwest topressed as a function of the canopy surface tempera-

the southeast, was approximately two hectare. Theture,, Eqs. [1], [2], [5], and [8] are numerically solved

taxonomical class of soil was Andisol with 80 % offorusing the Newton‒Raphson method（Press et al ,sand, 12 % of silt, and 8 % of clay.

2002）．Assuming that the initial value oftoawas equal, the Newton‒Raphson method solved Eq. [1] withrespect toas:Weather data,

incoming shortwave irradiance,（W m‒2），reﬂected shortwave irradiance,（W m‒2），

air temperature, （K），relative humidity,, andwind speed, （m s ‒1 ），were measured at height
+1

＝

−

（

）

（

）

[13]

= 2 m. Soil heat ﬂux, （W m‒2），was measured using
three heat flux plates （MF‒81, EKO Instruments
Co.,Ltd., Tokyo）at 0. 05m deep from the soil surface.

where the superscripts

and +1 indicate the number

Incoming and reflected shortwave irradiances, withof iterations, （ ）was the ﬁrst derivative of （ ）with

which albedo α was determined, were measured withrespect to, that might be numerically derived as：

pyronometers（MS‒601, EKO Instruments Co.,Ltd.,（ +Δ ）− （（CS500, Campbell Scientific Inc., Logan, UT），wereTokyo），an air temperature and humidity sensor
（ ）＝

−Δ ）

[14]

2Δ

used. Wind speed and wind direction were measured
with a three‒cup‒anemometer and a wind‒vane

where Δwas the small increment of, e.g.,= 1. 0 x 10‒6.

Δ（03001, Campbell Scientiﬁc Inc., Logan, UT）．Precipitation was measured with a tipping‒bucket rain gauge

satisfying Eq.

（K. Hattori & Co., Ltd., Tokyo）．Data were acquired[1] was found. The evapotranspiration rate, （kg m‒2

every second, and mean values were stored using a

After several iterations of Eq. [13],‒1s ），was estimated using Eq. [5] by applying the iteratively‒foundvalue. Dividing

by the density of3water,ρ = 1000 kg/m , and summing up

datalogger（CR23X, Campbell Scientific Inc., Logan,
UT）every 15 min.

/ρ between

A Bowen ratio system（Campbell Scientiﬁc Inc., Lo-sunrise and sunset estimated the daily evapotranspira-gan, UT）was installed alongside. Air temperature andtion,（mm d‒1）.

water vapor density of air were measured at heights= 2 m and2. 2 Bowen ratio method= 1 m. Air temperature was measured

The Bowen ratio method has been used to measurewith ﬁne ﬁre type‒E thermocouple junctions, and wa-

evapotranspiration in the ﬁeld as a standard method.

ter vapor density was measured with a cooled mirror

Taking the ratio,β= /hygrometer（Dew‒10, General Eastern Corp., Water-, called the Bowen ratio, andrearranging Eq. [1] with respect toprovidestown, MA）
．Fetch was at least 40 m radius, which satisﬁed the minimal fetch requirement, fetch > 20 （Hei-（Campbell, 1977）：

lman et al , 1989），surrounding the Bowen ratio
＝−

＋
1 ＋β

・

[15]

system. A net radiometer（Q 7. 1, Campbell ScientificInc., Logan, UT），1. 5 m high above the ground, andtwo heat flux plates（HFT 3, Campbell Scientific Inc.,

From Eqs. [5] and [8], the Bowen ratio, β, is expressed

Logan, UT），0. 08 m deep from the soil surface, were

土壌の物理性 第 122 号（2012）18

also installed. Soil temperatures at 0. 02 m and 0. 06 m

a heat ﬂux plate. We, however, did not correct

below the soil surface were measured with type‒Tused raw

to calculate

thermocouple junctions. Soil water content was alsoasmeasured with a CS 615 moisture sensor（Campbell

transpiration was obvious.

accounted for, butbecause just < 3 % as little
during daytime when evapo-

Scientific Inc., Logan, UT）at 0. 025 m below the soil

Energy ﬂux densities estimated with the energy bal-surface. Data for the Bowen ratio system were mea-

ance method were compared with those measured

sured every second, and mean values were stored ev-

with the Bowen ratio method（Fig. 3）．In Eqs. [9] andery 20 min. using a datalogger（CR 23 X, Campbell Sci-[10], crop height,

entiﬁc Inc., Logan, UT）．

time. The effects of crop height on ET will be discussed in the following section. Equation [2] of the en-

3. Results and Discussion

ergy balance method overly estimated 20 % as much

3. 1 Energy components
The maximal, was assumed to be 0. 1 m all themeasured with the net radiometer during mid-asvalue estimated with Eq. [1] wasfound at around 11：00 whereas the maximal

day whenvalue> 500W m‒2（Fig. 3A）．Overestimates of

may be attributed to the overestimate of the atmo-

was found at around 14：00（Fig. 1）．The values ofspheric emissivity, εa , calculated with Eq. [3]. Unlike

reached the maximal at around noon because the mag-Fig. 2A, Noborio et al.（1996b）reported that

nitude of shortwave irradiance was largely aﬀected bymated in a similar manner using Eq. [3] performed well

the sun s location（Fig. 3A）．Noborio et al.（1996 b）re-for the bare soil surface in Texas, U.S.A. When‒2

ported that the surface temperature estimated by them , however, estimates ofenergy balance method agreed well with that mea-

withsured at the bare soil surface.

overestimates of

Figure 2 shows that temporal changes in energy

esti< 500W

with Eq. [2] agreed wellmeasured. Overestimates ofresulted inby Eq. [5] of the energy balancemethod（Fig. 3B）．Likewise did< 500W m‒2,es-

ﬂux densities obtained using the Bowen ratio system

timated with Eq. [5] agreed well with that measured

for a clear day on July 27, 2003. The signs of all the en-with the Bowen ratio method with Eq. [15] whenergy ﬂux densities in Fig. 2 are expressed as positive
for convenience. The values of

andwere mea-< 300 ‒ 400W m ‒2. The resultant,, agreed wellwith both methods（Fig. 3C）although their phasesured using the instruments whereas the values ofstarted to shift by following the phase shift in

and3D）．In Fig. 3D, the amplitude ofwere estimated using Eqs. [15] and [16], respec-（Fig.

s agreed well；how-tively. Approximate 73 % of incoming total energy,

ever, their phases shifted. The phase shift might be re-, was consumed for evapotranspiration（ET），

sulted from diﬀerences in the installation depths of two, whereas approximate 18 % offor

was consumed.

and the Bowen ratio method in 0. 08 m deep. The heat

Mayocci and Bristow（1995）proposed that soil heat
ﬂux,

methods, the energy balance method in 0. 05 m deep

, be corrected for the heat storage of soil above

ﬂux plates at a shallower depth started to change earlier than those at a deeper depth. Because the contribution of

to the energy balance was small enoughcomparing with other components in Eq. [1], weFig. 1 Temporal changes in air temperature, a , measured
at the weather station in the ﬁeld and canopy temperature,, estimated using Eq. [1] by the energy balance method.
The crop height was assumed to be a constant as = 0. 1 m,
and data used for calculation were obtained on July 27, 2003.

Fig. 2 Energy ﬂux densities measured on July 27, 2003 with
the Bowen ratio system. Symbols of solid diamonds, open triangles, crosses, and open squares indicate , − , − , and− , respectively.

論文：Evaluation of energy-balance-based evapotranspiration in a grass ﬁeld
thought that the phase shift was negligible.
3. 2 Evapotranspiration

tween 0. 2 mm d ‒1 and 5 mm d ‒1 using a constantvalue（= 0. 1 m）agreed very well with those by the

Daily ETs between July 1 and 28, 2003 were calculated by accumulating

19

between sunrise and sunset.

Figure 4 showed that daily ET values with a range be-

Bowen ratio method with correlation coeﬃcient = 0. 96（probability< 0. 001），and they were close to the 1：1

line. In reality, however, crop height, , increased with

Fig. 3 Comparing energy ﬂux densities,（A） ,（B）− ,（C）− , and（D）− , between the energy balance method
and the Bowen ratio method. The densities were measured and estimated on July 27, 2003.

Fig. 4 Comparing daily evapotranspiration（ET）between
the energy balance method and the Bowen ratio method between July 1 and July 28, 2003.

Fig. 5 The dependence of evapotranspiration（ET）on thecrop height（h）varied with wind speed. Wind speed is described as u. Data used for calculation were obtained at 11:45
local standard time on July 27, 2003.

土壌の物理性 第 122 号（2012）20

time according to accumulating mean daily tempera-

technical assistance.

ture.
When varying

used for Eqs. [9], [10], and [11], daily ETs were a little
bit more overly estimated than those using（Fig. 5）．Increases in
eventually larger
ed withresulted in smaller= 0. 1 m
and. The ET relative to that calculat-= 0. 1m at approximately noontime in theclear day increased by 30 % as increases in the valuesofwhen wind speed, u（m）
，was larger（Fig. 5）．An

extreme case like this made an oﬀ placed datum indicated with Jul. 27 in Fig. 4. Unlike the case of Jul. 27,
the ETs of other days were properly estimated using
Eq. [1] as shown in Fig. 4. For the other days, overesdue to overestimates of εa with Eq. [3]timates ofcompensated underestimates of ET due to underestimates ofReferencesfrom 0. 05 m to 0. 9 m with time was, and eventually daily ETs estimated with

Eq. [1] agreed well with those measured by the Bowen
ratio method.

4. Conclusion
The energy balance method was applied to estimate
evapotranspiration（ET）using routine weather data.
Although it overly estimatedandonly when‒2> 500W m , estimates of daily ET ranging between
0. 2 mm d ‒1 and 5 mm d ‒1 agreed well with ET measured with the Bowen ration method. To properly estimate a full range of ET rates, atmospheric emissivity,
εa , expressed with Eq. [3] should be calibrated for Japanese environmental conditions or the use of a net radiometer to directly measureis recommended.

Evapotranspiration in the ﬁeld could be easily estimated by the energy balance method using routine weather data, i.e. shortwave irradiance, air temperature, relative humidity of air, wind speed, and/or soil heat ﬂux,
from a ﬁeld server such as reported by Manzano et al.
（2011）．

Acknowledgements
This research was supported in part by the Grant‒in‒Aid for Scientific Research（B）（No. 11460109, andNo. 15380160）of Japan Society for the Promotion of
Science（JSPS），and research grants from Livestock
Industry s Environmental Improvement Organization

Campbell, G.S., 1977：. Springer ‒ Verlag, New York, p. 138.
Campbell, G.S., 1985：. Elsevier, Amsterdam, p. 59.
Gong, L., Xu, C., Chen, D., Halldin, S.,and Chen Y.D., 2006：
Sensitivity of the Penman ‒ Monteith reference evapotranspiration to key climatic variables in the Changjiang（Yangtze River）basin. J. Hydrol. 329：620 ‒ 629.
Heilman, J.L., Brittin, C.L., and Neale, C.M.U., 1989： Fetch requirements for Bowen ratio measurements of latent andsensible heat ﬂuxes.
44：261 ‒ 273.
Howell, T.A., Evett, S.R., 2004： The Penman ‒ Monteith Method.
. Conservation and Production Laboratory. www.cprl.ars.usda.gov
Kustas, W.P., Stannard, D.I., and Allwine, K.J., 1996： Variability in surface energy ﬂux partitioning during Washita
92： Resulting eﬀects on Penman ‒ Monteith and Priestley ‒ Taylor parameters. Agric. Forest Meteorol. 82：
171 ‒ 193.
Manzano, V.J.P., Mizoguchi, M., Mitsuishi, S., and Ito, T., 2011：
IT ﬁeld monitoring in a Japanese system of rice intensiﬁcation (J ‒ SRI）. Paddy Water Environ. 9：249 ‒ 255.
Mayocci, C.L., and Bristow, K.L., 1995： Soil surface heat ﬂux：
some general questions and comments on measurements.
75：43 ‒ 50.
Monteith, J.L., and Unworth, M.H., 2008：. 3rd ed. Academic Press, Burlington,
MA, USA. p. 396.
Noborio, K., McInnes, K.J., Heilman, J.L., 1996a： Two ‒ dimensional model for water, heat, and solute transport in furrow ‒ irrigated soil： I. Theory.
60：
1001 ‒ 1009.
Noborio, K., McInnes, K.J., Heilman, J.L., 1996b： Two ‒ dimensional model for water, heat, and solute transport in furrow ‒ irrigated soil： II. Field evaluation.
60：1010 ‒ 1021.
Penman, H.L., 1948： Natural evaporation from open Water, baresoil and grass.
A193：120 ‒ 145.
Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P.,
1989：
nd

. Cambridge University Press, Cambridge, p.
366.
Van Bavel, C.H.M., and Hillel, D.I., 1976： Calculating potential andactual evaporation from a bare soil surface by simulation of
concurrent flow of water and heat.
17：453 ‒ 476.
Van Bavel, C.H.M., and Lascano, R.J., 1987：

and Kurita Water and Environment Foundation. We
are grateful to Mr. Muneaki Yokota for maintaining
the grass ﬁeld and his support for our research, and to
Ms. Sachiko Yamamoto of Meiji University for her. Soil and Crop Sciences Department, Texas Agricultural Experiment Station, Texas A&M
University, College Station, TX and Lubbock, TX, pp. 75.

論文：Evaluation of energy-balance-based evapotranspiration in a grass ﬁeld

要旨

蒸発散量（ET）の適切な推定は，農地におけるよりよい家畜ふん尿及び水管理を行う上で重要である．
ボーエン比法や渦相関法などの微気象学的方法が ET 測定には一般的であるが，特殊な測定器や複数の測定器が必要である．一方，熱収支法による ET 推定は，簡易に入手可能な気象観測データを使って行うことができる．熱収支法を使った ET 推定値をボーエン比法による測定値と比較して評価した．岩手県盛岡市近郊にあるリード・カナリーグラス牧草畑において，短波放射量，気温，相対湿度，風速などの気象データを測定した．また，ボーエン比法測定装置も同一ほ場内に設置した．牧草キャノピー表面における熱収支式は，キャノピー温度
ン・ラプソン法を使って‒2

放射量 （W m ）と潜熱フラックス
熱収支法で推定したとの関数として表される．蒸発散量を求めるためにニュートについてこの熱収支式を解いた．熱収支法では，> 500W m‒2 の時に純

‒2

（W m ）をわずかに過大評価した．しかしそれ以外の時は，および顕熱フラックス （W m‒2）は，ボーエン比法で測定したこれらの値と良く一致した．日の出から日没の間の蒸発散量の積算値を日蒸発散量として，2003 年 7 月 1 日から 7 月 28 日まで計算した．両法による日蒸発散量は， = 0. 96（ < 0. 001）で非常に良く一致した．熱収支法による日蒸発散量の推定は有効であると考えられる．
キーワード：蒸発散量，ボーエン比法，熱収支法，大気射出率，作物高さ

21