J. Jpn. Soc. Soil Phys.
土壌の物理性No. 136 p.15 ∼ 24 (2017)

Determination of irrigation depths
using a numerical model of crop growth and quantitative
weather forecast and evaluation of its effectthrough a field experiment for potato
Hassan M. ABD EL BAKI1 , Haruyuki FUJIMAKI1 , Ieyasu TOKUMOTO2 and Tadaomi SAITO1

Abstract: A scheme for determining irrigation depth using a numerical model of crop response to irrigation andquantitative weather forecast was presented. To optimize
each irrigation depth, a concept of virtual income, which is
proportional to an increment in transpiration amount during an irrigation interval, is introduced. A field experiment
was carried out to evaluate effectiveness of the presented
scheme in terms of net income considering the price ofwater. Potato was grown in summer season of 2015 using a drip irrigation system in Arid Land Research Center, Tottori, Japan. Two treatments were conducted: automated irrigation and proposed scheme with two replicatesfor each. Results indicated that predicted water content
agreed well with observation although some underestimation of water content due to overestimation of transpiration
was observed. Proposed scheme could save water by 27%, while yield was increased by 15 %, resulting in higher
net income as compared to automated irrigation. Basedon these results together with previous works, we can conclude that proposed scheme can at least realize similar net
income to automated irrigation systems without high initial investment.
Key Words : irrigation, weather forecast, transpiration, net
income1. Introduction
Rapidly increasing population and intensified scarcity ofwater resources bring a new emphasis on efficient use ofwater in irrigation. Farmers are still widely relying on theirintuition to determine an irrigation depth even in industrialized countries. Such conventional irrigation scheme
may have caused yield reduction or waste water. To save
irrigation water, a concept of deficit irrigation was intro1 Tottori University, 4-101 Koyamacho-minami, Tottori, 680-0001, Japan.

Corresponding author: Hassan M. EL BAKI
2 Saga University, 1 Honjo-machi, Saga, 840-8502, Japan.
2016 年 5 月 20 日受稿 2017 年 4 月 25 日受理

duced and many field studies has been carried out (Ati andNafaou, 2012; Makau et al., 2014). In such studies, water use efficiency or water productivity which is generally
defined as yield per unit amount of irrigated water havewidely been used as target value to be maximized. However, for a farmer, net income, not water use efficiency,
should be of primary concern. Therefore, we believe thatnet income should be the target value to be maximized.
Automated irrigation systems using sensors may be another alternative which have been developed to precisely
meet crop water requirements and respond to drought
stress quickly. Such systems require high initial investment to construct monitoring and controlling systems andhave difficulty in adjusting irrigation depth to weather forecasts. For example, it is obviously wasteful to apply full irrigation when rain is forecast for the next day. Automatedsystem may nevertheless do it whenever the currently monitored value reaches its threshold value. In these days, expensive monitoring using sensors can be altered by numerical simulation of water flow and crop growth. Nowadays,
personal computers are getting affordable even for farmers
in developing countries. Not only monitoring current status, a numerical model can predict upcoming conditions.
We may optimize irrigation depths such that net income
is maximized. Also, today, freely accessible quantitative
weather forecasts, whose accuracy is improving, have been
available on the web (e.g. accuweather.com). These technical as well as socio-economic progresses have enabled
us to optimize irrigation depths using quantitative weather
forecast as input data. Moreover, using a relationship between yield and transpiration (or evapotranspiration), numerical models can search irrigation depth such that net
income is maximized. Hence, these optimizations will result in maximizing net income for farmers.
Several researchers have proposed to use weather fore-

16

土壌の物理性

casts for irrigation scheduling. Venäläinen et al. (2005)
evaluated accuracy of SWAP (van Dam et al., 1997) and
AMBAV (Braden, 1995) models by inputting numerical weather forecast as atmospheric boundary conditions.
Wang and Cai (2009) presented methods which combine
the SWAP model and weather forecast. They suggested toapply water when predicted stress index (actual to potential transpiration ratio) becomes less than 0.85 and irrigation depth is determined to bring the root zone soil moisture to field capacity. They also presented an entire-season
optimization scheme to maximize net income considering
cost for water using genetic algorithm (GA). They evaluated potential advantage of their methods in terms of net
income by performing numerical experiments. Lorite et al.
(2015) presented a scheme which combines freely accessible weather forecast and AquaCrop model (Steduto et al.,2009) and evaluated the effect of uncertainty in weather
forecast on simulated yield. Irrigation depth is determinedso that soil moisture in the root zone returns to field capacity. AquaCrop is a water balance model which does not
use Richards equation to simulate water flow and therefore
soil water dynamics in root zone is not considered. Seidel
et al. (2015) used HYDRUS model to minimize irrigationwater applied. Delgoda et al. (2016) presented a scheme todetermine irrigation depth using weather forecast to minimize both root zone soil moisture deficit and irrigation
amount. They used a simple water balance model to calculate root zone soil moisture deficit. Fujimaki et al. (2014)
presented a new scheme to optimize irrigation depths using
weather forecast as input data for a numerical model whichsolves two-dimensional Richards’ equation such that net
income is maximized. They also presented results of preliminary two field experiments. The first experiment was
carried out in Institute des Régions Arides (IRA) in Medenine, Tunisia, in 2011–2012. The soil was loamy sandand the crop was Barley (Hordeum vulgar L. cv. Ardhaui).
The second one was carried out in Arid Land ResearchCenter in Tottori, Japan, in 2013. The crop was Sweet
Corn (Zea mays, Amaenbou86). These results still havenot been satisfactory to evaluate the effectiveness of the
new scheme and we need more experiments to evaluate theeffectiveness of the new scheme under various combination of soil, climate and crops. This paper presents outlineof the scheme and experimental results to evaluate the effectiveness of the scheme in terms of net income.

第 136 号(2017)

performed to estimate the current status using the previous
weather data ([1] in Fig. 1). The records of climatic condition were downloaded from the website of Japan Meteorological Agency. The numerical simulation is performed by
WASH 2D (Fujimaki et al., 2014), which solves governing equations, including Richards equation of water flow,
for two-dimensional movement of water, solute and heatin soils with the finite difference method. The WASH 2D
software is freely distributed with source code under thegeneral public license from website of Arid Land Research Center, Tottori University (http://www.alrc.tottoriu.ac.jp/fujimaki/download/WASH 2D).
Then, quantitative weather forecast is downloaded as
input data ([2] in Fig. 1). A software (WeatherForecastDownloader) has been developed to download theHTML file and parse the HTML for WeatherUnderground(http://www.wunderground.com) and Yahoo! Japan (http://weather.yahoo.co.jp/weather/jp/31/6910/31302.html) for
consecutive days. Note that we may not obtain all theweather data usable for numerical simulation from thesewebsites. Usually, quantitative weather forecasts provide values except for solar radiation. For example,
WeatherUnderground provides cloud cover instead of solar
radiation. In such case, empirically known relationship between cloud cover and the ratio of extraterrestrial radiation
to solar radiation may be applied. Yahoo! Japan provides
four qualitative descriptions, “clear”, “cloudy”, “rain”, and“heavy rain”. In this case, empirically determined average
ratio of extraterrestrial radiation to solar radiation for each
description (e.g. “clear” = 0.82, “cloudy” = 0.63, “rain”= 0.32) may be multiplied to extra-terrestrial short wave
radiation.
Using the quantitative weather forecast, both evaporation rate, E (cm s−1 ) and reference evapotranspiration rate,
ETp (cm s−1 ) are calculated separately in WASH 2D. The
E is calculated by a bulk transfer equation (van Bavel andHillel, 1976). The E is used as boundary conditions forwater flow in field soil. While, the ETp is calculated by

2. Outline of the scheme to determine
irrigation depth
Outline of the scheme to determine irrigation depth (Fujimaki et al., 2014) is illustrated in Fig. 1. To obtain an initial condition of an irrigation day, numerical simulation isFig. 1 Outline of the scheme to determine irrigation depth.
Four steps described in this figure are repeated until last irrigation event.

論文：Determination of irrigation depths using a numerical model and weather forecast

the Penman-Monteith equation (Allen et al., 1998). The
ETp is used to estimate the transpiration rate, Tr (cm s−1 ).
The potential transpiration rate, Tp (cm s−1 ) is calculated
by multiplying with basal crop coefficient (Kc ) at first.
Tp = ETp Kc(1)

A widely used macroscopic root water uptake model(Feddes and Raats, 2004) was used in predicting the water uptake rate, S (cm s−1 ) next.
S = Tp αw β(2)where αw and β are reduction coefficient and normalized
root density distribution, respectively. The αw is a functionof matric and osmotic potential. This function is called as
stress response function. WASH 2D uses so-called additive form stress response function:
(

αw =
1+

1

ψ
ψo
+
ψ50 ψo50)pwhere ψ50 , ψo50 and p are fitting parameters (vanGenuchten, 1987). The β , on the other hand, is describedasβ=0.75(brt + 1)drt −brt−1 (drt − z + zr0 )brt grt (1 − x2 grt −2 ) (4)where x is horizontal distance from the center of the plant(cm), brt is a fitting parameter, and drt and grt are depth andwidth of the root zone (cm), zr0 is the depth below whichroot exists (cm). The zr0 was newly introduced becauseroots do not generally develop in very near surface layer
except for plants grown under plastic mulch. Note that we
added new parameter zr0 to one presented in Fujimaki et al.
(2014) regarding to the two-dimensional root distribution.
Finally, Tr is computed by integrating the S over the rootzone.
Tr = Lx −1

∫∫

Sdxdz

predict τi until next irrigation day ([3] in Fig. 1). The
W is used as variable flux boundary conditions for waterflow in field soil. The maximum W , Wmax may be set atthe cumulative reference ET between irrigation intervals(= ETp × irrigation interval). The minimum W , Wmin is set
0. The third value of W , Wmid is set between these values(= (Wmax +Wmin )/2).
Based on the three pairs of W and τi , an economically
optimum W is estimated ([4] in Fig. 1). To determine theoptimum W , we introduce a ‘virtual net income’ during
each irrigation interval. Although actual income is realized
when crop is harvested and sold, we assume that a farmer
can obtain virtual income, which is proportional to an increment of dry matter attained during an interval. Also,
water must be priced high enough to give farmers incentive
to save water. The virtual net income, In ($ a−1 ), during aninterval is then defined as:
In = Pc ετi ki − PwW −Cot

(3)

(5)

where Lx is the width of the calculated root zone. Based on
the Tr values, we can estimate cumulative transpiration between irrigation intervals, τi , which dynamically responds
to matric and osmotic potential in soil.
Although drip irrigation is a fully 3-dimensional flow
problem, under certain conditions, the effects of individual
emitters along the drip line can be neglected (e.g. Li et al.,2015). If emitter distance is narrow, the system can be approximated as line source. The numerical simulations withthree different irrigation depths, W (cm) are performed to

17

(6)

where Pc is the producer price of crop ($ kg−1 DM), ε iscrop water use efficiency, which is defined as the ratio of
biomass produced to the rate of transpiration, ki is income
correction factor, which was introduced by Fujimaki et al.
(2014) to correct the possible underestimation of the contribution of transpiration during the initial stage, Pw is theprice of water ($ kg−1 ), and Cot is the other costs ($ ha−1 ).
In addition, response of τi to irrigation, W , was assumed tobe empirically described as

τi =

∫

Tr dt = at [1 − exp(btW )] + τ0(7)where at and bt are fitting parameters and τ0 is the τ at
W = 0. If yield is proportional to transpiration, relationshipbetween W and τi may also be described with Eq. (7).
Maximum net income is obtained at W at which derivativeof Eq. (6) for W becomes zero.
dIn= −Pc ε ki ai bi exp(btW ) − Pw = 0
dW

(8)

(
)
Pw
1
W = − lnbt
Pc ε ki ai bi(9)Therefore, if at and bt are known, optimum W can be estimated. To obtain these two values, the τmax and τmid , τvalues at Wmax and Wmid , respectively, are used.

τmax = at [1 − exp(btWmax )] + τ0

(10)

τmid = at [1 − exp(btWmid )] + τ0(11)

土壌の物理性

18
Rearranging Eq. (10) gives(2017)

value. Kc may be basically proportional to LAI and therefore it may be expressed as the same form.

τmax − τ0[1 − exp(btWmax )](12)τmax − τmid[exp(btWmid ) − exp(btWmax )]

(13)

at =

第 136 号

3. Materials and Methods(10) − (11) givesat =3.1 Field experiment

Therefore,τmax − τmid[exp(btWmid ) − exp(btWmax )]−τmax − τ0= 0 (14)[1 − exp(btWmax )]The value of bt can be easily searched using the bisection
method. Thus, by obtaining τi at three irrigation depths,
Wmin , Wmid and Wmax , we may estimate the optimum irrigation depth by assuming that the response of transpiration
during an interval to irrigation is described as an empirical equation with three unknown parameter values, unlike
non-linear optimization which requires many repetitions.
Since the optimization should be completed within a few
hours practically, this simple estimation method developedby Fujimaki et al. (2014) is more suitable than the normal one-dimensional search algorithms such as the golden
section method (Press et al., 1989). These steps describe
above are repeated until the last irrigation event.
A protocol for crop growth is prepared in WASH 2D because of plant grows during cultivation period. Leaf areaindex (LAI), I, is expressed as a function of cumulativetranspiration from germination, τ , since it may primarily
depend on cumulative transpiration.
I = aLAI [1 − exp(bLAI τ )](15)

where aLAI and bLAI are fitting parameters. Since Kc depends mainly on LAI, Kc is also expressed as a function ofτ:
Kc = akc [1 − exp(bkc τ )] + ckc(16)

where akc , bkc and ckc are fitting parameters. Moreover,the depth of root zone, drt , is also expressed as function ofτ:
drt = adrt [1 − exp(bdrt τ )] + cdrt

(17)

where adrt , bdrt and cdrt are fitting parameters. These functions are same form as Eq. (7) and they may express thatthe growth of leaves and root are nearly proportional to dry
matter production at early stage of growth but the slopes
gradually decrease and finally approach to near maximum

Treatments
A field experiment was carried out in Arid Land
Research Center in Tottori (35◦ 32’09”N 134◦ 12’39”E),
Japan, in 2015. Two treatments were established: crop was
irrigated with an automated irrigation system, treatment-A
and proposed method with simulation was applied to theother treatment, treatment-S. Each treatment had two plots
as replicates, each had a 15 m long and 16 m wide. To monitor water content, 12 TDR probes were inserted for eachtreatment and measurement was made at each hour. For
automated irrigation, probes were installed at the depths of
5 and 15 cm below six plants. Regarding to treatment-S,
TDR probes were installed at 6 locations ((x, z) = (0, 5),(0, 15), (0, 45), (15, 5), (15, 15), (45, 5)) with two replicates, where x is horizontal distance (cm) from drip tube
and plant. Evapotranspiration was measured for treatmentS with a weighing lysimeter whose diameter was 150 cm.
Irrigation
Irrigation was applied through a drip irrigation system whose lateral distance was 90 cm and emitter distance was 20 cm. Automated irrigation was set suchthat water was applied for one hour when average
θ at the depth of 15 cm became less than 0.09 m3
m−3 . Irrigation interval for treatment-S was set at twodays. The records of climatic condition were downloaded from the website of Japan Meteorological Agency(http://www.data.jma.go.jp/obd/stats/etrn) and quantitative
weather forecasts were downloaded from the website ofYahoo! JAPAN (http://www.yahoo.co.jp). Price of crop
were set at 0.7 $ kg−1 by referring producer price in the
USA in 2011 (FAOSTAT, http://faostat.fao.org/). Price ofwater was set at 0.00025 $ kg−1 based on that in Israel(Cornish et al., 2004). Liquid fertizer (N = 10 %, P2 O5 = 4%, K2 O = 8 %) and calcium chloride were mixed such thatdaily application rate became constant throughout growing season. Totally applied nitrogen was 3.8 g m−2 foreach treatment. Since salinity of irrigation water was very
low and current version of WASH 2D can simulate only
one solute, “conceptual nutrient solute” assuming that allof solute in uptaken water by roots is also uptaken. Ionic
diffusion coefficient of sodium chloride was used. Any
adsorption, precipitation, nor chemical reaction were notconsidered. We did not consider the effect of uptake ofnutrient on growth and assumed that growth depends simply on cumulative transpiration regardless of nutrient uptake.

論文：Determination of irrigation depths using a numerical model and weather forecast

19

Soil
Soil of the field was sand whose hydraulic properties areshown in Fig. 2. Solute transport parameters such as dispersivity (0.59 cm) and dependence of tortuousity factor
for ionic diffusion on water content were also measured
in laboratory (Fujimaki et al., 2012). Independently measured thermal properties such as dependence of thermal
conductivity and albedo on water content and were also
used. Thermal conductivity, kh (W cm−1 K−1 ), is given as
a function of water content:(kh = ah +bh

)
[
(
) ]
θ
θ eh
−(ah −dh ) exp −ch
(18)
θsat
θsat

where θsat is saturated θ , ah , bh , ch , dh , and eh are fitting parameters. We used values of 0.0061, 0.0032, 22.6,
0.0015, and 1.46, respectively. Albedo, αR , is expressed
as a function of average volumetric water content in top 1
cm, θ :

αR =αmax − αminb

1 + (aal θ ) al

+ αminFig. 2 Hydraulic properties of Tottori sand used in thisstudy.

(19)

where αmax , αmin , aal , and bal , are fitting parameters. Values of 0.224, 0.159, 8 and 3, respectively, were used forthe sand.
Plant
A cultivar of potato, May-Queen, was sown on April 14.
Since stress response function of the plant has not been determined, tentatively set parameter values listed in Table 1
were used. These values are comparable for canola (Yanagawa and Fujimaki, 2013). As shown in Fig. 3, parameter values for crop coefficient function (Eq. (16)) were
updated twice. First upward modification was made because we realized that with original parameter values, total transpiration would be only about 120 mm even without drought stress. Second downward modification wasmade because leaf area index measured on July 6 was only
0.59 and further increase was not expected. Parameters
values for root distribution and LAI were chosen basedon data obtained through growth measurement. Water
use efficiency was set at 0.003. Unfortunately, disease ofpotato blight (Phytophthora in f estans) was widespreadin June particularly for treatment-A in spite of applicationof fungicide and yield was thus smaller than general forboth treatments. Potato was harvested on July 21.
3.2 Numerical modeling
Width of the calculated region was 45 cm assuming symmetric system and depth of lower boundary was 50 cm.
Horizontal space increment was constant at 1 cm while
vertical increments were progressively increased from 0.25
cm at the top to 2.5 cm at the bottom. Time step was automatically regulated between 0.054 and 1.8 second.

Fig. 3 Crop coefficient for transpiration as a function of cumulative transpiration. Parameter values for crop coefficient
function were updated twice for representing plant growthwell during field experiment.

Table 1 Parameter values of plant stress response andgrowth properties.
Parameter

Value

Equation numberψ50 (cm)
ψo50 (cm)
p

−1000
−3000
3

Eq. (3)

brt
drt
grt
zr0

1
?
30
2

Eq. (4)

aLAI
bLAI

1
−0.05

Eq. (15)

aKC
bKC
cKC

0.4
−0.3
0.1

Eq. (16)

adrt
bdrt
cdrt

40
−0.4
5

Eq. (17)

20

土壌の物理性Initial condition for water flow was constant pressure
head at −40 cm while that for solute was constant at 0.1
g L−1 . Initial conditions for each two-days run were final
water content (including hysteretic parameter values) andsolute concentration of last run. Lower boundary condition
for water flow was gravitational flow while that for solutetransport was zero concentration gradient. Both right andleft boundary were impeameable. Upper boundary condition was atmospheric and drip irrigation was applied totopmost and leftmost element as a source term.

第 136 号(2017)

tion and root water uptake. On the other hand, the model
could relatively accurately simulate the internal drainage
which occurred after each irrigation for (x, z) = (0, 45) andnearly bare condition for (x, z) = (40, 5). In the (40, 5),daily change in water content was more significant par-4. Results and Discussion
Fig. 4 shows both measured and simulated LAI together
with measured biomass data. For the twice measurements,
the LAI was higher for the treatment S on June 9 despite
the biomass was almost the same. This trend was observed
until July 6. This relatively higher LAI might have led subsequent larger dry matter production, i. e., final dry matterproduction for the treatment S and the treatment A were
2.9 t ha−1 and 2.0 t ha−1 , respectively. However, both were
smaller than normal potato cultivation which have been reported to vary between 3.5 and 6.0 t ha−1 (Battilani and
Mannini, 1993). This poor growth may be due to late sowing date and potato blight. On the other hand, on June 8,
we realized that simulated LAI was getting overestimated,because we did not consider this poor growth until then.
This poor growth led the transpiration lower than that under normal growth. Hence, virtual net income during these
periods was also overestimated. Then we adjusted cumulative transpiration value downward (from 3.1 to 1.3 cm) sothat LAI dropped to near the actual one. Measured biomass
on June 8 was 34 g m−2 (0.34 t ha−1 ) and by dividing itwith the water use efficiency of 0.003, estimated cumulative transpiration of 1.1 cm was obtained. Considering
growth on June 9, cumulative transpiration was set at 1.3
cm. In simulations, we often assume ideal plant growth.
However, it is important to adjust the parameter for growthdepending on the cultivation processes and environment(including disease and pestilence). When poor growth isexpected owing to poor pest or disease control, lower water use efficiency or lower crop coefficient which results inlower transpiration should be used. We adjusted crop coefficient to reflect damage by disease. Thus, we will be able
to show more accurate virtual net income to farmers.
Fig. 5 shows the comparison between measured andsimulated water contents for update run (using actual
weather data) for a selected period. Legends x and z represent the horizontal distance from the drip tube and soil
depth, respectively. The results show that the model underestimated water content at (x, z) = (0, 15 cm). Thismight be due to an over-estimation of potential transpira-Fig. 4 Time evolution of leaf area index (LAI) and biomass.
Solid and dashed lines with circles are measured LAI fortreatment-A and treatment-S, respectively. Dot-and-dashline is simulated LAI. Solid and dashed lines with inverted
triangles are measured biomass data for treatment-A andtreatment-S, respectively.

Fig. 5 a) Measured and simulated volumetric water contents for treatment-S. b) Location of TDR probes. Legends x
and z represent the horizontal distance from the drip tube andsoil depth, respectively. Filled circle, square, and inverted triangles are the measured water contents and solid and dashedlines are simulated ones at three locations.

論文：Determination of irrigation depths using a numerical model and weather forecast

Fig. 6 Comparison of measured (dashed line) and simulated(solid line) evapotranspiration rate. Simulated evaporation
rate (dot line) also shown for comparison.

Fig. 7 Time evolution of cumulative rainfall and irrigation depths. Solid line and dot-and-dash line represent cumulative irrigation depths for treatment-S and treatment-A,
respectively.

ticularly after May 29. This was due to rainfall events in
those days as shown in Fig. 5. These results confirmed thatthe proposed scheme worked relatively well for irrigation
scheduling in this field experiment. Therefore, numericalsimulation of water flow and crop growth will provide relatively good prediction of crop water requirement.
In the proposed scheme, accurate estimation of evapotranspiration (ET) is important to optimizing irrigation
depth. If simulated ET largely deviated from measured
ones for daily scale, it means the first term of Eq. (6) is notaccurately estimated. Fig. 6 compares measured and simulated ET for a selected period. Evaporation rate is averagevalue across the soil surface. The simulation model tended
to overestimate ET owing to unexpectedly slow growthof leaf area. We also have discrepancy in hourly pattern.
Measured ET tends to more sharply rise in early morningand more steeply drop in early afternoon. One of these reasons would be underestimation in evaporation rate. Sharp
drop in the afternoon might partly be due to the formationof dry sand layer. In the simulation, however, evaporation
rate did not sharply decrease owing to larger leaf area thanactual one. Evaporation rate tends to decrease as leaf area

21

increases owing to shadowing and enhanced aerodynamic
resistance (van Bavel and Hillel, 1976). Both mechanisms
are incorporated into the numerical model and therefore
an overestimation of leaf area leads to an underestimationof evaporation rate. Thus, in the simulation, evaporation
rate persisted at low rates in the afternoon. Second reason might be a measurement error owing to thermal deformation of drip tube. Edge of the lysimeter was raisedby about 3 cm above the ground and two drip tubes wereon the lysimeter. In early morning when temperature was
sharply increasing, the polyethylene drip tube might havebecome loosing and it might have eased downward tension
and led underestimation of weight. Opposite mechanism
might have occurred in the afternoon.
Fig. 7 shows the time evolution of rainfall and irrigation.
Temporal change of cumulative irrigation depth for the
proposed scheme was similar to that for the automated irrigation. This result is in agreement with the previous study(Fujimaki et al., 2014). These results suggested that the
new scheme can alter automated irrigation system. Moreover, total amount of water applied was 86 mm for automated irrigation while proposed scheme applied 63 mm.
These low total amounts were due to abundant water supply by rainfall. Still, potato might not have survived without irrigation under drought period such as from May 19 to
May 28. The proposed scheme, treatment S, could save 27% of irrigation water comparing with treatment A. However, saving irrigation water could not always be expectedby using the proposed scheme. Fujimaki et al. (2014) reported that the proposed scheme gave 1.5 times more irrigation water compared with automated irrigation schemein sweet corn cultivation. Because the simulation model
did not consider the damage in the monitored plants as discussed above, ET was overestimated. Thus, saving irrigation water using the proposed scheme is largely affected by
ET estimation.
Despite the treatment S received a 27 % lower irrigation water than treatment A, it attained higher yield by 15%. As a result, the treatment S achieved higher net income than treatment A (1.28 times) as shown in Fig. 8.
Income corresponds to first term of Eq. (6) but we applied actual fresh weight of tuber and producer price inJapan (0.7 $ kg−1 ). Although we set price of crop fromproducer price of potato in the US in the optimization, weused price in Japan since we obtained negative net income
if we employed price in the US. Net income was calculated by subtracting cost for water and fertilizer from income. This result may demonstrate that not only saving
cost for equipment required for automated irrigation, theproposed scheme can enhance net income compared with
an automated irrigation scheme. This result could not always be obtained (Fujimaki et al., 2014), because the result

22

土壌の物理性

第 136 号(2017)

Finally, it might be worth reporting the accuracy of
weather forecast. Root mean square error between forecasted and actual daily effective rainfall was 8.2 mm asshown in Fig. 9. In the analysis, we set effective rainfall
as 30 mm. We had eight actual rain events when no rain
was forecasted. The largest error occurred in July 5 when
84 mm was forecasted while actual rain was 9 mm. In addition to error in prediction due to insufficient modelingand inaccurate parameter values, advantage of optimization may be partly offset by inaccuracy in weather forecast.
Still, we may expect that the accuracy will improve year by
year.
Fig. 8 Comparison between income and attained net income. ‘Automatic’ and ‘Simulated’ represent treatment-A
and treatment-S, respectively.

5. Conclusion
We presented a scheme for determining irrigation depth
using a numerical model of crop response to irrigation andquantitative weather forecast. A concept of virtual income
is presented to optimize irrigation depth for each irrigationinterval. A field experiment was carried out to compare
net income attained by the presented scheme with that by
the automated irrigation method. Results showed higher
net income of presented scheme although the accuracy ofsimulation needs to be improved in terms of potential transpiration, particularly. These results were compared with
our previous works reported by Fujimaki et al. (2014).
Based on these results together with previous works, weconcluded that proposed scheme can establish proper irrigation scheduling like automated irrigation systems without high initial investment.

Acknowledgments

Fig. 9 Comparison between forecasted and actual daily
rainfall. The dot line is the 1:1 line.

was sensitive to the crop growth. Even so, we could confirm that the new scheme can attain a similar net income
to automated irrigation scheme. Fujimaki et al. (2014)
compared net income by automated system and proposed
scheme in two experiments. Regarding to an experimentusing barley carried out in southern Tunisia, net income byproposed scheme was lower (0.86 times) than that by automated system. As for Corn in Tottori, opposite results(1.05 times) was obtained. Thus, summing up previous
three experiments, proposed scheme outperformed for two
in three trials.
Moreover, higher yield for treatment S might partly be
attributed to lower nutrient loss due to lower deep percolation by considering forecast rain events. Simulated uptakeof nutrients for treatment-A was lower than that for S by
39 %. Further evaluation of such a side effect of present
scheme requires further intensive studies on nutrient balance in the future.

We thank the staffs of Arid Land Research Center who
secure such facilities to perform that research. We also
thank to Mr. Mohamad Mahdavi for his great assistanceto our field work. We also thank Dr. Teruhito Miyamoto,organizer of this special issue, for his suggestions and help
to improve this paper.

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土壌の物理性24

要第 136 号(2017)

旨

天気予報と土壌物理シミュレーションモデルを組み合わせ，純収入を最大化させる灌水量決定法を提示した．毎回の潅水量を最適化するため，次の灌漑までの蒸散量に比例する仮想収入の概念を導入した．
砂丘圃場においてジャガイモを供試作物とした点滴灌漑による実験を行い，水分モニタリングに基づく自動灌漑区と，提示された方法に基づく灌漑区とで純収入を比較することにより，後者の効果を評価した．その結果，蒸散量の過大評価による水分の過小評価などの改善すべき課題が明らかとなったものの，提示された方法では 27 % 少ない潅水量で 15 % 多い収量が得られ，より高い純収入が得られた．これまでの圃場実験結果もふまえると，提示された方法は，少なくとも自動灌漑システムと同程度の純収入を与えうる，と言えよう．
キーワード：灌漑，天気予報，蒸散，純収入