Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .87.
of the irrigation return flow under different situations.
Return flow in Taiwan has been studied by many researchers. For example, Chien et al. (2000)
measured the amount of the return flow from a rice paddy field in northern Taiwan as 0.47 mm/day for
an increase inflow of 1 mm/day on a farm pond when the inflow was 3.18 mm/day. According to
several studies in Taiwan, irrigation return accounts for 10% to 60% of the total irrigation water in rice
paddy fields (Chien et al. 2000, Chien 2003). Although these researchers have provided many
interesting preliminary results, it seems that no systematic studies have been conducted on irrigation
and infiltration behavior in rice paddy fields. The purpose of this research was to construct a water
balance model to estimate the amount of return flow in rice paddy fields. In this research, a simple
computation framework is applied to include irrigation application in cropping seasons. The research
results may be of great interest to the managers attempting to provide a hydrograph of return flow and
an estimate of long-term return flow.
Methodology
At the initial stage of irrigation or precipitation, there is no surface runoff from a rice paddy field
because all of the irrigation water or precipitation is impounded by field ridges. As precipitation falls,
runoff may occur when the depth of the water exceeds the height of the field ridge. After the
cessation of the precipitation, part of the water trapped in the paddy field evaporates into the
atmosphere, part of the water infiltrates into the ground, and the rest stays on the surface, as shown in
Fig. 1. As the purpose of this research stated in the previous section, the research scope is limited in
one common irrigation block which consists of 5 or 6 irrigation units. There are other irrigation units
in the upstream and in the downstream. The units downstream may use return flow from the units
upstream. The study area which was used as a demonstration will be described in more details in the
following section.
.88. 一○一年度研究年報
Precipitation
Irrigation
Evapotranspiration
Surface return flow
Canal Return flow Return flow Return flow
Muddy Layer above hardpan above hardpan through levee
Hardpan
Non-puddled Subsoil Deep percolation Deep percolation
Groundwater Groundwater
inflow outflow
Fig. 1 Inflow and outflow for paddy field
The water cycle of a rice paddy hydrologic system can be characterized with a simple mass
balance equation where the amount of water stored may be related to the rate of inflow and outflow.
The general water budget equation (mass balance equation) is:
I − O = dS (1)
dt
in which I is input, O is output, t is time and S is storage. In general, mass balance equations can be written for
both surface water and subsurface water systems. When the paddy field is considered as a control volume, the
water budget equation, Eq. 1 is further written as follows:
P + IN + Ru + Rhu + Rlu − ET − DF − R − Rh − Rl = ∆S (2)
where P is the precipitation over the period of interest, IN is the irrigation flow, Ru is the surface
return flow from upstream, Ru is the subsurface return flow above the hardpan from upstream, Ru
h l
is the subsurface return flow through the levee from upstream, ET is the evapotranspiration, DF is the
deep percolation, R is the surface return flow (runoff) out of the paddy field, Rh is the subsurface
return flow above the hardpan out of the paddy field, Rl is the subsurface return flow through the levee
out of the paddy field and ∆S is the change in water storage on the paddy field.
This research developed a water balance model that describes evapotranspiration, infiltration, and
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .89.
return flow on the paddy field. The model consists of three modules, namely crop evapotranspiration
modules, infiltration module and return flow module. The FAO Penman-Monteith equation is
applied for estimating potential evapotranspiration. Then, evapotranspiration is estimated with the
crop coefficient. The Infiltration is calculated by the Horton equation (Aron 1992) which assumes an
exponentially decreased infiltration. Furthermore, the effect of soil moisture content on percolation and
infiltration is considered. The return flow in the modeling consists of three parts: the subsurface return flow
above the hardpan, the subsurface return flow through the levee, and surface return flow. Surface return flow is
calculated by applying the levee function. Darcy’s Law is applied for estimating subsurface return flow. The
three modules are explained in more detail in the following sections.
Crop Evapotranspiration Module
The FAO Penman-Monteith equation (Allen et al. 1998) is applied to estimate the reference
evapotranspiration ET0 (mm day-1),
0.408∆(Rn − G) + γ T 900 (es − ea )
∆+γ + 273 u2
ET0 = (3)
(1 + 0.34u2 )
where Rn is net radiation at the crop surface (MJ m-2 day-1), G is soil heat flux density (MJ m-2
day-1), es is saturation vapor pressure (kPa), ea is actual vapor pressure (kPa), T is air
temperature at 2 m height ( 0 C ), u2 is wind speed at 2 m height (m s-1), ∆ is slope of vapor
pressure curve (kPa 0 C -1 ), and γ is psychrometric constant (kPa 0 C -1).
Crop evapotranspiration ET0 , is calculated by multiplying the reference evapotranspiration by a
crop coefficient Kc , and is limited by the sum of the water of surface ponding storage and soil storage:
ET (t) = min[ET0 ⋅ Kc ; D(t) + S(t)] (4)
where D(t ) is the surface ponding water at time t , and S (t ) is the upper layer soil moisture
storage at time t . The value of the crop coefficient, Kc is dependent of various crop growing
period and is in the range of 0.60~1.50. The crop coefficient is determined by implanting date, the
growing phases and periods, and is location-dependent. The values of Kc by Chien (2003) were
adopted for model applications in this research.
Infiltration Module
Infiltration, estimated by the Horton equation, is modeled as a function of time. The module
.90. 一○一年度研究年報
assumes that infiltration begins at some rate and exponentially decreases until it reaches a constant rate.
The module requires three parameters: maximum infiltration rate f0 , steady-state infiltration rate f c ,
and constant k (cf. Chow et al. 1988; Wu and Haith 1993; Wu et al. 2001). Besides infiltration, the
effect of the underground percolation is also taken into account, and the soil drainage function, d(t),
proposed by Bauer (1974) is then used. Therefore, the rate of potential infiltration into the soil and
the percolation from the top soil to the lower layer soil at time t are given respectively as
f (t) = fc + ( f0 − fc ) exp(−kt) , (5)
d(t) = fc[1− exp(−kt)] . (6)
The initial conditions for dry soil can be regarded as the infiltration rate being equal to the maximum
infiltration capacity f0 , with no percolation. As time goes by, the infiltration rate gradually
decreases, while the percolation increases. According to hydrologic continuity, the change in soil
water storage equals the difference between infiltration and percolation. With Eq. 5 and Eq. 6, the
following is obtained
dS = f (t) − d(t) = fc + ( f0 − fc )exp(− kt)− fc[1− exp(− kt)] = f0 exp(− kt) . (7)
dt
With initial condition of dry soil assumed, the soil moisture storage at time t is then
S(t) = f0 [1 − exp(− kt)]. (8)
k
When time t goes to infinity, the soil moisture storage reaches to its maximum Ss and it is
Ss = f0 (9)
k
The deep percolation can be represented as
DF (t) = fcS (t) . (10)
Ss
The Horton equation relates to the infiltration rate as a function of time. The equation for calculating
infiltration, similar to the one proposed by Aron (1992) is applied in this research:
f p (t) = fc + ( f0 − f S s − S ( t) (11)
)
c Ss
where f p (t) is the potential infiltration rate (mm/hr) at time t, and Ss is the soil moisture content at
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .91.
saturation (mm). Ss is usually regarded as the basic soil property which can be obtained in a
standard laboratory test, but the air possibly trapped in the soil may affect its value. The potential
infiltration sets a limit for the effective infiltration caused by rainfall depth and the flow depth in the
paddy field. The effective infiltration is always less than the potential infiltration. Infiltration was
restricted by the available water in the surface pond store after evapotranspiration.
[ ]min
f (t ) = f p (t), D(t) − ET (t) , for D(t) ≥ ET (t)
0, for
e (12)
D(t) ≤ ET (t)
Therefore, soil moisture storage for time t + ∆t can be estimated by: (13)
S (t + ∆t) = ( fe (t) − d (t) − Rh (t))∆t + S (t)
where ∆t is one day.
Return Flow Module
The calculation for return flow in the modeling consists of three parts: surface return flow,
subsurface return flow above the hardpan, and subsurface return flow through the levee.
Surface Return Flow
To investigate the surface return flow during irrigation or rainfall events, this research assumes
that excess of water in the paddy fields is drained through a levee. It is also assumed that the change
of soil water content is negligible during a short period of irrigation or rainfall. In addition, with the
assumption that the topsoil is saturated at the beginning of the precipitation, the infiltration rate at the
moment is considered as constant.
In case the height (head) of the water surface is higher than the outlet but is lower than the levee, the
surface return flow is just the outflow from the paddy fields through the outlet. Applying the
equation of energy at two sections where one is sufficiently upstream and another one is at the outlet,
the surface return flow (the outflow from paddy fields) R can be calculated as the following (Graf
1998):
2 Hc U 2 3 U12 32
3 1 2 2g
R = LDCD 2g + 2g − (14)
where LD is the effective length of the levee, CD is the dimensionless discharge coefficient of the
.92. 一○一年度研究年報
outlet, g is acceleration of gravity, and H c is the height (head) of the water surface above the
outlet. The surface return flow is measured sufficiently upstream from the outlet and U1 is the
average velocity in the approach section measured at the flow depth of Hc .
Eq. 14 can be rewritten as:
R = LDCD 2 2 g H 3 2 (15)
3 c
in case of the kinetic energy, U12 2g , is neglected, notably for the case of a small approach velocity,
U1 . Let the outlet coefficient be defined as
Cw = CD 2 2g . (16)
3
Then Eq. 15 becomes
R = CwLD H c3 2 . (17)
When Hc is increasing and is higher than the levee, the surface return flow R is the sum of the the
outflow from the paddy fields over the levee as well as through the outlet. R becomes
R = Cwb Leb H 3 2 + CwLD Hc3 2 (18)
b
where Cwb is the levee coefficient, Leb is the effective levee length deducted by the outlet length,
and Hb is the height of the water surface over the levee.
Return Flow through Levee
Because the upper boundary of a levee is the water table, with an elevation equals to the hydraulic
head h, the boundary becomes part of the solution when predicting the hydraulic head distribution in
the aquifer. The Dupuit assumptions simplify such problems to the point where simple analytic
results can be developed. The Dupuit assumptions are: (1) streamlines are assumed to be horizontal
and equipotentials are assumed to be vertical; (2) the hydraulic gradient is assumed to be equal to the
slope of the water table and to be invariant with depth.
Darcy’s law gives the one dimension flow as
Rl = −K1h1 dh1 (19)
dx
in which R l is the return flow per unit length through levee, h1 is the hydraulic head of levee, K1
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .93.
is the hydraulic conductivity of levee. Following the Dupuit’s assumptions, i.e., (1) the velocity of
the flow to be proportional to the tangent of the hydraulic gradient instead of the sine; (2) the flow to
be horizontal and uniform everywhere in a vertical section, Eq. 18 can be transformed into the
following form:
( )Rl K1
= 2b h02 − hL2 (20)
where h0 is the hydraulic head on the upstream side of the levee, hL is the hydraulic head on the
downstream side of the levee or on the canal side, and b is width of the levee.
Return Flow above Hardpan
Within the return flow domain above hardpan for paddy fields, it is assumed that the water table is
below the top of the hardpan; hence atmospheric pressure prevails at the bottom of the hardpan. The
total flow rates ( qt ) are related to a fictitious value calculated by supposing only one layer below the
levee, the thickness of which is equal to the total thickness of the hardpan and muddy layer (m). The
hydraulic conductivity ( K * ) of the fictitious layer, which was derived and a mathematical
combination of hardpan and muddy layer, is equal to the parameter of the more pervious original layer
(Kovacs, 1981). The equations by Kovacs (1981) are considered suitable for paddy environment.
Kovacs’s equations provide better analytical solutions of horizontal and vertical infiltration for the soil
with sublayer of low hydraulic conductivity. The observation data for related studies either in paddy
fields or sandbox experiments show that Kovacs (1981)’s results are applicable in the analyses of
paddy field study. In paddy fields ( K2 > K3 ), the total flow rate qt can be expressed in the form of
mathematical equations (Kovacs, 1981) as well:
qt = K *(h2 − h0 ) sinh −1 (1.5 m) (21)
π b
in which
K* = K 2[ K3 + (1 − K3 ) sinh−1(1.5 m1 ) (22)
K2 K2 b]
sinh−1(1.5 m )
b
K2 is the hydraulic conductivity of muddy layer and K3 is the hydraulic conductivity of hardpan.
In this research the experiment results by Chien in 2003 are referenced for the determination of the
hydraulic conductivities K1 , K2 , and K3 . Chien (2003) conducted field experiments for
.94. 一○一年度研究年報
infiltrometer and falling head permeameter tests and the values of the hydraulic conductivities are
described in the next section. The return flow (flow rates through the muddy layer, Rh ) related to
the total flow rates can also be approximated (Kovacs 1981):
sinh−1[0.6 m m1 ( K3 K2 ) 2
3
)
( ]
bm
Rh = qt sinh−1(0.6 m) (23)
b
Unsaturated flow in the zone of paddy field can be analyzed by Eq. 21; however, the unsaturated
hydraulic conductivity Ku is a function of the water content as well as the negative pressure head
(Todd 1980). Water content data fit the following form
Ku = ( SD (t) − S0 )3 (24)
K2 1− S0 (25)
Rearrangement gives
Rh = − K ( S D (t) − S0 )3[ K3 + (1 − K3 )
1− S0 SD (t) − S0
2 S D (t) − S0
1− S0 1− S0
K 2 ( )3 K2( )3
sinh −1 (1.5 m1 ) sinh −1[0.6 m ( m1 (K3 K2 2 ]
b b m
) )3
] (h2 − h0 ) sinh −1 (1.5 m)
sinh−1(1.5 m ) sinh−1(0.6 m) π b
bb
in which S0 is the threshold saturation, and SD (t) is the degree of saturation at time t.
Model Applications
The model described above was applied to a rotational block of the Taoyuan Irrigation
Association (TIA), which is located in the northwest part of Taiwan. Irrigation Associations in
Taiwan are responsible for the construction and maintenance of irrigation facilities as well as for the
delivery of irrigation water to farm fields within their districts. There are about 340 rotational blocks
in the TIA. A rotational block is an irrigation operation element which is equipped with a pond (or
sometimes two ponds), irrigation lateral canals and drainage ditches. Usually a rotational block is of
about 50 hectares. As a rule of thumb, there are usually five units in a rotational block. The
irrigation operation is scheduled the same for a unit, which means paddy fields in the unit start and
stop irrigation water applications at the same time. The climate for the area is sub-tropical with an
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .95.
annual average temperature of about 21℃ and an average annual precipitation of about 1,900 mm.
The summer is humid and warm, while the winter is relatively cold. The soil in the TIA area consists
of four types: sandy loam, sandy clay, clay loam, and light clay soil.
This research selected rotational block No. 11-2 of the TIA as the study area. The water supply
for the rotational block is operated by the Group No. 11-2 of the Kwanyi Operation Station, TIA.
The irrigation water is carried by Lateral canal No. 11 (connected to the Taoyuan main canal) and its
location is depicted in Fig. 2. Chien and Wu (2003) charted the irrigation network system for
rotational block 11-2 as Fig. 3 to investigate the use of return flow in the area. Each square block
represents a single unit for irrigation. A circle with an identification number stands for the site
between inflow and outflow in the open ducts of the unit of interest. For example, the inflow points
for unit 3 are A31, A32, A33, A34, A35 and A39, while the outflow points are A310, A311, A312, A37
and A53. The outflow of unit 3 (through A310, A311, A312, A37 and A53) can be the inflow to unit
4 or unit5. The irrigation water supplied by Lateral canal No. 11 to unit 4 and unit 5 can be reduced
by using the return flow from unit 3. Rotational block No. 11-2 consists of five units which are
numbered from 1 to 5 (see Fig. 3). The irrigation area of rotational block No. 11-2 is 8.38, 8.33, 7.70,
7.53 and 14.61 hectares for units 1, 2, 3, 4 and 5, respectively.
The time period for the model simulation is the first rice cropping term in 1999 which is from
February 16 to July 10. Fig. 4 shows precipitation and irrigation water for the study period. The
climatologic data, including air temperatures, dewpoint temperature, relative humidity, precipitation,
wind speed, wind direction, net radiation, evaporation, soil heat flux, soil temperature, daylight hours,
solar radiation and soil moisture, were recorded at the paddy fields for the study period. During the
crop growing period, the paddy fields are to be drained twice. The first drainage is conducted so that
fertilizer can be applied. The drainage of the paddy field is also for the soil exposed to the sunshine
to provide seedlings more active tilling environment. This drainage duration is from April 25 to
April 29. The second drainage is from June 29 till harvest time and it is prepared for convenience of
harvesting machine application. The drainage usually causes decreasing of the degree of saturation
for the paddy soil; therefore this research model allows soil saturation for the drainage periods is not
as high as the one for most crop growing period. During most crop growing period, it is a custom in
Taiwan that the farmers have the degree of saturation for the paddy soil kept above 85%.
.96. 一○一年度研究年報
Fig. 2 Location for rotational block 11-2 of the Taoyuan Irrigation Association
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .97.
A01 A13 A19
A02 Unit 1
A110
A03 A111
A11
A29
A12
Unit 2 A27 A26
A14 Unit 3 A25 A42
A16 A24 A28
A41
A15 A312
A311
A114 A310
A17 A18 A53 A44 A43 A46
Unit 5 Unit 4
A21
A22
A23
A31
A32
A39
A33
A34 A37
A35
A61 A51
A38
A52
A54 A45 A47
Fig. 3 The irrigation network system for rotational block 11-2
.98. 一○一年度研究年報
Rainfall Irrigation Water
Irrigation Water (cm)12.00 0
Rainfall (cm)10.0020
8.00 40
6.00 60
4.00 80
2.00 100
0.00 120
140
160
16-Feb-99
23-Feb-99
2-Mar-99
9-Mar-99
16-Mar-99
23-Mar-99
30-Mar-99
6-Apr-99
13-Apr-99
20-Apr-99
27-Apr-99
4-May-99
11-May-99
18-May-99
25-May-99
1-Jun-99
8-Jun-99
15-Jun-99
22-Jun-99
29-Jun-99
6-Jul-99
Date
Fig. 4 Precipitation and irrigation water for study period
Results and Discussion
The soil type for rotational block 11-2 is clay loam and its irrigation water requirement is 1,016
mm. Irrigation water requirement for the TIA is obtained by conducting field experiments and the
amount of irrigation water requirement consists of crop evapotranspiration and deep percolation. As
for the simulation, Table 1 lists the values for the parameters used in the water balance model. For
rotational block No. 11-2 in the first rice cropping term in 1999, the water balance model gives the
following results:
(1) The simulation results by the water balance model were split into two cases. Case A
simulated the present situation in which return flow was not used in irrigation, while Case B simulated
the situation in which return flow from upstream unit (e.g., unit 3) was used in the downstream units
(e.g., unit 4 and unit 5). The simulation results for clay loam (Table 1) told that the irrigation water
of 660.0 mm needed originally (from lateral canal No. 11) was dropped to 618.3 mm. It could be
seen that the return flow upstream of 47.7 mm was used in the downstream units. The outflow
(including evapotranspiration, deep percolation and return flow) were the same for Case A and Case B,
because the sum of the inflow (from irrigation water, precipitation and return flow upstream) for both
cases were the same.
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .99.
Table 1 Values for the parameters used in the water balance model
Parameters Values Parameters Values
b (cm) 30 K1 (cm/day) 5
H D (cm) 10 K2 (cm/day) 15
LD (cm) 30 K3 (cm/day) 0.5
Cw 1.4 m1 (cm) 20
Cwb 1.4 m2 (cm) 30
f c (cm/day) 1.5 f0 (cm/day) 15
Table 2 Simulation results of the water balance model
Inflow Outflow
Irrigat Precipi Return Effective Evapo- Deep Return Flow Consumption
ion -tation Flow Rainfall transpir Percolati
Soil Type Upstre Subsurfa Surface
Water am ation on ce Return Return Sum
Flow Flow
(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm)
(4)=(2)- (6) (7) (9)=(7)+
(1) (2) (3) (8) (5) (8) (8) (10)=(1)+(3)+(4)
Case A
Clay loam 666.0 755.5 0.0 310.5 502.8 429.5 44.2 445.0 489.2 976.5
Sandy 0.0 358.3 502.8 664.9 40.5 397.2 437.8 1208.2
Loam 849.9 755.5 0.0 402.6 502.8 538.8 40.1 352.9 392.9 1081.6
Sandy 0.0 260.2 502.8 336.0 45.8 495.3 541.1 884.6
Clay 679.0 755.5
Light clay
soil 624.4 755.5
Case B
Clay loam 618.3 755.5 47.7 310.5 502.8 429.5 44.2 445.0 489.2 976.5
43.1 358.3 502.8 664.9 40.5 397.2 437.8 1208.2
Sandy 43.1 402.6 502.8 538.8 40.1 352.9 392.9 1081.6
Loam 806.8 755.5 49.4 260.2 502.8 336.0 45.8 495.3 541.1 884.6
Sandy
Clay 635.9 755.5
Light clay
soil 575.0 755.5
(2) Because irrigation water requirement is dependent of soil types for the paddy fields, it is of
interest to see the Case A and Case B simulated for various soil types. Besides clay loam, Table 1
lists the simulation results for sandy loam, sand clay, and light clay soil. Irrigation water requirement
.100. 一○一年度研究年報
are 1,271, 1,058, and 968 mm for the sandy loam, sandy clay and light clay soil, respectively in the
TIA. The simulation results (Table 2) showed that the irrigation water of 849.9 mm, 679.0 mm and
624.4 mm were dropped to 806.8 mm, 635.9 mm and 575.0 mm for sandy loam, sandy clay, and light
clay soil, respectively. The decreases in irrigation water are supplemented by the return flow
upstream which is 5% to 8% of the irrigation water in Case A.
(3) To show the importance of return flow used in irrigation application, it is to express the
percentage of the outflow for return flow, deep percolation and evapotranspiration. The simulation
was conducted for the four soil types: sandy loam, sandy clay, clay loam, and light clay soil whose
contents of clay are increasing. Fig. 5 shows the percentage from the results in Table 1. The
percentages of return flow and evapotranspiration for various soil types are increasing as the contents
of clay are increasing. The percentages of return flow are from 27% to 39%, and the
evapotranspiration are from 31% to 37%. On the other hand, the percentages of deep percolation are
decreasing as the contents of clay are increasing. The percentages of the deep percolation are from
42% to 24%.
100%
Return flow, deep percolation and 90%
evapotranspiration accounting
percentages of outflow 80%
70%
60%
50%
40%
30%
20%
10%
0% Sandy Clay Clay loam Light clay soil
Sandy Loam
Return Flow 27% 27% 34% 39%
Deep Percolation 42% 38% 31% 24%
Evapotranspiration 31% 35% 35% 37%
Soil type
Fig. 5 Return flow, deep percolation and evapotranspiration accounting percentages of outflow
(4) The return flow in the simulation includes subsurface return flow and surface return flow.
Surface return flow mainly comes from significant precipitation. When there is precipitation in the
rotational block, the units both upstream and downstream have almost the same amount of
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .101.
precipitation. The unit downstream may not need to use surface return flow due to precipitation from
upstream of the unit upstream. It is of interest to see the return flow without taking into account of
surface return flow. The percentages thus calculated from Table 1 are shown in Fig. 6. Fig. 6
gives the similar percentage trends as in Fig. 5, i.e., the percentages of the return flow and
evapotranspiration for various soil types are increasing as the contents of clay are increasing, while the
percentage of the deep percolation are decreasing as the contents of clay are increasing.
(5) The simulation time period is from February 16 to July 10 in 1999. The depth of ponding
water, subsurface return flow and degree of saturation for the soil of muddy layer during the time
period are shown in Fig. 7. The depth of ponding water is the height (head) of the water surface at
the time of interest, and it may be zero if there is no ponding. For example, at the beginning period
of July in Fig. 7 there is no ponding water and the height of the water surface is zero. It is seen in Fig.
7 that the subsurface return flow was increasing as the depth of ponding water was increasing. The
degree of saturation for the soil was above 85% for the entire simulation period except on the two
periods of April 25 to April 29 and June 29 to harvest time. The two periods was scheduled for
drainage of the paddy fields.
Subsurface return flow, deep percolation 100%
and evapotranspiration accounting
percentages of consumption 90%
80%
70%
60% Sandy Clay Clay loam Light clay soil
50%
40%
30%
20%
10%
0%
Sandy Loam
Subsurface Return Flow 3% 4% 5% 5%
Deep Percolation 55% 50% 44% 38%
Evapotranspiration 42% 46% 51% 57%
Soil type
Fig. 6 Subsurface return flow, deep percolation and evapotranspiration accounting percentages of consumption
.102. 一○一年度研究年報
Depth of Ponding Water Subsurface Return Flow Degree of Saturation
25 120
Depth of Ponding Water (cm)
Subsurface Return Flow (0.1mm)
16-Feb-99
23-Feb-99
2-Mar-99
9-Mar-99
16-Mar-99
23-Mar-99
30-Mar-99
6-Apr-99
13-Apr-99
20-Apr-99
27-Apr-99
4-May-99
11-May-99
18-May-99
25-May-99
1-Jun-99
8-Jun-99
15-Jun-99
22-Jun-99
29-Jun-99
6-Jul-99
Degree of Saturation (%)
20 100
80
15
60
10
40
5 20
00
Date
Fig. 7 Depth of ponding water, subsurface return flow and degree of saturation during irrigation or
rainfall event (February 16-July 10, 1999)
(6) Based on the simulation results of Table 1, it was analyzed of a change of the irrigation water
for inflow by 20%, 40% or higher. For example, the irrigation water for sandy loam in Case A is
849.9 mm and it is changed to 953.6 mm for an increase of 20%. The irrigation water of 934.9 mm
was then input to the simulation model to obtain return flow of 527.4 mm. The simulations were also
performed for sandy clay, clay loam and light clay soil, and the results were drawn in Fig. 8. Fig. 9
and Fig. 10 show the subsurface return flow and deep percolation with changes of irrigation water for
inflow in Case A.
Return Flow (mm) 1600 Light Clay Soil
1400 Clay Loam
1200 Sandy Clay
1000 Sandy Loam
800 Irrigation Water (Seen Table 1)
600
400 200 400 600 800 1000 1200 1400 1600 1800 2000
200 Irrigation Water for Inflow (mm)
0
0
Fig. 8 Return flow by the water balance model
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .103.
75
Subsurface Return Flow (mm) 50
25 Light Clay Soil
Clay Loam
0 Sandy Clay
0 Sandy Loam
Irrigation Water (Seen Table 1)
800
700 200 400 600 800 1000 1200 1400 1600 1800 2000
600 Irrigation Water for Inflow (mm)
500
400 Fig. 9 Subsurface return flow by the water balance model
300
Deep percolation (mm) 200 Sandy Loam
100 Sandy Clay
Clay Loam
0 Light Clay Soil
0 Irrigation Water (Seen Table 1)
200 400 600 800 1000 1200 1400 1600 1800 2000
Irrigation Water for Inflow (mm)
Fig. 10 Deep percolation by the water balance model
It can be seen from Fig. 8 that the increases of irrigation water cause the increases of the return
flow. After the irrigation water reaches 849.9 mm for sandy loam (or 679.0 mm for sandy clay, 666.0
mm for clay loam and 624.4 mm for light clay soil), most of the increases in the irrigation water
provide the increases of the return flow. Fig. 9 shows that the increases of irrigation water result in
slight increases of the subsurface return flow, while Fig. 10 shows that the increases of irrigation water
cause almost no change in the deep percolation.
Conclusions
This research was trying to reduce the total irrigation water by accurately estimating the use of
return flow from the upstream units as a secondary supply of irrigation water to the downstream units.
The return flow from the model consists of surface return flow, subsurface return flow above the
.104. 一○一年度研究年報
hardpan, and subsurface return flow through the levee. In this research, a simple computation
framework for the water balance model was applied to the case in which the field irrigation applied in
different soil types for various presumed irrigation water. Five units of rotational block 11-2 in the
TIA was selected as the study area and real field data in the first cropping term in 1999 were used.
The water balance model described in this research can be useful in estimating the quantity of the
return flow for rice paddy fields in cropping seasons. The water balance model is intuitive and uses
readily available input data.
Two study cases were simulated in the research. Case A simulated the present situation using no
return flow at rotational block No. 11-2 and Case B simulated the one using return flow. The
decrease in irrigation water for Case B is supplemented by the return flow from upstream units, and
the amount is 7% of the irrigation water in Case A for which the soil type is clay loam. Besides clay
loam, three more soil types have been investigated in the research and they are sandy loam, sandy clay,
and light clay soil. The water balance model gives return flow for different soil types. The
percentages of return flow for the four soil types are increasing as the contents of clay are increasing,
and it is suggested that paddy fields with light clay soil result in more return flow. Most of return
flow is from surface part, which means precipitation over the paddy fields contributes the most.
More precipitation in the upstream causes more return flow in the downstream, however the return
flow in the downstream may not be used for irrigation.
The model in the research was applied in the situation when the irrigation system was designed so
that irrigation water can be delivered into five units of a rotational block. When the relation between
inflow and outflow is known, as the irrigation network system in Fig. 3, the model can be extended to
a larger irrigation system which is more than one rotational block. There are various time period for
irrigation operation in different areas. To obtain more insights about return flow in paddy fields,
different time periods of irrigation operation have to be taken into account in the future research.
References
1. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration, FAO Irrigation and
Drainage Paper 56, Food and Agriculture Organization of the United Nations, Rome, Italy
2. Aron G (1992) Adoption of Horton and SCS infiltration equation to complex storms, Journal of
Irrigation and Drainage Engineering, ASCE, 118(2):275-284
3. Bauer SW (1974) A modified Horton equation during intermittent rainfall, Hydrologic Science
Bulletin, 19(2/6):219-229
Modeling Irrigation Return Flow for the Return Flow Reuse System in Paddy Fields .105.
4. Bouman BAM, Wopereis MCS, Kropff MJ, ten Berge HFM, Tuong TP (1994) Water use
efficiency of flooded rice fields. (II) Percolation and seepage losses. Agricultural Water
Management, 26:291–304
5. Chien CP (2003) Experiments and Simulation for Infiltration and Return Flow in Paddy Fields,
PhD Thesis, Department of Civil Engineering, National Central University, Taiwan (in Chinese)
6. Chien CP, Lee TC, Lee YJ, Wu RS, Wen JC, Neou JC (2000) Measurement and primitive study
on the return flow for paddy field, Proceeding of the Conference of Chinese Society of
Agriculture Engineering in 2000, pp393-399 (in Chinese)
7. Chien, C. P., Wu RS, (2003) Experimental and modeling studies on return flow in the runoff
reuse system, Journal of the Chinese Agriculture Engineering, 49(3) : 30-45. (in Chinese)
8. Chow VT, Maidment DR, Mays LW (1988) Applied hydrology, McGraw-Hill Book Company,
New York, USA
9. Graf WH (1998) Fluvial hydraulics, John Wiley & Sons Ltd., Chichester, England
10. Gronning Engineering Company (1989) Ground water development, augmentation and exchange
plans for the city of Colorado Springs, Rep., Denver, Colorado
11. Huang HC, Liu CW, Chen SK, Chen JS (2003) Analysis of percolation and seepage through
paddy bunds, Journal of Hydrology, 284:13–25
12. Kovacs G (1981) Seepage hydraulics, Elsevier Scientific Publishing Company, New York, USA
13. Oad R, DiSpigno M (1997) Water Rights to Return Flow from Urban Landscape Irrigation,
Journal of Irrigation and Drainage Engineering, ASCE, 123(4):293-299
14. Oad R, Lusk K, Podmore T (1997) Consumptive use and return flows in urban lawn water use,
Journal of Irrigation and Drainage Engineering, ASCE, 123(1):62-69
15. Todd DV (1980) Groundwater hydrology, John Wiley & Sons Ltd, New York, USA
16. Tuong TP, Wopereis MCS, Marquez JA, Kropff MJ (1994) Mechanisms and control of
percolation losses in irrigated puddle rice fields, Soil Sci. Soc. Am. J. 58:1794–1803
17. Walker SH, Rushton KR (1984) Verification of lateral percolation losses from irrigated rice fields
by a numerical model, Journal of Hydrology, 71:335–351
18. Wetstein JH, Hasfurther VR, Kerr GL (1989) Return flow analysis of a flood irrigated alluvial
aquifer: Final Report to Wyoming Water Research Center and Wyoming Water Development
Commission
.106. 一○一年度研究年報
19. Wheeler WW and Associates (1987) Lysimeter Study, Rep., Englewood, Colorado
20. Wu RS, Haith DA (1993) Land use, climate and water supply, Journal of Water Resources
Planning and Management, ASCE, 119(6):685-704
21. Wu RS, Sue WR, Chien CB, Chen CH, Chang JS, Lin KM (2001) A simulation model for
investigating the effects of rice paddy fields on the runoff system, Mathematical and Computer
Modeling, 33: 649-658
Study on Agricultural Benefits by Increasing Capacity ….. .107.
Study on Agricultural Benefits by Increasing
Capacity of Water Ponds-A Case Study at Taoyuan
Paddy Fields
Agricultural Engineering Agricultural Engineering Agricultural Engineering
Research Center Research Center Research Center
Wen-Tsun Fang Chuan-Pin Chien Shu-Chen Chen
Abstract
In Taiwan agricultural water is frequently reduced or suspended for water resources re-allocation
during drought. To cope with such a situation, the irrigation district of the Shihmen Reservoir in the
northern Taiwan fully utilizes the functions of water ponds to regulate water resources so that
industrial and domestic water demands can be met. Constructing new water ponds is indeed able to
increase water storage for irrigation. However, when it is compared with the way of dredging or
excavating the existing water ponds, constructing new water ponds is not easily accepted by the public
because of environmental protection and land acquisition. Dredging water ponds is to obtain a larger
storage capacity so that more flexibility may be acquired in water allocation during drought.
Furthermore, it is practical in engineering point of view. This study presents a formulation of the
pond dredging problem for an irrigation system. The formulation is implemented as optimization
programs and applied to the area irrigated by the eighth lateral of the Taoyuan Irrigation Association.
The irrigation area is a paddy field of 2,283.8 hectares and consists of 32 water ponds whose storage
capacity is analyzed as dredging is conducted. Two models are presented, the first minimizes the
water extracted from the Reservoir in a cropping season, while the second maximizes agricultural
financial net benefits. Various allowable dredging ratios are used in the two models for different
study cases. The first model shows that the water supplied by the Reservoir decreases as the ratio
increases and it reaches the minimum (2,520.3 104m3) when the ratio is 0.5. The second model
displays that the maximum agricultural financial net benefit increases as the ratio increases and it
reaches the highest (NT$6,996 104) when the ratio is 0.5, a similar result to that of the first model.
However the dredging priorities of 32 water ponds for the two models are different because of the
optimization objectives. The simulation results provide references to the performance improvement
of water ponds. With such improvement, water ponds can possess an optimal capacity and a better
本篇論文原刊載於「Paddy and Water Environment，Vol.10(3)」，2012 年 9 月。
.108. 一○一年度研究年報
regional water allocation during drought can be achieved.
Keywords Water pond．Optimization．Dredging．Agricultural net benefit．Water allocation
Introduction
Significant problems of water shortage are contributing to a growing water crisis in many
countries. In Taiwan agricultural water occupies the largest share of water supply; however it is
frequently reduced or suspended for water resources re-allocation at the time of water shortage.
Consequently the agriculture departments of the government have to conceive approaches to utilizing
agricultural water more efficiently. The Shihmen Reservoir which is the largest multi-purpose
reservoir in the northern Taiwan supplies water for agricultural, domestic and industrial uses. The
agricultural district irrigated by the Shihmen Reservoir is of a pond irrigation system which is
designed to be capable of satisfying paddy water demands with conjunction functions of canals laterals,
sub-laterals, river diversion weirs and water ponds. The agricultural district with thousands of
irrigation ponds are of a unique geographic feature. Water ponds are providing not only their original
irrigation functions, but also other biological functions, such as waterbird diversity (Fang et al. 2009).
The pond irrigation system may be operated optimally to cope with the situations of water shortage
when a part of agricultural water is transferred to other sectors. However, there were still periods of
time with rainfall less than the minimum amount, and then inadequate stream input flow for the
Shihmen Reservoir occurred. With a limited reservoir capacity, a part of the irrigation areas of the
Shihmen Reservoir were set to lie fallow or transferred into upland farms at the first cropping terms of
Years 2002, 2003 and 2004 consecutively.
However, as the pond irrigation system is approaching its optimal irrigation functions (Liu et al.
2004) and water is more needed for domestic and industrial uses (Su 2003), there is an emergent need
to promote the functions of the existing water ponds. One of the promotion ways is to increase their
storage capacity by dredging (or excavating). The ponds have received water through canals and
laterals from the Shihmen Reservoir or through diversion weirs from natural streams. With heavy
rainfall or typhoons, the effective capacity of a pond is often reduced following sedimentation. The
effective capacity for a pond might be currently only 70% of the original designed capacity due to
sediment accumulation for years. Dredging can not only remove sediment accumulation to retrieve
the original capacity but also gain an additional capacity more than originally designed, which is in the
case that the impervious substratum of a pond is reconstructed at a deeper position. On the other
hand, pond dredging might render no alteration of farmland landscapes and then causes less
socioeconomic and environmental issues. With increases of the pond capacity, more water can be
Study on Agricultural Benefits by Increasing Capacity ….. .109.
provided to agriculture or even to industries by the optimal operation and management of the pond
irrigation system.
This study tries to investigate the problem of dredging the ponds of an irrigation system
belonging to the Taoyuan Irrigation Association (TIA) to increase the storage capacity by using the
optimization programming. The amount of water conserved and the agricultural net benefits due to
dredging the ponds are analyzed. The results of the dredging priority and volumes for the ponds are
to be provided to the TIA for references. With such improvements, the ponds of interests have the
optimal effective capacity so that the pond irrigation system will reach a minimal water supply from
the Reservoir or maximal agricultural net benefits.
An optimization model for cropping-plan placement on field plots by employing the mixed 0-1
programming technique was presented by Chono et al. (2011). The objective of the optimization
model is to reduce total nitrogen discharged from field plots to the downstream end of the drainage
canals in order to balance an achievement of economic goal and environmental conservation. The
trade-off curve and corresponding patterns of cropping-plan is useful in the decision-making for
irrigation management. Soundharajan and Sudheer (2009) proposed a framework for developing
optimal irrigation schedules for rice crop under water deficit conditions. Their study suggested that
the calibrated crop growth model combining with an optimization algorithm can lead to achieve
maximum water use efficiency for water deficit conditions. For an agricultural district, two
conflicting objectives, i.e., minimization of water withdrawal from a river and maximization of rice
production, are usually both required for management in agriculture. Zhang et al. (2007) presented a
stochastic multiobjective optimization model to allocate irrigation waters to blocks of paddy fields in
the district. The two conflicting objectives are expressed in linear objective functions. The
optimization model by Zhang et al. (2007) considered water source from a river only; however water
for irrigation may be from various kinds of sources. For a pond irrigation system, the conjunctive
operation with water from a reservoir, river diversion weirs and rainfall collection is usually scheduled
by irrigation associations. As for the conjunctive operation of water ponds irrigation, the Shihmen
Irrigation Association (SIA 1981; SIA 1989) gave basic in-situ operation rules. The AERC (1996)
and Fang & Peng (1996) used linear programming for the conjunctive operation of water ponds for a
sub-lateral with minimal water supply from the main canal; however, water quality was not discussed.
Chien and Fang (2000) took into consideration of river water quality for the optimal programming of
the combined operation at the Kwanfu canal irrigation area of the TIA. The operation efficiency of
the pond irrigation systems at the SIA and TIA from 1992 to 2001 was investigated by Chien and Fang
(2003). With “ten-day” as a traditional time period of water operation in Taiwan which will be
explained later, their result shows that the irrigation district of the TIA would have 12-19 ten-day
.110. 一○一年度研究年報
periods with possible shortage of water in a year if water ponds did not provide the storage capacity
for water allocation. For example, on the bottom ten-day period of August, 1992, the irrigation
district by the Taoyuan main canal of the TIA had a water shortage of 13.55CMS between the planned
flow requirement (25.697CMS) and actual extracted flow (12.147CMS). The shortage means that
there was additional water of 1,288 104m3 from ponds to cover the water need. It is realized that
water ponds at the district have significant contribution to agricultural water allocation.
Hsieh et al. (2004) investigated water utilization for ponds at Taoyuan agricultural district and
found that surplus water of 6 104m3 a day can be supplied to industrial use if Ponds 11-19, 11-20, 11-
21 and 11-23 are dredged down at a depth of 0.8-1.81 m and the embankment height of Ponds 11-22 is
raised. AERC (2003) reviewed the functions for the ponds of the TIA and SIA and selected 20 water
ponds for feasibility assessment of increasing pond capacity. The feasibility assessment includes four
kinds of engineering improvements: (1) Raising the embankment height; (2) Volume dredging; (3) A
combination of raising and dredging; and (4) Areal augmentation for ponds. Four ways of
improvement have their own limitations and advantages and disadvantage (AERC 2003). Raising the
embankment height increases storage capacity, however the bottom elevations of flow inlets as well as
spillway have to be raised for water accommodation. Consequently the corresponding watercourses
are to be readjusted. A pond with higher embankment and larger capacity often brings a safety threat
to neighboring residents, and opposition and protest always follow engineering projects. As for
volume dredging, it is of lower cost and is able to remove sediments which have accumulated for years
and have occupied the effective capacity. It also has the same problem of inlet bottom elevation as
raising the embankment height. Most of water ponds have impervious sub-layers for preventing
from water leakage. If the sub-layer is devastated due to dredging, a new one is supposed to be
constructed and the total construction expenses will be raised. A mass of soil and sediments from
dredging is to be processed or dumped, and this is supposed to meet environmental standards. On the
other hand, volume dredging has no safety threat to neighboring residents. A combination of raising
the embankment height and dredging pond volume is an economic way if soil and sediments dredged
can be compacted and adapted for embankment. Areal augmentation may be carried out either
through expanding a pond into a bigger one by land acquisition or through integrating several
neighboring ponds. The larger pond area may provide an abundant source for groundwater recharge
and a sightseeing attraction for leisure and recreation. Regional socio-economic development is
therefore promoted. However, the expense for engineering and land acquisition is comparatively
high and environmental impacts on the surrounding happen. The planning and construction of areal
augmentation for ponds usually takes time; therefore it is considered as a long-term option. In
conclusion, the combination of raising the embankment height and dredging pond capacity is a better
Study on Agricultural Benefits by Increasing Capacity ….. .111.
way for present situation if the consideration of financial analysis is limited to agricultural sector.
Materials and method
Study area
Shihmen Reservoir irrigation district
The Shihmen Reservoir is a multi-purpose hydraulic facility which is located at the upstream of
an important foodstuff production district in the northern Taiwan. The district mainly consists of
paddy fields whose irrigation water management is operated by the TIA and the SIA. The district is
bordered on the east by the foothills of the Central Mountain Ridge, on the northeast by the Tanshui
River, on the west by the Taiwan Strait and on the southwest by the Fengshan Creek. The southeast
part of the district is at a high elevation, so the streams flow northwest into the Taiwan Strait with an
inclined slope of 1%. The irrigated district is split into two parts by the Shihmen main canal. The
SIA is responsible for the irrigation water operation of the southern part. The northern part has three
areas: the Taoyuan main canal irrigation area, Kwanfu canal irrigation area and Siayou irrigation area
which are managed by the TIA. The streams in the district are short, and it usually takes less than a
day to flow from upstream to downstream. Therefore rainfall is difficult to be detained for utilization.
Most of the soil in the district of the TIA is of clay loam and sandy loam. Clay loam is the primary
soil for the SIA.
The TIA operates a complete irrigation network, which is a combination of the Shihmen
Reservoir, 1 leading canal (24.8km), main canals (86km), laterals (446km), sub-laterals and ditches
(2,206km), 285 water ponds and 346 diversion weirs. The 285 water ponds have a total effective
storage capacity of 4,653 104m3. The area irrigated by the TIA is of 19,908 hectares. On the other
hand, the SIA owns an irrigation system of 460 water ponds with total effective storage capacity of
1,092 104m3, and the SIA’s irrigation area is of 7,396 hectares. Through field investigation, it shows
that the TIA and SIA have 97 and 95 water ponds, respectively, which are equipped with canals and
diversion weirs for extracting water (AERC 2003).
According to the original construction design of the Shihmen Reservoir, it can only supply about
48% of the total irrigation demand while the other water sources, such as effective rainfall, water
collected through pond catchment area or water extracted by diversion weirs, cover the rest of the
needs (Fang & Chien 2003). All water is supposed to be allocated to the farmland through canals,
laterals, sub-laterals and ditches, although overflow from upstream to downstream occurs from time to
time during heavy rainfall or typhoons. More effective utilization of water can be achieved through a
delicate operation of water ponds.
.112. 一○一年度研究年報
Pond irrigation system for study area
This study selects a pond irrigation system of a lateral at the TIA as an example. A pond
irrigation system of a lateral is preferred if it is spatially independent of other parts. The analyses of
the models for such a pond irrigation system are therefore not much affected by other lateral systems
at the TIA. The results will be more feasible in applications. The TIA has 12 operation stations,
and each is in charge of the operation and maintenance of one or two laterals. These laterals are
connected through a canal called the Taoyuan main canal. This study selects Lateral 8 and its
corresponding irrigation system as the study area. Lateral 8 belongs to the Tsaota Operation Station.
The statistics of water ponds, such as irrigation area, catchment area and effective capacity, are listed
in Table 1. Although the Taoyuan County is a developed district for economic activities, the
irrigation area by the Tsaota Operation Station is still not urbanized. A non-urbanized area keeps its
irrigation system more complete. On the other hand, it provides spatial flexibility for any
engineering improvement, such as areal augmentation for ponds or soil disposal for pond volume
dredging. In addition, Lateral 8 is connected to 32 water ponds and 20 diversion weirs, and thus
forms a complicated irrigation system. A complicated irrigation system can provide a proof to the
optimization model established in this study to be adapted to other similar systems. One pond was
originally designed to supply water to only one rotational block. However, at present there is no one-
to-one relationship between ponds and rotational blocks because of desuetude of ponds or rotational
blocks. The Taoyuan main canal provides water from the Shihmen Reservoir to water ponds for
storage. There are only Ponds 8-12 & Ponds 8-17 for which water is directly conveyed through
Lateral 8 from diversion weirs to the ponds. 20 diversion weirs are extracting water from Shuang-
Xi-Kuo Creek, Tsaota Creek, Da-Lun-Wei-Go Creek and Ta-Zi-Jiao Creek. These are listed as in
Table 2.
Table 1 Statistics of water ponds for Lateral 8 at the TIA
Pond Water Sources Land Area Irrigation Catchment Max. Area with Effective
No. (ha) Area Water full storage Capacity (m³)
(ha) Area* Depth
8-3 (m2) (m) (ha) 90,233
8-4 181,189
8-5 Canal 5.1236 83.75 25,061 2.44 4.5340 122,081
8-6 193,602
8-7 Canal 11.0734 76.51 149,699 5.20 6.2465 255,096
8-8 177,176
8-9 Canal 7.6303 62.5 45,444 4.58 5.0640
8-10 54,378
8-11 Canal 9.6947 74.4 93,896 4.35 6.7683 51,518
8-12 253,655
Canal 8.6022 65.18 80,196 3.46 7.0750 87,185
Canal 8.1321 59.83 118,957 4.60 6.2742
Canal 4.4794 67.39 11,695 3.87 2.6579
Canal 2.6149 39.28 200,156 2.75 2.1876
Canal 12.0734 93.97 95,901 4.75 10.4152
Canal, Weir 5.3477 90.79 14,034 3.99 5.2726
Study on Agricultural Benefits by Increasing Capacity ….. .113.
8-13 Canal 3.7803 96.95 17,042 4.02 2.7520 129,996
7.4248 56.86 46,447 4.50 5.2730 122,932
8-14 Canal 11.7378 138,672 4.26 9.2437 247,151
5.5846 70.7 155,380 4.24 4.3363
8-15 Canal 10.3635 66.78 718,757 3.45 8.7170 95,210
13.1802 92.52 150,368 5.05 7.3278 131,365
8-16 Canal 17.7241 82.95 33,081 4.30 11.5880 317,868
5.9412 109.42 182,112 3.99 4.4132 410,443
8-17 Canal, Weir 12.7993 19.96 101,582 3.66 11.0950
9.1232 82.91 212,519 4.24 7.0985 95,431
8-19 Canal 12.6819 81.07 266,986 4.24 10.4440 360,380
8.7419 99.67 60,147 3.68 5.4995 241,903
8-20 Canal 3.3788 31.93 105,591 2.94 1.8530 273,040
9.6868 161,395 4.30 7.4591 124,095
8-21 Canal 5.1252 29.8 144,019 4.10 3.4560
15.0867 40.6 122,967 4.39 8.3120 34,970
8-22 Canal 5.7075 50.46 385,943 3.69 4.5880 133,697
12.0439 74.56 7,351 5.12 11.6968
8-23 Canal 9.1231 136.02 21,720 5.45 6.4919 86,779
5.7248 62.78 122,299 6.09 5.1770 145,483
8-24 Canal 5.1315 41.98 131,989 2.10 5.0710
5.3818 115.74 97,238 4.04 3.0283 58,694
8-25 Canal 69.62 256,736
56.92 256,736
8-26 Canal 233,906
189,868
8-27 Canal
93,183
8-28 Canal
8-29 Canal
8-30 Canal
8N30 Canal
8-31 Canal
8-32 Canal
8-33 Canal
8-35 Canal
* Estimated by this study.
Table 2 Data for flow extracted by weirs for Lateral 8
Weir No. Stream extracted Max. Flow extracted Rotational Block No.
(CMS) for Service
53
54-1 Shuang-Xi-Kuo Creek 0.032 8-12
54-2
54-4 Shuang-Xi-Kuo Creek 0.043 8-26
54-7
54-8 Shuang-Xi-Kuo Creek 0.017 8-27
54-9
54-10 Shuang-Xi-Kuo Creek 0.006 8-13
58-6
56-2 Shuang-Xi-Kuo Creek 0.017 8-12
56-4
56-5 Shuang-Xi-Kuo Creek 0.012 8-28
56-6
56-7 Shuang-Xi-Kuo Creek 0.013 8-17
55
Shuang-Xi-Kuo Creek 0.021 8-17
55-1
56-3 Tsaota Creek 0.004 8N30
57-1
Da-Lun-Wei-Go Creek 0.008 8-32
57-3
Da-Lun-Wei-Go Creek 0.010 8-32
Da-Lun-Wei-Go Creek 0.038 8-32
Da-Lun-Wei-Go Creek 0.021 8-33
Da-Lun-Wei-Go Creek 0.012 8-35
Ta-Zi-Jiao Creek 0.024 8-24
Ta-Zi-Jiao Creek 0.052 8-23、8-31、35
Ta-Zi-Jiao Creek 0.015 8-35
Ta-Zi-Jiao Creek 0.025 8-16
Ta-Zi-Jiao Creek 0.005 8-16、24
.114. 一○一年度研究年報
57-4 Ta-Zi-Jiao Creek 0.013 8-16、24
Optimization models for the capacity changes of water ponds
This study uses LINGO 8.0 to seek for optimal solutions. LINGO 8.0 is a tool for utilizing
linear and nonlinear optimization to formulate large problems concisely, solve them, and analyze the
solutions. Optimization usually finds the answer that yields the best result; i.e. attains the highest
profit or achieves the lowest cost. Because a real irrigation system usually is quite complicated, a
large number of constraints and variables may be in need of problem formulation as well as numerical
calculation. LINGO 8.0 provides unlimited constraints and variables in programming, so it is quite
suitable for this study. The various components for an irrigation system are to be clearly defined, and
the system can then be schematized graphically as a network. The analysis model is thus established.
The followings describe the schematic network of the irrigation system and related irrigation data.
Two optimization models (Model 1 and Model 2) are established in this study. Each model has its
own objective functions subject to the same restrictions. Correlation coefficients (CC) between the
dredging volumes obtained from the optimization simulations and pond characteristics will be
calculated. There are three kinds of characteristics used in the CC calculation which are pond
effective capacity, pond catchment area and gate water demand for the rotational block corresponding
to the pond. The values of CC may reveal the importance of the characteristics in considering pond
priority for volume dredging at a large system.
Irrigation system network
A pond irrigation system consists of several main components which are water ponds, rotational
blocks, water sources, diversion points, water courses and drainage points (Hong 1988; Chien & Fang
2000), as in Fig. 1. A water pond is depicted as a triangle with a number inside indicating the serial
number of the water pond. For example, 8-5 means the fifth water pond of Lateral 8. A rectangle
stands for a rotational block irrigated and drained through watercourses. The words and number
inside the rectangle are soil type and area in hectare for the block. An oval-shaped ellipse is used for
water source. Two kinds of water sources in this study are conveyed: one is through the Taoyuan
main canal from the Shihmen Reservoir; and the other is from natural streams. The fourth symbol is
for branch points where irrigation water is diverted to ditches, water ponds and water intake gates
from the main lateral. Solid lines are for natural streams, irrigation laterals, sub-laterals or ditches.
Drainage points for which irrigation tail water is drained out are shown as squares with solid circles
inside.
Study on Agricultural Benefits by Increasing Capacity ….. .115.
Fig. 1 Symbols for irrigation networks and schematic diagram for a simple irrigation system
A simple irrigation system following the symbols description is shown at the bottom of Fig. 1.
The solid line on the upside is the principal water source from the Reservoir. The one downside is
the auxiliary water source from natural streams. The rotational block is of 62.0 hectares with the soil
type of clay loam. The amount of irrigation water needed for the block is pre-calculated according to
the cropping consumption, soil type and irrigation area, and the amount is defined as the gate water
demand. Besides water from the laterals of the Reservoir and diverted by weirs from natural streams,
water ponds also collect runoff by the catchment area during rainfall. This study depicts the
schematic network diagram of the system irrigated by Lateral 8 of the TIA, as shown in Fig. 2.
.116. 一○一年度研究年報
Fig. 2 Schematic diagram of the irrigation system network for the TIA Lateral 8
Gate water demand
The water demand for paddy fields covers the periods for transplanting, active tillering, booting, and
ripening (Chen 1977). According to farmers’ tradition in Taiwan, the time period of the operation for
water needed in fields is ten days which is the time interval used in the optimization model. A month
can then be divided into three ten-day periods. The first two ten-day periods commence from the
Study on Agricultural Benefits by Increasing Capacity ….. .117.
first day to the twentieth day of the month, while the remaining days belong to the third ten-day period
where the number of days may be 8, 9, or 10 depending on which month is of interest. Irrigation
water demand is field water demand deducted by effective rainfall, while gate water demand is the
sum of irrigation water demand and conveyance losses through ditches insides the rotational block.
For convenience of estimating conveyance losses, it is a custom that losses are calculated by the
percentage of water totally conveyed through the ditches. The numbers of percentage are usually
obtained from the field investigation by irrigation associations. This study follows the irrigation
scheduling plan provided by the TIA to give the gate water demand for rotational blocks (TIA 2004).
The conveyance losses outside rotational blocks are included in the optimization models. There are
four kinds of estimation assumed for conveyance losses according to field situations. The irrigation
scheduling plan by the TIA provides the percentages of conveyance losses (TIA 2004). For the first
situation where water flows from diversion weirs to water ponds, it is assumed there is no loss during
conveyance. The percentages of conveyance losses for the others are:
1. 13.02% for which water flows from the lateral to water ponds;
2. 13% for which water flows from water ponds to rotational blocks; and
3. 13% for which water flows from diversion weirs to rotational blocks.
Rainfall collected by water ponds
In Taiwan most of water ponds are able to collect runoff from rainfall over their catchment areas.
The coverage of catchment area was changing as the adjacent region was affected by human activities.
The field investigation was usually conducted to obtain reliable catchment areas. The catchment
areas of the water ponds for the TIA were delineated by the AERC (1998), however the catchment
areas are to be re-delineated for accurate estimation due to the rapid economic growth. This study
utilizes the geographic information system developed for the TIA to manually delineate catchment
areas for water ponds, and the corresponding catchment areas are listed in Table 1. The daily rainfall
records from 1955 to 2002 at Tsaota Operation Station are adopted and convert to the average ten-day
rainfall in the region for the optimization models. The rational method is used for constructing
rainfall-runoff relationships in this study for simplicity. Although the runoff coefficient C is the least
precise variable of the rational method, a proper selection of the runoff coefficient may lead to the
good estimation of discharge. According to Article 18 of the Technical Regulation for Soil and Water
Conservation (SWCB, 2003), it is suggested that the runoff coefficient for the uncultivated catchment
area with non-agricultural utilization is in the range of 0.75~0.95. Considering that the areas at
Tsaota Operation Station are developed upon impervious surfaces, the runoff coefficient C is assumed
as 0.9.
.118. 一○一年度研究年報
Objective functions
For an irrigation area, the changes of water supply for a cropping season are usually of interest.
With the financial analysis introduced, the agricultural net benefit (NB) from water supply can also be
understood. This study establishes two kinds of models. Model 1 is to reach the minimal annual
water supply from the reservoir to the irrigation area. Model 2 is to have the maximal annual
agricultural net benefit for the area (Loucks et al. 1981). Since Model 1 is concerned of water only
and is relatively simple, the objective function for Model 1 will be described following Model 2. For
Model 2, let the agricultural benefit from rotational block k be I k and the total cost is denoted
asTCk . For the whole irrigation area, the total net benefit is the sum of agricultural net benefits at all
rotational blocks. Therefore the objective function for Model 2 can be written in the following form:
∑Max NB = (Ik − TCk ) . (1)
k
Denoting y as the rice production per hectare and Ak as the paddy field area in hectare for
rotation block k, we have the following expression for benefit:
I k = Ak Pr y , (2)
where Pr is the price for the rice. Equation (2) can be rewritten in terms of water amount instead of
the rotational block area. Let q k be the water amount needed per hectare in rotation block k. The
value of q k is dependent of the soil properties in the field and varies from one block to another.
Usually it is determined through the field investigation by the Irrigation Associations. The symbol
Qk denotes the water amount needed in rotational block k according to the irrigation scheduling plan.
When water is not distributed to rotational block k as planned, the benefit from rice production will be
decreased. The decreases in benefit are included as negative terms in expressing I k , and the benefit
for rotational block k is:
Ik = Pr y Qk − L(Dk ) − G(Ek ), (3)
qk
in which L(Dk ) and G(Ek ) are the benefit decreases due to the shortage of water amount Dk
and the excess water amount Ek , respectively. The costs for paddy field practice in Taiwan usually
consist of different investments either from paddy lands, irrigation water, fertilizers and pesticides,
labors, irrigation practicing equipments, paddy seedling and financial loans. Those investment costs
for rotational block k are expressed as TCkD , TCkW , TCkF , TCkL , TCkE , TCkS and rM B ,
k
Study on Agricultural Benefits by Increasing Capacity ….. .119.
respectively, and therefore TCk is calculated as follows:
TCk = TC D + TC W + TC F + TCkL + TC E + TC S + rM B . (4)
k k k k k k
The objective function, Equation (1), to maximize the NB for the whole irrigation area can be re-
written as:
∑Max Pr y − L(Dk )− G(Ek )
NB = Qk
qk
k
]− TCkD − TCkW
− TCkF − TCkL − TCkE − TCkS − rM B . (5)
k
Denoting bk as
bk = Pr y − TCkD − TCkF − TCkL − TCkE − TCkS − rM B . (6)
qk Qk k
A new form of objective function for Equation 5 is obtained:
∑Max NB = [bkQk − L(Dk ) − G(Ek )] − C lQl − C wQw − C rQr − C cQc . (7)
k
The last four terms of Equation (7) are for costs of different water sources, which is originally from
TCkW . TCkW of Equation 5 is split into terms of four water resources in Equation 7. The terms for
different rotational blocks are summed by multiplying the water rate, C , and the water amount
needed, Q . With superscripts l, w, r and c representing water from the reservoir, water drawn by
diversion weirs, irrigation return flow and rainfall runoff collected by water pond catchment area,
respectively, Equation 7 for the objective function is then obtained. The objective function is to
maximize the annual agricultural net benefit under the combination of various water amounts needed
(Qk, Dk, Ek, Ql, Qw, Qr and Qc). The coefficients (Cl, Cw, Cr and Cc) for the function bk stand for the
linear relationship between water amount and the objective function.
The objective function, Equation 7, is to be summed over the whole year and becomes
∑ ∑[ ( ) ( )]N M − C lQil − C wQiw − C rQir c Qic
Max NB = bk Qk ,i −L Dk .i − G Ek.i − C ,2 (8)
k =1
i=1
in which N is the number of time periods for water operation in a year and M is the number of
rotational blocks. Considering the time interval of available input data as ten-days, N is equal to 36.
M is 32 for Lateral 8 of the TIA. Using the same notations for Model 2 with WR indicating water
.120. 一○一年度研究年報
from the Shihmen Reservoir, the objective function for Model 1 is:
Max WR = ∑ ∑N M Qil . (9)
i=1 k =1
Model restrictions
There are six restrictions for the models, which are:
(1) The water pond storages at the initial and final stages are prescribed as the known values;
(2) Gate water demand for all rotational blocks is satisfied;
(3) Inflow and outflow (or yield) for network nodes, water ponds, diversion works and drainage points
are in balance;
(4) Pond water storage is less than the assumed effective capacity at any time;
(5) Flow rate for all watercourses is less than the conveyance capacity rate; and
(6) Irrigation practices should use water which meets the quality standard of electrical conductance
(EC).
Usually no change for the initial storage from one year to the next is assumed in the study of
water ponds (SIA 1989; Fang & Peng 1996); however prescribed pond storages at the initial and final
stages are adopted in the study. Restriction (1) gives flexibility for a situation when the year is in
shortage or in abundance of water. Irrigation Associations may want to change the initial storages of
water ponds to carry more water over the next year. Restrictions (2) and (3) are about gate water
demands for the rotational blocks and water balance at the nodes. It is of interest in this study to
realize the effects due to the change of water pond capacity by dredging. Allowable dredging ratios
(ADR), defined as the quotient of the maximum allowable dredging volume and the present effective
capacity for the pond, are assumed in the two optimization models for 11 study cases (ADR=0.0, 0.1,
0.2… and 1.0), and thus the pond effective capacity is allowed to be changed. Restriction (4) is
corresponding to the assumed effective capacity. In reality canals, laterals or ditches have limitations
in water transmission. Restriction (5) affects significantly simulation results, particularly when water
is in high demand at the rotational blocks.
It is generally recognized that the quality of irrigation water is just as important as its quantity.
Lateral 8 is located downstream of the Taoyuan main canal. The quality for irrigation water may be
of problems from time to time. Particularly, water of different quality mingles together, such as water
from creeks and from the Shihmen Reservoir. Usually water from the Shihmen Reservoir is of better
Study on Agricultural Benefits by Increasing Capacity ….. .121.
quality than that from others. When water extracted from creeks is of poor quality, it is quite
common that operators mingle much water from the reservoir with water from other sources to meet
water quality standards. Although there are many quality standards monitored for irrigation water,
EC as a measure of water salinity, is the most popular indicator. It is not only its importance as an
indicator for evaluating irrigation water, but also its easiness in measuring at laboratory and field.
Furthermore, the EC data observed by the Irrigation Associations in Taiwan are available at specified
sampling sites (Hsu & Tan 2010). On the other hand, irrigation water flowing into rotational blocks
is mingled with water from different sources, and this is a treatment of dilution for better water quality.
It is suggested to use the linear weighting calculation for EC for dilution of water with different EC’s
(Chang et al. 1997). The observation data availability and linear weighting calculation facilitate the
optimization modeling using EC as a restriction in this study. The limit of EC for water quality is
then one of the restrictions adopted in this study. According to the quality standard of EC for
irrigation water set by the government (Chang et al. 1997), Restriction (6) is written in a mathematical
form as:
ECk,i ≤ 750 (µmhos / cm) (250C), (10)
in which ECk,i is the EC of irrigation water for rotational block k at the initial stage of ith ten-day.
Input data for optimization models
The irrigation scheduling plan is stipulated by the TIA at the beginning of the cropping year, and
gate water demand for Lateral 8 is set according to the plan. The costs and benefits for irrigation in
agriculture as well as the engineering construction costs for pond dredging are discussed.
Gate water demand
The TIA examines and surveys the farmers’ intention for the maximum probable area for
irrigation on September 30 every year, and the amount of the areas will be used in preparation for the
irrigation scheduling plan for the next year. The TIA irrigation scheduling plan for year 2004 shows
that the total irrigation area for Lateral 8 is about 2,283.8 hectares and the gate water demand is of
5,036 104m3 (TIA 2004). Considering about 30% of the irrigation area is routinely suspended for
fallow, the gate water demand allows a discount of 30% that drops to about 3,525 104m3. The
changes for the gate water demand are depicted in Fig. 3.
.122. 一○一年度研究年報
Fig. 3 Ten-day changes of gate water demand for Lateral 8
Costs and benefits for irrigation in agriculture
Chien and Fang (2000) calculated the costs and benefits for irrigation in agriculture. They used
gate water demand and related record data for the TIA’s Kwanfu canal irrigation area in 1996. Their
calculation for the costs and benefits used the financial statistics in agriculture around 1996.
Simulations were more actual, and their calculation is referenced in this study.
(1) According to the reports by the Water Resources Bureau, the Ministry of Economic Affairs (WRB
1998), the field water demand in agriculture in the northern Taiwan is 20,984 tons per hectare.
The rice costs in 1996 are estimated following the statistics provided by the Agriculture and Food
Bureau, Taiwan Provincial Government. At the first cropping term agricultural revenue is
NT$126,010 per hectare. The total expenditure is NT$105,423 per hectare, including the
fertilizer fee of NT$5,829, pesticide fee of NT$4,057, seedling fee of NT$6,862, herbicide fee of
NT$1,147, labor fee of NT$62,586, facility and materials fee of NT$352, water pumping fee of
NT$1,670 and indirect expenses (as land rents for farmers’ storage housing and capital interests
for cultivation facilities) of NT$22,920. At the second cropping term agricultural revenue is
NT$103,253 per hectare. The total expenditure is NT$95,325, including the fertilizer fee,
pesticide fee, seedling fee, herbicide fee and facility and materials fee of NT$18,455, labor fee of
NT$61,653, water pumping fee of NT$818 and indirect expense of NT$14,399. The
membership fees for the TIA were not collected in 1996 and will be considered as indirect
expenses in case the membership fees are imposed in the future. According to what is described
in the above, the benefit for a cubic meter of water is about NT$1.4. Provided that land rent and
capital interests are not taken into consideration, the benefit is then NT$3.3. Alternatively, the
indirect expense is taken as 25% of the total expense and the benefit is about NT$2.8.
Study on Agricultural Benefits by Increasing Capacity ….. .123.
(2) Overflow water may be transferred to domestic and industrial use in case water conservation
measures are taken. According to the data from the Council for Integral Planning of Water
Resources, the Ministry of Economic Affairs, the water price for the Taiwan Water Corporation to
use water transferred from the TIA is NT$1.55 in 1993 (CIPWR 1995). The rice price purchased
by the government is NT$19/kg in 1993 and is NT$21/kg in 1996. Therefore, the transferring
water price is adjusted to be NT$1.7 on the basis of rice price changes. Furthermore, the lost due
to overflow is assumed to be calculated in accordance with the transferring water price, i.e.,
NT$1.7/m3.
(3) During drought the transferring of water from agriculture sector to others is often enforced to meet
the needs. In addition to the fee of NT$1.7 for intensive irrigation management, farmers’ loss of
yearly earnings is estimated as NT$0.3/m3 of water price. Consequently it is assumed that the
insufficiency of irrigation water causes a loss of NT$2.0/m3.
(4) The unit cost of allocation charged by the Shihmen Reservoir for transferring water from the TIA
to the Taiwan Water Corporation is NT$0.85/m3 in 1993. Following the price changes of rice
purchased by the government, this unit cost is modified to be NT$0.9/m3.
(5) Using diversion weirs for extracting water is charged at 0.018kg of rice, i.e., NT$0.4/m3. The
costs for return flow and surface runoff collected by water ponds are both assumed as half of the
cost for using diversion weirs, which are NT$0.2/m3.
(6) The fees or expenses described above are introduced as the data established in 1996 or its
neighboring years; however the hydrological data are in 2004. These can be converted to the
data in the same year, based upon the wholesale price indexes (WPI). The Taiwan WPI was
104.15 in 1996 (on a basis as the WPI standardized being 100 in 2001) and the WPI was 109.74 in
2004 (DGBAS 2005). It is the multiplication coefficient of 1.0537(=109.74/104.15) which can
be used to convert fees or expenses into the values in 2004.
Dredging expenses for water ponds
The dredging expense is calculated according to the method used in AERC (2003) which
estimated the expenses of bottom dredging and embankment height raising for the water ponds of
Lateral 10 of the TIA. AERC (2003) made references of the dredging expenses for reservoirs,
however the expenses are not the same for water ponds as for reservoirs because water ponds usually
scatter and volumes for dredging are smaller. The dredging expenses are estimated as NT$150 per
cubic meter. The dumping expenses of soil wastes are NT$150 per cubic meter. The dredging
expenses for various items and the calculation formulas are listed in Table 3. The expenses consist of
.124. 一○一年度研究年報
three parts which are (I) Direct expenses, (II) Indirect expense and (III) Engineering preparation
expense. The financial analysis for this study does not consider the embankment height raising.
The dredging issue is to increase the pond capacity without changing any topological interrelation of
the irrigation system. Therefore the construction for transmission pipes and intake pipes is not taken
into consideration.
Table 3 Dredging expenses for water ponds
Items Unit Cost(NT$) Notes
(I) Direct Expenses
1.Dredging m3 150
2.Waste dumping m3 150
3.Secondary items set 5% of Items 1 & 2
4.Miscellaneous set 5% of Items 1-3
5.Construction Safety & Environmental Protection set 2% of Items 1-4
(II) Indirect Expense set 5% of Item (I)
(III) Engineering Preparation Expense set 20% of Item (I)
Total Expenses Sum of Items (I), (II) & (III)
Simulation results and discussion
With the increasing storage capacity of water ponds at Lateral 8 of the TIA and meeting the
minimum irrigation requirement, this study conducts simulations for the two optimization models.
There are 11 study cases for each simulation. Case 1 is to find out the optimization simulation when
there is no dredging conducted for the present pond storage. The effective capacities of ponds for
various ADR’s (0.1, 0.2,…, and 1.0) are used as the constraints in the programming, and the
corresponding simulations are numbered as Cases 2, 3,… and 11. ADR in the simulations means that
the dredging volume for a water pond is flexible. To an extent of pond dredging, it is decided
according to the objective function. The simulation results for the two models are summarized as the
followings.
For Model 1, temporal ten-day changes for water from Lateral 8 to ponds are shown in Fig. 4 and
Cases 1 and 11 are illustrated as examples. Case 1 is the optimization result for present situation,
while Case 11 is for the situation in which the same amount of present effective capacity of a pond is
allowed for dredging. It is shown in Fig. 4 that Case 1 and Case 11 have a similar trend of water
supplied but there still exist differences in several ten-day periods. It is noted that water has lower
peaks for Case 11 than for Case 1 at several ten-day periods. This is because Case 11 is with a larger
Study on Agricultural Benefits by Increasing Capacity ….. .125.
effective capacity of a pond. Fig. 5 depicts the sum of water stored at the ponds at the end of every
ten-day period. It can be seen that there are no big differences of water storage for Case 1 and Case
11 around the beginning and the end of the year. It is at the time of irrigation water in need most
which has larger differences between the two cases. Fig. 5 also reveals that water stored at the ponds
in most ten-day periods is less for Case 11 than for Case 1. A larger effective capacity of a pond
results in the flexibility in water allocation and less water is to be stored. The simulation results are
listed in Table 4, which consists of (a) Water supplied to the lateral by the Reservoir, (b) Increase of
water with respect to the previous case, (c) Gate water demand, (d) Dredging expenses, (e) Dredging
volume, (f) Increase of dredging volume with respect to the previous case and (g) Ratios of dredging
volume to effective capacity. The numerical results are illustrated in Figs. 6-8, which are (a), (b) and
(e) as described above, respectively.
Fig. 4 Ten-day changes for water from Lateral 8 to ponds (Model 1)
.126. 一○一年度研究年報
Fig. 5 Ten-day changes for water stored at ponds (Model 1)
Table 4 Results for minimizing water supplied by the Reservoir (Model 1)
Case 1 2 3 4 56
ADR 0.0 0.1 0.2 0.3 0.4 0.5
Water supplied to 25,248,107 25,235,436 25,222,765 25,215,598 25,208,850 25,202,848
the lateral (m3)
Increases or - -12,671 -12,671 -7,167 -6,748 -6,002
Decreases (m3)
Gate water 35,252,540 35,252,540 35,252,540 35,252,540 35,252,540 35,252,540
demand (m3)
Dredging expense 0 138,591,685 175,731,739 298,287,372 59,461,463 62,257,277
(NT$)
Dredging volume 0 328,645 416,716 707,334 141,002 147,632
(m3)
Increases or - 328,645 88,071 290,618 -566,332 6,630
Decreases* (m3)
Dredging
volume/Eff. 0.0000 0.0597 0.0757 0.1285 0.0256 0.0268
capacity
Note: * means increases or decreases of dredging volume with respect to the previous case.
Table 4 Results for minimizing water supplied by the Reservoir (Model 1) (continued)
Case 7 8 9 10 11
1.0
ADR 0.6 0.7 0.8 0.9 25,202,848
Water supplied to 25,202,848 25,202,848 25,202,848 25,202,848 0
the lateral (m3)
Increases or 0000
Decreases (m3)
Study on Agricultural Benefits by Increasing Capacity ….. .127.
Gate water demand 35,252,540 35,252,540 35,252,540 35,252,540 35,252,540
(m3)
Dredging expense 109,518,061 35,053,325 18,912,639 23,134,840 39,134,326
(NT$)
Dredging volume 259,702 83,123 44,848 54,860 92,800
(m3)
Increases or 112,070 -176,580 -38,275 10,012 37,940
Dredging 0.0472 0.0151 0.0081 0.0100 0.0169
Note: * means increases or decreases of dredging volume with respect to the previous case.
Fig. 6 Water supplied to Lateral 8 from the Reservoir (Model 1)
Fig. 7 Decreases with respect to the previous case for water from the Reservoir (Model 1)
.128. 一○一年度研究年報
Fig. 8 Total dredging volume for ponds at Lateral 8 (Model 1)
The results for minimizing water supplied by the Reservoir to the lateral are shown in Table 4 and
Figs. 4-8. Without any dredging, water supplied to the lateral is about 2,524.8 104m3 per year. As
expected, the water amount is decreasing as the case number is increasing (see Fig. 6). For Case 6
(ADR=0.5), water supplied to the lateral reaches the minimum and it is 2,520.3 104m3. As ADR is
increasing to 1.0, it keeps the same amount of water. Fig. 8 shows the changes of the total dredging
volume for the lateral at different ADRs. With ADR=0.3 (Case 4), the total dredging volume reaches
the maximum (70.7 104m3). Although ADR keeps increasing, the total dredging volume drops to
about 4 104m3~5 104m3 for Cases 8-11. The trend of Fig. 8 shows that not every allowable
dredging volume from various ADRs contributes to an optimal irrigation simulation. The main
reason is that an optimal simulation follows the objective function and restrictions. It may be argued
that among 32 ponds there exist several ponds with optimal dredging effects. When ADR is small,
these ponds are not able to give best performance even if dredging is conducted on these ponds.
When ADR is over 0.5, the model automatically and gradually increases the dredging volume on the
ponds with best dredging performance. At the same time the model cuts the dredging volume on
those ponds with poor dredging performance as ADR increases. In other words, the total dredging
volume for Lateral 8 is not increasing as ADR is increasing, although it seems that a larger ADR
means a larger dredging volume. These can be realized from Fig. 8. Table 6 lists the dredging
volumes for the ponds with various ADRs. Without considering dredging expenses and related costs
for additional water transmission, the total dredging volume drops to about 44,848m3 when ADR=0.8
and water conserved has reached the maximum. For ADR=0.8, Table 6 shows that only three water
Study on Agricultural Benefits by Increasing Capacity ….. .129.
ponds (Ponds 8-10, 8-29, 8-30) are dredged to reach the optimal objective and the corresponding
dredging volumes are 10,668m3, 5,482m3 and 28,699m3, respectively. The ratios of dredging volume
to effective capacity are 0.21, 0.04, and 0.49, respectively. It is obvious that these three water ponds
have a high priority for dredging to reach the objective.
Fig. 9 shows temporal ten-day changes of water from the lateral to ponds for Case 1 and Case 11
of Model 2. The sum of water storage of a pond in every ten-day period for Lateral 8 varies as
shown in Fig. 10 and the trend is similar to that of Fig. 5. It can be seen that there are no big
differences of water storage for Case 1 and Case 11 around the beginning and the end of the year. It
is at the time of irrigation water in need most which has larger differences between the two cases.
The simulation results are listed in Table 5, which consists of (a) Water supplied to the lateral by the
Reservoir, (b) Increase of water with respect to the previous case, (c) Gate water demand, (d)
Agricultural net benefits, (e) Dredging expenses, (f) Dredging volume, (g) Increase of dredging
volume with respect to the previous case and (h) Ratios of dredging volume to effective capacity.
The results are illustrated in Figs. 11-14, which are agricultural net benefits, agricultural net benefit
increases with respect to the previous case, water supplied to the lateral from the Reservoir and total
dredging volume, respectively. The results for maximizing agricultural net benefits are shown in
Table 5 and Figs. 9-14. Without any dredging, the agricultural net benefit and water supplied from
the Reservoir to the lateral are about NT$6,985.3 104 and 2,524.8 104m3, respectively. As expected,
the agricultural net benefit is increasing as the case number is increasing (see Fig. 11). The results
are similar to those discussed in the previous paragraph and the agricultural net benefit reaches the
highest (about NT$6,995.7 104) when ADR=0.5. As ADR is increasing above 0.5, the agricultural
net benefit is no longer increasing. The increase in agricultural net benefit with respect to the
previous case keeps decreasing as ADR is increasing, as shown in Fig. 12. However the increase
vanishes as Cases 6-11 have the same net benefits. Fig. 12 and Fig. 7 have similar trends. The
comparison between Fig. 13 and Fig. 6 indicates that the same amount of water supplied from the
Reservoir to the lateral for Model 1 and Model 2 although the two models have different objective
functions. The total dredging volumes for various ADRs are shown in Fig. 14. There are three peak
values which are of 65.1 104m3, 61.1 104m3, and 70.0 104m3 for ADR=0.4, 0.7, and 0.9, respectively.
The trend is similar to those discussed above because agricultural net benefit also reaches highest after
ADR=0.5. The lowest dredging volume appears when ADR=0.6. Therefore it is inferred that there
exist water ponds in an irrigation system that has a better dredging effect with the agricultural net
benefit as the objective. The results of dredging volumes for maximizing agricultural net benefits at
various ADRs are listed in Table 7. It is obviously known that the dredging expense is basically
proportional to the dredging volume. For ADR=0.6 (water conserved the most), total dredging
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volume is about 26.7 104m3 and Table 6 exhibits that Ponds 8-4, 8-9, 8-10, 8-11, 8-13, 8-14, 8-15, 8-
19, 8-22, 8-25, 8-28 and 8-30 are to be dredged and the ratios of dredging volume to effective capacity
are 0.14, 0.18, 0.31, 0.29, 0.01, 0.07, 0.12, 0.04, 0.11, 0.02, 0.13 and 0.6, respectively. It is obvious
that the twelve water ponds have a high priority for dredging to reach the objective.
Fig. 9 Ten-day changes for water from Lateral 8 to ponds (Model 2)
Fig. 10 Ten-day changes for water stored at ponds (Model 2)
Study on Agricultural Benefits by Increasing Capacity ….. .131.
Fig. 11 Agricultural net benefits for Lateral 8 (Model 2)
Fig. 12 Net benefit increases with respect to the previous case for Lateral 8 (Model 2)
.132. 一○一年度研究年報
Fig. 13 Water supplied to Lateral 8 from the Reservoir (Model 2)
Fig. 14 Total dredging volume for ponds at Lateral 8 (Model 2)
Case Table 5 Results for maximizing agricultural net benefits (Model 2) 6
12 3 4 5 0.5
ADR 0 0.1 0.2 0.3 0.4
25,202,848
Water supplied 25,248,107 25,235,436 25,222,765 25,215,598 25,208,850
to the lateral
(m3)
Study on Agricultural Benefits by Increasing Capacity ….. .133.
Increases
or Decreases - -12,671 -12,671 -7,167 -6,748 -6,003
(m3)
Gate water 35,252,540 35,252,540 35,252,540 35,252,540 35,252,540 35,252,540
demand (m3)
Agricultural net 69,852,763 69,881,955 69,911,147 69,927,658 69,943,204 69,957,033
benefits (NT$)
Dredging 0 135,426,437 145,303,536 194,461,555 274,578,595 144,353,788
expense (NT$)
Dredging 0 321,139 344,561 461,130 651,113 342,309
volume (m3)
Increases
or Decreases* - 321,139 23,422 116,569 189,983 -308,805
(m3)
Dredging
volume/Eff. 0 0.0583 0.0626 0.0838 0.1183 0.0622
capacity
Note: * means increases or decreases of dredging volume with respect to the previous case.
Table 5 Results for maximizing agricultural net benefits (Model 2) (continued)
Case 7 8 9 10 11
ADR 0.6 0.7 0.8 0.9 1
Water supplied to 25,202,848 25,202,848 25,202,848 25,202,848 25,202,848
the lateral (m3)
Increases or 00000
Decreases (m3)
Gate water 35,252,540 35,252,540 35,252,540 35,252,540 35,252,540
demand (m3)
Agricultural net 69,957,033 69,957,033 69,957,033 69,957,033 69,957,033
benefits (NT$)
Dredging expense 112,716,337 257,857,160 193,600,766 295,121,583 272,610,833
(NT$)
Dredging volume 267,286 611,461 459,089 699,827 646,447
(m3)
Increases or -75,023 344,175 -152,372 240,738 -53,380
Decreases* (m3)
Dredging
volume/Eff. 0.0485 0.1111 0.0834 0.1271 0.1174
capacity
Note: * means increases or decreases of dredging volume with respect to the previous case.
The discussion of (2) and (3) is based on the establishment and calculation of optimization
models. For larger areas with hundreds of water ponds, it will take time and efforts in constructing
the optimization models. However, with the simulation results in this study, a simple relationship
between dredging volumes and pond characteristics may be revealed and this relationship can be
.134. 一○一年度研究年報
references for analyzing pond dredging at a large area. This study calculates the correlation
coefficients between pond dredging volumes and three pond characteristics which are pond effective
capacity, pond catchment area and gate water demand. The last three rows of Table 6 and Table 7
show the values of CCs. Table 6 is for minimizing water supplied by the Reservoir, and the smallest
total dredging volume for the minimal water occurs at ADR=0.8. The values for the three kinds of
CCs are -0.295, 0.354 and 0.352, respectively. On the other hand, Table 7 is for maximizing
agricultural net benefits, and the smallest total dredging volume for the maximal net benefit occurs at
ADR=0.6. The values for the three kinds of CCs are 0.191, 0.074 and 0.277, respectively. As a
rough estimation for minimizing water supplied, the pond catchment area and pond gate water demand
may be used as reference indexes for the volume dredging priority. In other words, volume dredging
is supposed to be conducted in a water pond owning a larger catchment area and larger gate water
demand to obtain high efficiency, in case there is no optimization model available. For maximizing
agricultural net benefits, the gate water demand corresponding to the pond is then the most important
factor in considering the priority of pond volume dredging.
Table 6 Pond dredging volumes and correlation coefficients for various ADRs (Model 1)
ADR
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Pond No. Pond Dredging Vol. (m3)
8-3 9,023 18,047 19,243 0 0 19,243 0 0 0 0
8-4 18,119 14,534 54,357 0 0 0 0 0 0 0
8-5 12,208 24,416 36,624 0 0 0 0 0 0 0
8-6 19,360 776 28,008 0 0 0 0 0 0 0
8-7 0 0 0 0 0 0 0 0 0 0
8-8 17,718 0 53,153 0 22,508 0 0 0 0 0
8-9 5,438 0 11,558 0 0 0 0 0 0 0
8-10 5,152 10,304 10,668 10,668 10,668 16,218 10,668 10,668 10,668 10,668
8-11 25,366 0 36,331 0 0 0 0 0 0 0
8-12 0 0 0 0 0 0 0 0 0 0
8-13 13,000 25,999 12,718 661 12,718 661 0 0 0 0
8-14 0 188 8,704 0 0 13,995 0 0 0 0
8-15 24,715 0 0 0 0 0 0 0 0 0
8-16 0 0 24,671 0 0 0 0 0 0 0
8-17 0 0 0 0 0 0 0 0 0 0
8-19 31,787 63,574 43,259 4,744 4,744 4,744 43,259 0 0 43,259
8-20 26,315 82,089 0 53,287 0 0 0 0 0 0
8-21 0 0 0 0 0 0 0 0 0 0
8-22 36,038 72,076 85,254 39,367 1,673 0 0 0 0 0
8-23 24,190 0 21,150 0 0 0 0 0 0 0
8-24 27,304 0 497 0 20,556 497 497 0 0 497
8-25 1,305 0 3,103 8,797 2,677 47,408 0 0 0 0
8-26 0 6,994 0 0 0 0 0 0 0 0
8-27 0 0 0 0 0 0 0 0 0 0
8-28 1,873 7,892 3,280 0 43,390 7,774 0 0 0 9,677
8-29 14,548 8,105 33,245 0 0 31,076 0 5,482 15,494 0
Study on Agricultural Benefits by Increasing Capacity ….. .135.
8-30 5,869 11,739 17,608 23,478 28,699 28,699 28,699 28,699 28,699 28,699
8-N30 0 0 77,021 0 0 0 0 0 0 0
8-31 0 51,347 77,021 0 0 0 0 0 0 0
8-32 0 0 0 0 0 0 0 0 0 0
8-33 0 0 49,862 0 0 89,388 0 0 0 0
8-35 9,318 18,637 0 0 0 0 0 0 0 0
Sum (m3) 328,645 416,716 707,334 141,002 147,632 259,702 83,123 44,848 54,860 92,800
CC1 0.644 0.561 0.397 0.462 -0.189 -0.162 0.068 -0.295 -0.285 0.037
CC2 -0.035 -0.199 -0.221 -0.007 0.220 0.021 0.233 0.354 0.320 0.234
CC3 0.397 0.201 -0.003 0.347 0.148 -0.042 0.275 0.352 0.328 0.246
Note: CC1, CC2 and CC3 are the correlation coefficients between pond dredging volumes and pond effective
capacity, pond catchment area and gate water demand, respectively.
Table 7 Pond dredging volumes and correlation coefficients for various ADRs (Model 2)
ADR
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Pond No. Pond Dredging Vol. (m3)
8-3 9,023 18,047 27,070 34,080 0 0 19,243 19,243 19,243 19,243
8-4 0 11,950 0 41,168 0 25,932 9,214 0 163,070 9,837
8-5 1,770 1,770 25,666 0 0 0 30,319 25,666 25,666 25,666
8-6 19,360 8,088 20,676 0 0 0 28,008 18,274 28,008 0
8-7 0 0 0 0 0 0 0 0 0 0
8-8 17,718 31,023 15,013 0 3,276 0 22,508 42,600 29,155 31,023
8-9 0 9,021 11,303 0 3,132 9,947 0 0 0 0
8-10 5,152 10,304 10,668 10,668 10,668 16,218 10,668 10,668 10,668 10,668
8-11 25,366 1,039 23,929 36,331 0 73,911 36,331 0 37,974 73,911
8-12 0 0 0 0 0 0 0 0 0 0
8-13 54 12,718 12,718 48,211 54 661 13,894 19,230 19,230 19,230
8-14 12,293 21,700 3,923 8,704 1,975 8,704 9,833 11,099 0 56,367
8-15 0 0 0 0 0 29,485 52,209 4,287 0 0
8-16 0 0 0 0 0 0 0 0 0 0
8-17 0 0 0 0 0 0 0 0 0 0
8-19 31,787 4,744 0 127,147 79,605 13,628 4,744 4,744 4,744 4,744
8-20 41,044 82,089 0 87,425 60,823 0 53,287 0 635 635
8-21 0 0 0 0 0 0 0 0 0 0
8-22 36,038 4,686 108,114 85,254 0 39,367 20,926 20,926 20,926 20,926
8-23 19,942 0 4,914 0 0 0 0 0 0 0
8-24 27,304 497 53,299 84,784 0 0 13,260 13,260 13,260 13,260
8-25 6,704 16,087 19,260 49,638 5,634 2,677 0 1,305 8,797 16,087
8-26 3,497 0 0 0 0 0 0 0 0 0
8-27 0 0 0 0 0 0 0 0 0 0
8-28 8,678 9,047 2,813 0 0 11,539 21,554 889 605 6,606
8-29 14,548 29,005 0 0 0 0 30,436 5,482 30,755 25,480
8-30 5,869 11,739 17,608 23,478 29,347 35,216 41,086 41,803 41,803 41,803
8-N30 0000000000
8-31 25,674 0 77,021 0 0 0 179,715 205,389 231,062 256,736
8-32 0 46,781 0 0 116,953 0 0 0 0 0
8-33 0 14,226 27,135 14,226 30,841 0 14,226 14,226 14,226 14,226
8-35 9,318 0 0 0 0 0 0 0 0 0
Sum (m3) 321,139 344,561 461,130 651,113 342,309 267,286 611,462 459,089 699,827 646,447
CC1 0.688 0.313 0.358 0.568 0.364 0.191 0.297 0.130 0.142 0.145
CC2 -0.102 -0.184 -0.102 -0.034 0.014 0.074 -0.157 -0.122 -0.100 -0.160
.136. 一○一年度研究年報
CC3 0.248 0.357 0.063 0.368 0.448 0.277 0.007 -0.107 -0.053 -0.111
Note: CC1, CC2 and CC3 are the correlation coefficients between pond dredging volumes and pond effective
capacity, pond catchment area and gate water demand, respectively.
Conclusions
The irrigation water for the Lateral 8 of the TIA comes from the Shihmen Reservoir, water pond
collection, river weirs and irrigation return flow. Water conveyed through the main canal and laterals
from the Shihmen Reservoir is the principal source for irrigation, while the rests are auxiliary. The
capability of water ponds for storing and allocating water either from principal or auxiliary sources
can be enhanced by increasing the effective storage capacity of ponds. The enhancement of pond
capability can not only help satisfying gate water demand but also conserve water for the Reservoir or
obtain agricultural net benefits.
The combination for various pond volume dredging of 32 water ponds is complicated. This
study adopts ADRs in programming simulations. ADRs provide water ponds the flexibility for the
dredging volume in the programming. It is then easy to obtain the optimum combinations of pond
dredging volumes for corresponding objectives. The optimum combinations are the references to the
TIA for planning the performance improvement of water ponds. The problem formulation in this
study, in fact, focuses on the increase of pond capacity without changing the topological interrelation
of the irrigation system. The formulation therefore can be applied to any engineering improvements
concerning pond capacity only, say raising the embankment height.
A simple relationship between dredging volumes and pond characteristics is revealed from the
simulation results, and this relationship can be references for analyzing pond dredging at a large area
with hundreds of ponds. For minimizing water supplied, the pond catchment area and pond gate
water demand may be reference indexes for volume dredging priority. For maximizing agricultural
net benefits, the gate water demand corresponding to the pond is the most important factor in
considering the priority of pond volume dredging. Irrigation water quality problems are most
concerned in agriculture. Because the water quality data are not collected in rivers as well as in
ponds, this study cannot simulate the situation of poor pond water quality which will need clean water
from reservoirs for diluting. However, the two models have been pre-conditional on the
establishment of water quality among the LINGO programs. If water quality information is ready for
use in the future, the irrigation system can be further simulated.
This study follows present conditions of the irrigation system to establish the optimization
models for realizing the effects due to the changes of pond effective capacity. Scrutinizing the
simulation results with care shows that the supply and utilization of auxiliary water resources have no
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