IJERD – International Journal of Environmental and Rural Development (2023) 14-1

Research article
erd

Development of a Simple-Concept Water Allocation Modelat the Farm-Block-Level for Efficient Water Management
NAOHISA NAKASHIMA*
Department of Agro-environmental Science,
Obihiro University of Agriculture and Veterinary Medicine, Obihiro, Japan
Email: nnakashima@obihiro.ac.jp

TETSURO FUKUDA
Hino-sato, Munakata City, Fukuoka Prefecture, Japan
Received 4 February 2023

Accepted 8 May 2023(*Corresponding Author)

Abstract It is crucial to establish appropriate water management in agriculture. Due tofinancial difficulties, it is also necessary for farmers to work together with government
agencies in water management. Existing water allocation models, however, require much
effort to collect data. They are also black boxes difficult for farmers to understand, which may
discourage farmers from participating in irrigation planning. In this study, we attempted toconstruct a farm-block-level water balance model with a simple tank model concept and easilycollectible data. The model consists of two parts that reproduce the water distribution processfrom the farm block intake to each field (Canal Tank Model; CTM) and the water balance
process in the paddy field (Paddy Tank Model; PTM), respectively. The model coefficientswere identified using data from 2002 to 2003, and the model validity was evaluated using datafrom 2004 and 2005. The CTM coefficients were identified for 2002 and 2003 because of thedifferent land use patterns. The CTM runoff coefficients and hole heights were changed ondays when the farmers were considered to have operated diversion ratios significantly. The
PTM coefficients were identified using the SDFP method and trial and error referring to thegroundwater level. However, the PTM seepage holes were fixed to the corresponding values
that the vertical seepage was approximately 5 mm/d based on the on-site survey. As a result,despite the arbitrary water manipulation by farmers, the same CTM coefficients for 2002,
2003, 2004 and 2005, when the land use pattern was similar, were able to reproduce the water
allocation well. This water allocation model can be used to estimate the optimal delivery water
management rate and to quantitatively evaluate the excess water withdrawal resulting from thelabor reduction in water management.
Keywords water balance model, excess water withdrawal, participation irrigation
management (PIM), prediction of water demand

INTRODUCTION
More than 90% of the total irrigation water is used for rice production (Khepar et al., 2000). However,the Organization for Economic Cooperation and Development (OECD) has addressed the idea that
irrigation water is consumed unproductively and inefficiently (Fujimoto and Tomosho, 2003). On
the other hand, recently, participation in irrigation management (PIM) is under great practice aroundthe world. This method is for all farmers to get enough water, which is difficult to achieve with a
top-down system, because of the financial pressure to maintain the irrigation system and the difficultyof taking care of fringe in the system by only the government (Saito, 2010). Yamamoto (2005)
recommended that water use efficiency during abnormal dry spells should be improved by promoting
PIM in paddy field irrigation in the Asian monsoon region. Irrigated water allocation models or waterbalance models become one of the decision-making support systems for SVP (Shared Vision
Planning) in PIM. Murase and Kawasaki (2004) suggested that when consensus gets formed,
optimization and equity become essential factors. Trade-offs achieve equity among the interests ofⒸ ISERD

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stakeholders under optimized conditions. It suggests that equity is only contented once optimizationis contented for water allocation. Then, the water balance components need to be quantified throughfield experiments. However, quantifying water balance components are often complicated becauseof the excessive time and expenditure involved in the execution (Khepar et al., 2000), especially indeveloping countries where water scarcity is a common phenomenon and optimized water allocationis strongly demanded.
In addition, the water balance model in a small district at the end of an irrigation system inwhich farmers' water demand finally needs to be met should be simulated to make satisfactorydecision-making. In the case of open ditches, taking water into paddy fields is related to each otherfield. Thus, the degree of freedom of water management in each paddy field declines (Toyota et al.,1984). Toyota et al. (1984) declared that this agreement between water management in ditches andfields greatly affected water intake into paddy fields. Hence farm-block-level analysis was necessary.
The smaller the analysis area, however, the more significant the impact of human disturbance,
making it difficult to simulate water allocation in small-scale fields. The delivery water requirement
would differ from the degree of each farmer’s diverging operation at a small canal (Furuki et al.,1979). This large human activity impact caused a few model developments of simulating water
allocation at a farm-block level.
To explain human activity with a physical model could be a fault, but a statistical model might
be acceptable. The tank model could reproduce this uncertainty, described as a semi-physical andsemi-statistics model.
OBJECTIVE
This paper aims to develop a conceptual water allocation model acceptable to some land-use andirrigation systems changes and access to understanding decision-making processes. This model
calculates the water balance and allocating process in the small-scale paddy fields area through thesemi-physical and semi-statistic tank model.
METHODOLOGY
Target Area
The study area is typical paddy fields (farm-block-level, about 30 ha) located in the middle area of
the Chikugo River in Fukuoka Prefecture, Japan (Fig. 1).

12

B-4

55

8

32

45

54

A-4

Water intake

30 40
11

B-3
5

To downstream

3

B-1
50

A-2
31 41 28

51
100 m

1

46
4
9

Water intake

29

A-1

To downstream
0

7
47

B-2
10

A-3

2

49 6

Water intake

Velocity survey points(and) Water-stage recorder

Farm ditch
Drainage ditch

Fig. 1 The irrigation system and survey points in the study area
The number indicates each branch or release point. Irrigation started from three points (Nos.1, 3, and 9). The black andwhite circles show the survey points where water discharge was measured weekly. The water-stage recorders were installedat the white circle points. The different colored hatches describe the targeted areas for irrigation intakes water from threepoints.

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The area was separated into A- and B-blocks by north and south roads. Moreover, each block
was broken into four sub-blocks corresponding with field-block-level by north and south runningfarm roads and ditches. Each sub-block was regarded as one big paddy lot in this research. The study
area had changed its crop planting (land-use) pattern. The land-use pattern was similar in 2002 and2004 when the whole B-block cultivated the soya bean, and in 2003 and 2005 when part of the Bblock (B-2 and B-3 sub-block) was used for the soya bean. The land-use changes made the water
allocation complex and significantly affected the model parameters.
Measurement of Water Flow in Ditches
A propeller current meter and water stage recorders measured the water velocity and water level in
only one direction in a branch point in the ditches (Fig. 1, B-direction). The former measurement was
conducted once every week and the latter were recorded hourly. The scale observed the water level
simultaneously with the propeller measurement, multiplied by velocity to estimate the observed
discharge. The balance equation calculated the water discharge in the other direction (D-direction)
in a branch point from the observed discharge, which is also considered an observed flow in themodel. The water level measured hourly by the water stage recorder was converted to the discharge
by using the following approximate formula obtained from the relationship between the weekly
measured flow and the water level:
𝑄 = 𝛼ℎ𝛽(1)where Q is discharged, h is measured water level,  and  are coefficients of approximate expression.
Measurement of Water Balance in Paddy Fields

Fig. 2 The structure of the canal tank model (CTM, a), paddy tank model (PTM, b)
and its layout in the allocation model (c)Each CTM was installed at the branch point and PTM was placed in each block. B-direction was where water velocity wasmeasured, and D-direction was where the water flow was calculated by water balance.

We targeted three paddy fields from A-2, B-2, and B-3 sub-blocks. The ponding water depth wasmeasured hourly by a data logger. The precipitation (R) was observed at the nearby A-2 sub-block.
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The elevation of the overflow weir at the outlet was measured weekly because a farmer did notfrequently operate the outlet and used to calculate the amount of water release (Qout) by overflow
computing. Evapotranspiration (ET) was estimated by multiplying the ET ratio and potential ET by
the Penman method from meteorological data. Percolation (P) was estimated by the water balance
equation as:
𝑃 = 𝑄𝑖𝑛 + 𝑅 − 𝐸𝑇 − 𝑄𝑜𝑢𝑡 + ∆ℎ(2)where h was a variation of ponding depth. All values were averaged or totaled daily. N-type waterrequirement survey evaluated the groundwater recharge from paddy fields. The vertical percolation
was about 5 mm/d at the middle point in the field free from levee seepage. The groundwater level
was measured hourly near No.1 (which was used to calibrate the paddy tank model). The amount ofwater runoff from paddy fields at block level was estimated from observed discharge in the drainage
ditches (Fig. 1) by outflow minus inflow in the drainage.
Model for Water Allocation Through Ditches
The whole water distribution process in the study area was represented in two parts; in ditches andinside paddy fields. At the first step of computation of water allocation, the canal tank model (CTM,
Fig. 2a) described the water distribution process through ditches, CTM installed at each branch point(Fig. 2c). The pipe size in CTM represented the water dividing rate at a branch for each direction,
including wastewater ratio (e.g., branch point No.3). The outflow yi from each i-th number of a pipe
was computed as:
𝑦𝑖 = 𝑎𝑖 (𝑥 − ℎ𝑖 )1.5 (𝑥 ≥ ℎ𝑖 )(3)where ai is the coefficient of discharge, x is the storage water depth, hi is the pipe height, and an
output flow occurs only when the storage water depth is higher than the pipe height.
The parameters were calibrated manually but in a rational manner. The water-dividing operation
depends on the land-use pattern and rice growth stage (e.g., rooting, ripening, etc.); thus, the pipe
size parameter was determined by each period manual to consist of observed discharge. The biggest
impacts on the water allocation operation were mid-summer drainage and water stopped before
maturation. The timing of changing parameters was decided from the paddy water depth of the survey
fields. The heavy rain causing excess irrigation water also changed the drainage operation at water
release points. CTM parameters were calibrated in 2002 and 2003 (calibration period) and validated
in 2004 and 2005. The parameter determined in 2002 was applied to 2004 with a similar land-use
pattern year, and the parameter in 2003 was applied to 2005 for the same reason.
Model for Water Balance in Paddy Fields at Sub-Block-Level
The paddy tank model (PTM) structure is shown in Fig. 2 bottom left. The pipe of a0 represented avertical percolation reaching the groundwater: a1 represented a lateral percolation through the leveedraining to the drainage ditches: a2 described water release from a surface and a3 was for groundwater
flow. The sum of lateral percolation and the water release defined the runoff from paddy fields. This
simple model can adapt to a flexible scale. For example, Jayadi et al. (2000) applied one PTM to 300
ha paddies. In this study, PTM described block-level paddy fields, i.e., A-block and B-block.
The input data for PTM were precipitation, ET, and paddy water intake calculated from CTM.
The target output for determining parameters was the groundwater level (GWL). SDFP (Kadoya andNagai, 1980) and the trial-and-error method decided the parameters. The vertical percolation a0 was
determined without the optimization method because the N-type water requirement was about 5
mm/d; therefore, a0 was estimated at 0.070 or 0.075. The ponding depth, the height of the levee, andthe outlet overflow weir height in the site were considered to decide the storage depth in the uppertank. The parameter calibrated by data in 2002 and 2003 was applied to data in 2004 and 2005 forⒸ ISERD

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testing the versatility. As with CTM validation, the identified model coefficients for 2002 wereapplied to the coefficients in 2004, when land use was similar, and the coefficients identified in 2003
were applied to the coefficients in 2005. Hereafter we call 2002 and 2003 a calibration period and2004 and 2005 a validation period.
RESULTS AND DISCUSSION
Applicability of CTM
The simulated water allocation through irrigation ditches by CTM in calibration terms showed good
agreement with the observed flows (Fig. 3a), especially at the endpoint of the irrigation system No.
55 (Fig. 2c) where recorded hourly flow (absolute errors was 5.5 mm/d). No. 46 reproduced reverse
flow when a reversal of hydrodynamic gradient occurred between adjacent branches, and water
flowed through the irrigation ditch opposite the normal flow direction.
CTM well-predicted water allocation in 2004 and 2005 (Fig. 3b, absolute error at No.55 were
6.3 and 18.0 mm/d, respectively), indicating that CTM has robust reproducibility to some extent
regardless of drought season or rainy season because 2002 was drought and 2004 was rainy season.
Also, good agreement suggested that water allocation operation was similar when the land use pattern
was similar.
The CTM concept is apparent, simple, and easy to customize. CTM merely requires discharge
data in irrigation ditches. Taniguchi and Satoh (2006) described that grasping the actual water usage
required a series of observations of quantitative water allocation and enormous instruments andefforts. CTM can be one of the resolutions for these problems. Resource Division Planning
Department Kyushu Agricultural Administration Office (1997) applied the CTM to about 4,600 ha
district in Kasegawa, Saga prefecture, to analyze water distribution. The more the command area
becomes extensive, the more the number of operation points changing the water-diverging ratio
increases. Consequently, diversion operation increases its randomness and decreases the effect on
the tank parameters, leading the parameters to be decided at one value. CTM has to be improved in
the following two aspects. First, the present CTM could not precisely explain the reverse flow that
occurred frequently and extensively. Second, long-term data needs to be collected to increase theaccuracy of CTM's prediction.
Applicability of PTM
The estimated GWL from PTM demonstrated well fitted with the observed value, shown in Fig. 4a.
PTM also simulated the water runoff from A-block and its relative error was around 50% and 28%
in 2002 and 2003, respectively (Fig. 4b). An unsteady flow and seepage from the weir shutter werean obstacle to measuring the drainage discharge, causing some outlier values, and leading to thefitting error being worse. However, the calculated flow reproduced the other observed trend well,and the identified parameters could be used for prediction.
The prediction of GWL and runoff from paddy fields, shown in Fig. 4, demonstrated good
agreement with observed values and proved PTM’s versatility. However, although simulated GWL
in 2004 well matched with observed GWL, the predicted runoff had difficulties at reproducibility.
The relative error of runoff in 2004 was about 200% due to the failure to reproduce the small observed
values in the denominator of the relative error equation. The high error in 2004 was caused by using
the same parameter through 2004 and 2005 even though the land use pattern changed. However, theprediction in 2005 showed good fitting simulation both for GWL and runoff.
Future development was that the model's sensitivity to land use should be improved. In thisstudy, the block level was considered to be one paddy tank. However, the sub-block could be
regarded as one paddy tank to improve sensitivity, and the model would deal with various land use
patterns in more detail. Furthermore, the paddy lot management schedule should be taken for
calibrating PTM parameters into account. The PTM coefficient could be changed according to therice growing stage or water management schedule.
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Fig. 3 Water allocation in ditches
The black solid line, outline of a green circle, and red square stand observed flow in the B-direction and D-direction,
respectively. The green and red solid lines represent CTM's simulated values in B- and D-direction, respectively. The minus
value at No.46 demonstrates the reverse flow.

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In this study, the simulation model was developed to predict water allocation and balance witheasily available data at the farm block level. Kuo et al. (2006) calculated the water demand of paddy
and upland crops by CROPWAT designed by Smith (1991) at the ChiaNan Irrigation Associationthat could estimate the soil moisture but not include the paddy lot water management or delivery
water management, thus could not evaluate the water productivity. The present model in this study
can estimate and consider both lot water management from PTM and delivery water managementfrom CTM. The proposed model can also apply to farm and large-scale levels, including complex
land use areas.

Fig. 4 Comparison between calculated and observed GWL (a) and water runoff (b) frompaddy fields in the calibration term (2002-2003) and validation term (2004-2005)
Solid lines are calculated and dotted lines are observed values (a).

The developed model becomes a decision-making support system for SVP (Shared Vision
Planning) in PIM. Murase and Kawasaki (2004) suggested that optimization and equity were
essential for forming consensus. The equity is comforted by trade-offs among stakeholders' interests
under optimized conditions. This model can optimize water management or land use patterns bysimulating the water balance and allocation process. Thanks to the tank model's semi-physicalcharacteristics, the participant intuitively understands the operation of the water diversion and waterbalance component to which the model parameters correspond.
CONCLUSION
This study calculated water balance through irrigation ditches and paddy fields in the area using
understandability concepts and accessible collecting data by connecting the canal tank model (CTM)to the paddy tank model (PTM). An easily understandable and collectible data structure is essential
for the decision-making process. The present model parameters are consistent and capable ofpredicting water allocation and balance with similar land use patterns. For example, a simulation by
CTM and PTM under a scenario of saving irrigation water because of a lack of precipitation could
predict how the groundwater level would change. If the groundwater level could be predictable, it
could avoid wet or drought injury to the crop.
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Using available data for this type of study is important because it is difficult to gather large
amounts of actual data on water allocation at every branch of the irrigation system every week forseveral years. This paper aims to build a model based on a simple tank model concept and data thatcan be easily collected. The data used in this study spans from 2003 to 2005. Nonetheless, we havedemonstrated that it is possible to develop an accurate model for our intended purpose, as the methodof collecting actual data has remained consistent even today. In the future, the remaining issue is toaccommodate the changing land use, and the PTM parameters should be calibrated at each paddy,
upland, and greenhouse (Kato, 2005). To some extent, the tank model parameters have generality
attributed to the semi-physical character, which means that human activity to change irrigation
management can be reproduced by the present model.
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