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A study on pesticide runoff from paddy fields to a river in rural region—2: development and application of a mathematical model
ARTICLE IN PRESS
Water Research 38 (2004) 3023–3030
A study on pesticide runoff from paddy fields to a river in rural region—2: development and application of a mathematical model Yoshio Nakanoa,*, Tomohiko Yoshidaa, Takanobu Inoueb a
Department of Environmental Chemistry and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8502, Japan b Department of Civil Engineering, Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan Received 29 January 2003; received in revised form 14 January 2004; accepted 16 February 2004
Abstract A mathematical model was developed to predict the runoff of pesticides from paddy fields to a river in a rural region. The model comprises three submodels: (1) submodel for river flow, (2) submodel for pesticide behavior in paddy fields, (3) submodel for pesticide behavior in a river. The tank model was applied to predict the river flow and the paddy water. In order to reproduce the actual behavior of pesticides in paddy fields, the kinetics of the transport and reaction mechanisms of pesticides applied to paddy fields were considered in the model. The model was applied to the Kozakura River Basin where the detailed field survey was conducted. The model reflected well the runoff characteristics of pesticides obtained from the detailed field survey. r 2004 Published by Elsevier Ltd. Keywords: Runoff; Mathematical model; Pesticide behavior; River basin; Kinetics
1. Introduction The use of agrochemical has dramatically increased with demands for increase in the yields of agricultural production. The adverse effects of certain agrochemicals to aquatic ecosystems and human health, however, have become known because of their acute or chronic toxicity. Among various kinds of agrochemical, pesticides applied to paddy fields have become much concern especially in Japan, because about 40% of the pesticides used are applied to paddy fields [1] and they can easily flow out to aquatic environments, causing hazard environmental problems. Thus, it is important to evaluate the runoff of pesticides applied to paddy fields to a river in a rural region. It is known that a mathematical model is a *Corresponding author. Tel.: +81-45-924-5432; fax: +8145-924-5441. E-mail address: [email protected] (Y. Nakano). 0043-1354/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.watres.2004.02.014
valuable tool for such evaluation. Some models have been reported to predict the runoff of pesticides from a specific paddy field [2–6]. However, only a few models have been developed to predict the runoff of pesticides from paddy fields to a river [3,7]. In these models, the behavior of pesticides in paddy fields is assumed as equilibrium. However, the actual behavior of pesticides is not necessarily in equilibrium but in kinetics. Thus, a mathematical model, taking into consideration particularly the principal transport and reaction mechanisms of pesticides in paddy fields, was developed in this paper for the evaluation of pesticide runoff from paddy fields to a river in detail. To validate this model, the simulation was performed to compare with the detailed results of a field survey that are obtained by frequent observations at many stations along a river. The detailed field survey was carried out in the Kozakura River Basin, as described in a companion paper [8].
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Nomenclature Bi Cw,1 Cw,n Cs,n CRw Cws Ds En F Fo Hi,k hw hs KL Kf ks kdw kds ksorp kdes Lg
infiltration rate coefficient of each bottom outlet in tanks, 1/h pesticide concentration in surface water, mg/ m3 pesticide concentration in soil water of the nth soil layer, mg/m3 pesticide concentration in soil of the nth soil layer, mg/m3 pesticide concentration in river, mg/m3 water solubility of pesticide, mg/m3 surface diffusion coefficient in soil, m2/s evapotranspiration, mm/h calculated flow rate of river water, m3/s observed flow rate of river water, m3/s height of each side outlet in tanks, mm depth of surface water, m thickness of a soil layer, m volatilization rate of pesticide, m/s partition coefficient of pesticide between water and soil, m3/kg volumetric coefficient of mass transfer of pesticide with dissolution, 1/s degradation rate coefficient of pesticide in water, 1/s degradation rate coefficient of pesticide in soil, 1/s adsorption rate coefficient of pesticide, 1/s desorption rate coefficient of pesticide, 1/s penetration rate of water, m/s
2. Model The framework of the model is shown in Fig. 1. One subunit of a river basin is divided into ‘‘Paddy Area’’ consisting of paddy fields and ‘‘Other Area’’ except paddy fields. Both applied pesticides and paddy water are discharged from Paddy Area to the river, but only water is discharged from Other Area. Water for irrigation is supplied into Paddy Area from the river by pumps, and some are returned to the river again in the form of surface runoff water through a ditch. The pesticide runoff from paddy fields to the river can be evaluated by estimating these flows of pesticides and water in the model.
Loff Lig Moff Mdown Mup m OA PA Pi Qi,k QT Ra Ri,k s Ti t Uj j x e g
surface runoff rate of water to river, m/s surface runoff rate of water related to irrigation–runoff process, mm/h runoff rate of pesticide from paddy field area to river, mg/s rate of pesticide flowing to downstream of river, mg/s rate of pesticide flowing from upstream of river, mg/s Fruendlich exponent of pesticide, dimensionless total area of Other Area, km2 total area of Paddy Area, km2 infiltration rate from each tank, mm/h runoff rate from each tank, mm/h total runoff rate from four-stage tanks, mm/h rainfall, mm/h runoff rate coefficient of each side outlet, 1/h the number of side outlets of each tank, dimensionless water level in each tank, mm time, s, h total runoff amount of water from jth sub basin to river, m3/s the number of sub basin, dimensionless the number of data, dimensionless porosity of first layer of soil, dimensionless bulk density of soil, kg/m3
model that is well-known as a simulation model of the rainfall–runoff process [9,10]. A river basin is conceptually characterized by four-stage tanks in the tank model [11]. The upper two-stage tanks have two side outlets, and other lower two-stage tanks have one side outlet. The side outlets and the bottom ones are available for simulation of the runoff and infiltration processes, respectively. The changes of the water level in each tank can be expressed as follows: ! s X dTi ¼ Ra En Qi;k Pi ; dt k¼1 i¼1 ! s X dTi ¼ Pi1 Qi;k Pi ; dt k¼1 i¼2;3;4
2.1. Submodel for river flow The rain on a basin flows into a river through surface, intermediate and base runoff processes. It also reaches the groundwater by infiltration and spreads in the atmosphere via evapotranspiration. The flow of river can thus be described by the following rainfall–runoff process. The submodel for river flow was constructed with the tank
Qi;k ¼ Ri;k ðTi Hi;k Þ; Pi ¼ Bi Ti : The total runoff rate from four-stage tanks (mm/h), QT, can be expressed by QT ¼
4 X s X i¼1 k¼1
Qi;k :
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Pesticide Water Rainfall
Leaching
Applicatin
Rainfall
Evapotranspiration
Volatilization
Paddy Area Submodel for paddy water Submodel for pesticide behavior in paddy fields
Infiltration
Evapotranspiration
Other Area
Infiltration
Sub model for water
Runoff
Runoff
Irrigation
Stream Sub model for river flow
Downstream
Sub model for pesticide behavior in ariver
j+ 1 th sub basin
Upstream j-1 th sub basin
j th sub basin
Fig. 1. Framework of the model in one sub unit of a river basin.
Values of the coefficients of the tank model differ in Paddy Area and Other Area, because the hydrological condition of Paddy Area is different from that of Other Area. Therefore, the runoff amount of water from one sub basin to a river is expressed as Uj ¼ ðQT jPaddy
Area
PA þ QT jOther
Area
OAÞ=3:6:
In the basin that has paddy fields, the flow rate of river water is not only related to the rainfall–runoff process but also to the irrigation–runoff process associated with the water management of paddy fields, as shown in Fig. 1. However, the influence of the irrigation–runoff process to the river flow was not as large as that of the rainfall–runoff process. Thus the flow rate of river water in jth subbasin (m3/s), Fj, can be expressed by Fj ¼ Fj1 þ Uj :
2.2. Submodel for pesticide behavior in paddy fields The submodel for pesticides behavior in paddy fields was constructed based on the behaviors of pesticides in a
paddy field that was shown in a paper [6]. The model was developed by specially considering the kinetics of the transport and reaction mechanisms of pesticides applied to a paddy field. In this submodel, Paddy Area was divided into surface water, soil water and soil. The mass balance equation for each compartment can be described as follows:surface water and first layer of soil water: dðhW þ ehS ÞCW;1 dt ¼ ðhW þ ehS ÞkS ðCWS CW;1 Þ Lg CW;1 Loff CW;1 KL CW;1 ðhW þ ehS Þkdw CW;1 ghS ksorp 1=m
ðKf CW;1 CS;1 Þ
1=m
½Kf CW;1 > CS;1 ;
dðhW þ ehS ÞCW;1 dt ¼ ðhW þ ehS ÞkS ðCWS CW;1 Þ Lg CW;1 Loff CW;1 KL CW;1 ðhW þ ehS Þkdw CW;1 þ ghS kdes 1=m
ðCS;1 Kf CW;1 Þ
1=m
½CS;1 XKf CW;1 :
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nth layer of soil water ðn ¼ 2; 3; 4yÞ: dCW;n dt ¼ Lg CW;n1 ehS kdw CW;n Lg CW;n ghS ksorp dCW;n dt ¼ Lg CW;n1 ehS kdw CW;n Lg CW;n þ ghS kdes 1=m
½CS;n XKf CW;n :
nth layer of soil ðn ¼ 1; 2; 3; 4yÞ:
Mdown ¼ Moff þ Mup ; CRW ¼ ðMoff þ Mup Þ=F :
dCS;n ghS dt 1=m ¼ ghS ksorp ðKf CW;1 CS;n Þ þ AgDS ðCS;n1 CS;n Þ=hS ghS kds CS;n AgDS
1=m
ðCS;n Kf CW;n Þ ghS kds CS;n AgDS 1=m
½CS;n XKf CW;n :
These ordinary differential equations for the pesticide behaviors in paddy fields can be solved numerically using the Runge–Kutta–Gill method. To estimate the behaviors of pesticides between Paddy Area and a river, the irrigation water and the surface runoff water should be considered as the carrier of pesticides, as shown in Fig. 1. Concentrations of pesticides in a river are much lower than those in paddy fields. Thus, it is presumed that the amount of pesticides carried by irrigation from the river to paddy fields has no effective influence on the pesticide behaviors in paddy fields. Surface runoff water can be classified into two types. One is related to the rainfall–runoff process and the other is related to the irrigation–runoff process. The first type can be estimated by the submodel for the rainfall–runoff process. Therefore, the surface runoff rate of water from paddy fields into the river can be expressed as P2 Ps Qi;k jPaddy Area þ Lig Loff ¼ i¼1 k¼1 : 3:6 106 Only the runoffs from the top- and second-stage tanks in the tank model of Paddy Area are effective for the surface runoff related to the rainfall–runoff process.
The model was validated using the results obtained from the detailed field survey in the companion paper [8]. The field survey was carried out over a period of 23, April to 30, June in 1998 every day (in May) or every two days (23 to 30 in April and 2 to 30 in June) at six survey sites (St. 1 to St. 6) along the Kozakura River, Ibaraki, Prefecture, Japan (Fig. 2). In this study, the basin is divided into three subbasins (‘‘Region 1’’,
Kawamata river St . 6
St . 5
Region 1
St . 2
St . 1
St . 4 St . 3
Region 3
Region 2 Fig. 2. Location of the Kozakura river basin.
Table 1 Characteristics of subbasins in the Kozakura River Basin
2.3. Submodel for pesticide behavior in a river The following assumptions were made in the development of the submodel for pesticide behaviors in a river for simplicity: (1) pesticides released into a river are
er
dCS;n dt ¼ AgDS ðCS;n1 CS;n Þ=hS ghS kdes
ghS
ðCS;n CS;nþ1 Þ=hS
3. Simulation conditions
1=m
½Kf CW;n > CS;n ;
riv
ðCS;n CS;nþ1 Þ=hS
Moff ¼ ðCW;1 Loff PAÞ 106 ;
ra
1=m
ðCS;n Kf CW;n Þ
ku
ehS
1=m
½Kf CW;n > CS;n ;
za
1=m
ðKf CW;n CS;n Þ
Ko
ehS
completely mixed with the river water in one sub basin immediately, (2) the losses of pesticides in streaming from upstream to downstream and in discharging from paddy fields to a river are ignored, since the residence time of pesticides in one sub basin is short, and (3) there are few suspended solids in a river and effect of them on the pesticide behaviors in a river is negligible, that is conformed by the field survey. With these assumptions, the behaviors of pesticides in a river can be predicted using the results of above two submodels as follows:
Region 1 Region 2 Region 3
Basin area (km2)
Paddy fields area (km2)
Other area (km2)
8.22 3.26 3.91
0.29 0.12 0.78
7.93 3.14 3.13
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model were determined by minimizing the estimation function Z:
‘‘Region 2’’, and ‘‘Region 3’’) according to the settlement area, as shown in Fig. 2. Most of the irrigation water is supplied from the river to the paddy fields using the pumping facilities. The characteristics of each subbasin are shown in Table 1. The simulation of pesticide runoff from paddy fields to a river was carried out with two types of herbicides such as pretilachlor and mefenacet that have different physicochemical properties among those observed in the field survey. Pretilachlor has high water solubility (50 000 ppb), while mefenacet has relatively low water solubility (4000 ppb). The ability of the model was evaluated by comparing the simulation results with those in the field survey.
Z¼
ðFo;i Fi Þ2 =Fo;i :
The flow rate of river water calculated using these coefficients is presented in Fig. 3, together with the observed one and the rainfall data. The model successfully described the profiles of the observed flow rate of river water. 4.2. Pesticide behavior in a river The application amount and term of pesticides were obtained by means of a questionnaire collected directly from the all farmers in these basins. The environmental conditions of the paddy fields are shown in Table 2. The water depth of the paddy fields was 0.05 m constantly. The thickness of each soil layer was defined as 0.025 m. The soil properties were derived from the references [3,6,13]. To find the surface runoff rate of water from paddy fields to the river, Loff, the surface runoff rate related to the irrigation–runoff process, Lig, must be considered. However, it is difficult to measure Lig, thus Lig was assumed to be 0.10 mm/h, that is, 30% of the maximum irrigation rate (0.33 mm/h) calculated from the power consumption and ability of the pumping facilities in the basin. Table 2 also shows physiochemical
4.1. River flow The required input data for predicting the flow rate of river water are rainfall and evapotranspiration. Hourly rainfall data were obtained from the Yasato Meteorological Station near the field survey area. Evapotranspiration was 2.5 mm/day on rainy days and 5.0 mm/day on other days for Paddy Area [12]; it was 1.0 mm/day on rainy days and 2.0 mm/day on other days for Other Area. The simulation was carried out using these input data based on a day. The coefficients in the tank
Rainfall Rainf allll (mm/ h) (mm/h)
x X i¼1
4. Results and discussion
obse serv rv ed rive r flow. observed river flow
predicted ow pred ted river predicted riverflow flow
20 20
3027
15 10 10 5
00 44
St.2.2 St St.2
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
4/27
Ri ver flow (m 3/s /s)
1
00 44
4/23
3/s) 3/s) River f low flow rate(m (m River
3
22
St.3.3 St St.3
3
22 1
00 44
St.5 St St.5.5
3
22 1
00 6/30 6/30
6/26 6/26
6/22 6/22
6/18 6/18
6/14 6/14
6/10 6/10
6/6 6/6
6/2 6/2
5/29 5/29
5/25 5/25
5/21 5/21
5/17 5/17
5/13 5/13
5/9 5/9
5/5 5/5
5/1 5/1
4/27 4/27
4/23 4/23
Time ((day) Time(day) Fig. 3. River flow at each station and rainfall data at Yasato meteorological station.
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Table 2 Environmental conditions of paddy fields and physicochemical properties of pesticides Environmental conditions of paddy fields
Symbol
Depth of surface water (m) Thickness of each soil (m) Soil bulk density (kg/m3) Porosity of the soil Penetration rate of water (m/s) Surface runoff rate of water from paddy fields to a river per a unit area of paddy fields related to the irrigation–runoff process (mm/h)
hW hS g e Lg
0.05 0.025 1500 0.47 1.2 107
Lig
0.1
Physicochemical properties of pesticides
Symbol
Mefenacet
Pretilachlor
Water solubility (mg/m3) Dissolution rate constant (/s) Volatilization rate (m/s) Degradation rate constant in water (/s) Degradation rate constant in soil (/s) Partition coefficient (m3/kg) Fruendlich exponent Adsorption rate constant (/s) Desorption rate constant (/s) Surface diffusion coefficient (m2/s)
CWS kS KL kdw kds Kf m ksorp kdes Ds
4000 4.6 106 4.0 1013 3.9 107 1.4 106 4.8 102 1.17 1.4 105 2.3 106 8.7 1011
50 000 3.5 106a 6.8 1010 8.2 107b 4.3 107b 5.6 103a 1.15a 1.4 105 2.3 106 8.7 1011
All properties of mefenacet are cited from Ref. [6]. a Measured value. b Cited from Ref. [12]. Values are estimated from Ref. [6].
properties of pesticides that were used in the simulation. These values are cited from the references [3,6,12–14]. Fig. 4 shows, for an example, the simulation results and the data obtained from the field survey on mefenacet and pretilachlor at St. 2, St. 3, and St. 5, together with the application amount and term of the herbicides at each region. The results of mefenacet and pretilachlor were in closer agreement with the field data. The runoff rates of pesticides estimated from the simulation results and the actual runoff rates (observation) are shown in Table 3, with the application amounts collected directly through the all farmers in these regions. The runoff rates were within 9.5–12%. The runoff rate of mefenacet that has relatively low solubility was approximately the same as pretilachlor that has high solubility. This tendency was also pointed out in the field survey in the companion paper [8]. The concentration of pesticides in the river began to increase immediately after application, as can be seen in Fig. 4. This fact will give us a useful information that the stop flowing of paddy water just after application of herbicides is an important way to reduce the loading to aquatic ecosystems. From the simulation results, it is attested that the surface runoff of paddy water actually continued all the time. The simulation results also show the reason why the increase of the concentration of the
pesticides in the river during rainy days was observed in May and not in June. In May, the pesticide runoff from paddy fields markedly increased during rainy days since the runoff of paddy water was raised by rainfall. However, the pesticides hardly flowed out of the paddy fields after June 10th although the rainfall occurred many times during the period. It was demonstrated from the simulation that the pesticides adsorbed onto the paddy soils are hardly released to the paddy water during the period. The simulation results indicated that the behavior of pesticides in paddy fields strongly affects the pesticide runoff profiles.
5. Conclusion From the viewpoint of kinetics, the mathematical model was developed to predict the runoff of pesticides from paddy fields to a river. The developed model was applied to the river basin in a rural region. The model reflected well the runoff profiles of pesticides obtained from the detailed field survey. This emphasizes that the model, taking into consideration the kinetics of pesticides in paddy fields, is capable of estimating and reproducing the actual runoff characteristics of pesticides.
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Mefenacet observed co concentratio entratio n. observed concentration
00 2
44 6
6/30
6/26
6/22
6/18
6/14
6/10
6/
6/2
5/29
5/9
5/5
5/1
St.3
88 00 2
44 6
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
4/27
4/23
St.5 St .5
88 00 2
44 6
Appl ic icat at ionamount am ount ((kg) Application (kg)
St.2 St .2
4/27
88 6/30 6/30
6/26 6/26
6/22 6/22
6/18 6/18
6/14 6/14
6/10 6/10
6/6 6/6
6/2 6/2
5/29 5/29
5/25 5/25
5/21 5/21
5/17 5/17
5/13 5/13
5/9 5/9
5/5 5/5
5/1 5/1
4/27 4/27
4/23 4/23
25 25 20 15 15 10 55 00 25 25 20 15 15 10 55 00 25 25 20 15 15 10 55 00
4/23
Concentra ion Conc ncent rtat ion n(ppb) (ppb) ( pb)
application amount application app ication am ount . predicted pred icted con concent ent r ation . predicted concentration
Time(day)
Fig. 6(b). Time courses of concentration and application amount of mefenacet. applicat io ion n amount amo unt . pre ict ed predict d concent concent r at ion.
obser served co concent ncent r at io ion. n.
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
St.3 St .3
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
4/27
4/23
St.5
6/30 6/30
6/26 6/26
6/22 6/22
6/18 6/18
6/14 6/14
6/10 6/10
6/6 6/6
6/2 6/2
5/29 5/29
5/25 5/25
5/21 5/21
5/17 5/17
5/13 5/13
5/9 5/9
5/5 5/5
5/1 5/1
4/27 4/27
4/23 4/23
00 11 22 33 00 11 22 33 00 11 22 33
Appcat lication am ount (kg) g) Appli ion amount (kg)
St.2 St .2
4/27
15 15 10 10 55 00 15 15 10 10 55 00 15 15 10 10 55 00
4/23
Concentration Concent r at ion(ppb) Conce (ppb)
Pretil achlor
Time(day) Time(day)
Fig. 4. Time courses of concentration and application amount of mefenacet and pretilachlor.
Table 3 Predicted and observed runoff rates of pesticides during the field survey Application amount (kg)
Mefenacet Pretilachlor
22.1 6.6
Runoff amount (kg)
Runoff rate (%)
Observation
Simulation
Observation
Simulation
3.2 0.93
2.1 0.79
14.5 14.1
9.5 11.9
References [1] Takagi H, Aizawa T, Kasahara M, Magara Y. Behaviour of pesticides in the water resource from the paddy area. Water Supply 1995;13:119–24. [2] Johnson BR. A simple adsorption/dilution model for rice herbicides. Bull Environ Contam Toxicol 1991;47: 244–50. [3] Li S, Migita J. Pesticide runoff from paddy field and its impact on receiving water. Wat Sci Tech 1992;25(11): 69–76.
[4] Inao K, Kitamura Y. Pesticide paddy field model (PADDY) for predicting pesticide concentrations in water and soil in paddy fields. Pestic Sci 1999;55:38–46. [5] Kibe K, Takahashi M, Kameya T, Urano K. Adsorption rate equation of herbicides in paddy soils. J Pestic Sci 2000;25:234–9 [in Japanese]. [6] Yoshida T, Nakano Y. Behaviour of pesticides in a paddy field with rapid water penetration. Chem Eng Japan 2000;26(6):842–8 [in Japanese]. [7] Nagafuchi O. Study on characteristics and modeling of pesticides runoff from paddy fields. Doctor Thesis, Yamaguchi University, 1998, p. 71–94 [in Japanese].
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[8] Nakano Y, Miyazaki A, Yoshida T, Ono K, Inoue T. A study on pesticide runoff from paddy fields to a river in rural region—1: field survey of pesticide runoff in the Kozakura river, Japan. Water Res, 2004; in press. doi: 10.1016/j.watres.2004.02.013 [9] Sugawara M. On the analysis of runoff structure about several Japanese rivers. Jpn J Geophys 1961;2(4):1–76. [10] Sugawara M. Automatic calibration of the tank model. Hydro Sci Bull 1979;24:375–88. [11] Suimonkenkyukaihen in the Ministry of Construction, 9th ed. Calculation issue of an outflow of water 2, Corporation
of Japan Construction Technical Association, Tokyo; 1987. [12] Takagi H, Inao K, Kitamura Y. Mathematical model and simulation for behavior of pesticides in paddy fields, Proceedings of the 14th Symposium on Environmental Science of Pesticide 1996, p. 65–80. [13] Kanazawa J. Biodegradability of pesticides in water by microbes in activated sludge, soil and sediment. Environ Monit Assess 1987;9:57–70. [14] Tomlin C. The pesticide manual, tenth ed. London: British Crop Protection Council; 1994.
Water Research 38 (2004) 3023–3030
A study on pesticide runoff from paddy fields to a river in rural region—2: development and application of a mathematical model Yoshio Nakanoa,*, Tomohiko Yoshidaa, Takanobu Inoueb a
Department of Environmental Chemistry and Engineering, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, Kanagawa 226-8502, Japan b Department of Civil Engineering, Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan Received 29 January 2003; received in revised form 14 January 2004; accepted 16 February 2004
Abstract A mathematical model was developed to predict the runoff of pesticides from paddy fields to a river in a rural region. The model comprises three submodels: (1) submodel for river flow, (2) submodel for pesticide behavior in paddy fields, (3) submodel for pesticide behavior in a river. The tank model was applied to predict the river flow and the paddy water. In order to reproduce the actual behavior of pesticides in paddy fields, the kinetics of the transport and reaction mechanisms of pesticides applied to paddy fields were considered in the model. The model was applied to the Kozakura River Basin where the detailed field survey was conducted. The model reflected well the runoff characteristics of pesticides obtained from the detailed field survey. r 2004 Published by Elsevier Ltd. Keywords: Runoff; Mathematical model; Pesticide behavior; River basin; Kinetics
1. Introduction The use of agrochemical has dramatically increased with demands for increase in the yields of agricultural production. The adverse effects of certain agrochemicals to aquatic ecosystems and human health, however, have become known because of their acute or chronic toxicity. Among various kinds of agrochemical, pesticides applied to paddy fields have become much concern especially in Japan, because about 40% of the pesticides used are applied to paddy fields [1] and they can easily flow out to aquatic environments, causing hazard environmental problems. Thus, it is important to evaluate the runoff of pesticides applied to paddy fields to a river in a rural region. It is known that a mathematical model is a *Corresponding author. Tel.: +81-45-924-5432; fax: +8145-924-5441. E-mail address: [email protected] (Y. Nakano). 0043-1354/$ - see front matter r 2004 Published by Elsevier Ltd. doi:10.1016/j.watres.2004.02.014
valuable tool for such evaluation. Some models have been reported to predict the runoff of pesticides from a specific paddy field [2–6]. However, only a few models have been developed to predict the runoff of pesticides from paddy fields to a river [3,7]. In these models, the behavior of pesticides in paddy fields is assumed as equilibrium. However, the actual behavior of pesticides is not necessarily in equilibrium but in kinetics. Thus, a mathematical model, taking into consideration particularly the principal transport and reaction mechanisms of pesticides in paddy fields, was developed in this paper for the evaluation of pesticide runoff from paddy fields to a river in detail. To validate this model, the simulation was performed to compare with the detailed results of a field survey that are obtained by frequent observations at many stations along a river. The detailed field survey was carried out in the Kozakura River Basin, as described in a companion paper [8].
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Nomenclature Bi Cw,1 Cw,n Cs,n CRw Cws Ds En F Fo Hi,k hw hs KL Kf ks kdw kds ksorp kdes Lg
infiltration rate coefficient of each bottom outlet in tanks, 1/h pesticide concentration in surface water, mg/ m3 pesticide concentration in soil water of the nth soil layer, mg/m3 pesticide concentration in soil of the nth soil layer, mg/m3 pesticide concentration in river, mg/m3 water solubility of pesticide, mg/m3 surface diffusion coefficient in soil, m2/s evapotranspiration, mm/h calculated flow rate of river water, m3/s observed flow rate of river water, m3/s height of each side outlet in tanks, mm depth of surface water, m thickness of a soil layer, m volatilization rate of pesticide, m/s partition coefficient of pesticide between water and soil, m3/kg volumetric coefficient of mass transfer of pesticide with dissolution, 1/s degradation rate coefficient of pesticide in water, 1/s degradation rate coefficient of pesticide in soil, 1/s adsorption rate coefficient of pesticide, 1/s desorption rate coefficient of pesticide, 1/s penetration rate of water, m/s
2. Model The framework of the model is shown in Fig. 1. One subunit of a river basin is divided into ‘‘Paddy Area’’ consisting of paddy fields and ‘‘Other Area’’ except paddy fields. Both applied pesticides and paddy water are discharged from Paddy Area to the river, but only water is discharged from Other Area. Water for irrigation is supplied into Paddy Area from the river by pumps, and some are returned to the river again in the form of surface runoff water through a ditch. The pesticide runoff from paddy fields to the river can be evaluated by estimating these flows of pesticides and water in the model.
Loff Lig Moff Mdown Mup m OA PA Pi Qi,k QT Ra Ri,k s Ti t Uj j x e g
surface runoff rate of water to river, m/s surface runoff rate of water related to irrigation–runoff process, mm/h runoff rate of pesticide from paddy field area to river, mg/s rate of pesticide flowing to downstream of river, mg/s rate of pesticide flowing from upstream of river, mg/s Fruendlich exponent of pesticide, dimensionless total area of Other Area, km2 total area of Paddy Area, km2 infiltration rate from each tank, mm/h runoff rate from each tank, mm/h total runoff rate from four-stage tanks, mm/h rainfall, mm/h runoff rate coefficient of each side outlet, 1/h the number of side outlets of each tank, dimensionless water level in each tank, mm time, s, h total runoff amount of water from jth sub basin to river, m3/s the number of sub basin, dimensionless the number of data, dimensionless porosity of first layer of soil, dimensionless bulk density of soil, kg/m3
model that is well-known as a simulation model of the rainfall–runoff process [9,10]. A river basin is conceptually characterized by four-stage tanks in the tank model [11]. The upper two-stage tanks have two side outlets, and other lower two-stage tanks have one side outlet. The side outlets and the bottom ones are available for simulation of the runoff and infiltration processes, respectively. The changes of the water level in each tank can be expressed as follows: ! s X dTi ¼ Ra En Qi;k Pi ; dt k¼1 i¼1 ! s X dTi ¼ Pi1 Qi;k Pi ; dt k¼1 i¼2;3;4
2.1. Submodel for river flow The rain on a basin flows into a river through surface, intermediate and base runoff processes. It also reaches the groundwater by infiltration and spreads in the atmosphere via evapotranspiration. The flow of river can thus be described by the following rainfall–runoff process. The submodel for river flow was constructed with the tank
Qi;k ¼ Ri;k ðTi Hi;k Þ; Pi ¼ Bi Ti : The total runoff rate from four-stage tanks (mm/h), QT, can be expressed by QT ¼
4 X s X i¼1 k¼1
Qi;k :
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Pesticide Water Rainfall
Leaching
Applicatin
Rainfall
Evapotranspiration
Volatilization
Paddy Area Submodel for paddy water Submodel for pesticide behavior in paddy fields
Infiltration
Evapotranspiration
Other Area
Infiltration
Sub model for water
Runoff
Runoff
Irrigation
Stream Sub model for river flow
Downstream
Sub model for pesticide behavior in ariver
j+ 1 th sub basin
Upstream j-1 th sub basin
j th sub basin
Fig. 1. Framework of the model in one sub unit of a river basin.
Values of the coefficients of the tank model differ in Paddy Area and Other Area, because the hydrological condition of Paddy Area is different from that of Other Area. Therefore, the runoff amount of water from one sub basin to a river is expressed as Uj ¼ ðQT jPaddy
Area
PA þ QT jOther
Area
OAÞ=3:6:
In the basin that has paddy fields, the flow rate of river water is not only related to the rainfall–runoff process but also to the irrigation–runoff process associated with the water management of paddy fields, as shown in Fig. 1. However, the influence of the irrigation–runoff process to the river flow was not as large as that of the rainfall–runoff process. Thus the flow rate of river water in jth subbasin (m3/s), Fj, can be expressed by Fj ¼ Fj1 þ Uj :
2.2. Submodel for pesticide behavior in paddy fields The submodel for pesticides behavior in paddy fields was constructed based on the behaviors of pesticides in a
paddy field that was shown in a paper [6]. The model was developed by specially considering the kinetics of the transport and reaction mechanisms of pesticides applied to a paddy field. In this submodel, Paddy Area was divided into surface water, soil water and soil. The mass balance equation for each compartment can be described as follows:surface water and first layer of soil water: dðhW þ ehS ÞCW;1 dt ¼ ðhW þ ehS ÞkS ðCWS CW;1 Þ Lg CW;1 Loff CW;1 KL CW;1 ðhW þ ehS Þkdw CW;1 ghS ksorp 1=m
ðKf CW;1 CS;1 Þ
1=m
½Kf CW;1 > CS;1 ;
dðhW þ ehS ÞCW;1 dt ¼ ðhW þ ehS ÞkS ðCWS CW;1 Þ Lg CW;1 Loff CW;1 KL CW;1 ðhW þ ehS Þkdw CW;1 þ ghS kdes 1=m
ðCS;1 Kf CW;1 Þ
1=m
½CS;1 XKf CW;1 :
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nth layer of soil water ðn ¼ 2; 3; 4yÞ: dCW;n dt ¼ Lg CW;n1 ehS kdw CW;n Lg CW;n ghS ksorp dCW;n dt ¼ Lg CW;n1 ehS kdw CW;n Lg CW;n þ ghS kdes 1=m
½CS;n XKf CW;n :
nth layer of soil ðn ¼ 1; 2; 3; 4yÞ:
Mdown ¼ Moff þ Mup ; CRW ¼ ðMoff þ Mup Þ=F :
dCS;n ghS dt 1=m ¼ ghS ksorp ðKf CW;1 CS;n Þ þ AgDS ðCS;n1 CS;n Þ=hS ghS kds CS;n AgDS
1=m
ðCS;n Kf CW;n Þ ghS kds CS;n AgDS 1=m
½CS;n XKf CW;n :
These ordinary differential equations for the pesticide behaviors in paddy fields can be solved numerically using the Runge–Kutta–Gill method. To estimate the behaviors of pesticides between Paddy Area and a river, the irrigation water and the surface runoff water should be considered as the carrier of pesticides, as shown in Fig. 1. Concentrations of pesticides in a river are much lower than those in paddy fields. Thus, it is presumed that the amount of pesticides carried by irrigation from the river to paddy fields has no effective influence on the pesticide behaviors in paddy fields. Surface runoff water can be classified into two types. One is related to the rainfall–runoff process and the other is related to the irrigation–runoff process. The first type can be estimated by the submodel for the rainfall–runoff process. Therefore, the surface runoff rate of water from paddy fields into the river can be expressed as P2 Ps Qi;k jPaddy Area þ Lig Loff ¼ i¼1 k¼1 : 3:6 106 Only the runoffs from the top- and second-stage tanks in the tank model of Paddy Area are effective for the surface runoff related to the rainfall–runoff process.
The model was validated using the results obtained from the detailed field survey in the companion paper [8]. The field survey was carried out over a period of 23, April to 30, June in 1998 every day (in May) or every two days (23 to 30 in April and 2 to 30 in June) at six survey sites (St. 1 to St. 6) along the Kozakura River, Ibaraki, Prefecture, Japan (Fig. 2). In this study, the basin is divided into three subbasins (‘‘Region 1’’,
Kawamata river St . 6
St . 5
Region 1
St . 2
St . 1
St . 4 St . 3
Region 3
Region 2 Fig. 2. Location of the Kozakura river basin.
Table 1 Characteristics of subbasins in the Kozakura River Basin
2.3. Submodel for pesticide behavior in a river The following assumptions were made in the development of the submodel for pesticide behaviors in a river for simplicity: (1) pesticides released into a river are
er
dCS;n dt ¼ AgDS ðCS;n1 CS;n Þ=hS ghS kdes
ghS
ðCS;n CS;nþ1 Þ=hS
3. Simulation conditions
1=m
½Kf CW;n > CS;n ;
riv
ðCS;n CS;nþ1 Þ=hS
Moff ¼ ðCW;1 Loff PAÞ 106 ;
ra
1=m
ðCS;n Kf CW;n Þ
ku
ehS
1=m
½Kf CW;n > CS;n ;
za
1=m
ðKf CW;n CS;n Þ
Ko
ehS
completely mixed with the river water in one sub basin immediately, (2) the losses of pesticides in streaming from upstream to downstream and in discharging from paddy fields to a river are ignored, since the residence time of pesticides in one sub basin is short, and (3) there are few suspended solids in a river and effect of them on the pesticide behaviors in a river is negligible, that is conformed by the field survey. With these assumptions, the behaviors of pesticides in a river can be predicted using the results of above two submodels as follows:
Region 1 Region 2 Region 3
Basin area (km2)
Paddy fields area (km2)
Other area (km2)
8.22 3.26 3.91
0.29 0.12 0.78
7.93 3.14 3.13
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model were determined by minimizing the estimation function Z:
‘‘Region 2’’, and ‘‘Region 3’’) according to the settlement area, as shown in Fig. 2. Most of the irrigation water is supplied from the river to the paddy fields using the pumping facilities. The characteristics of each subbasin are shown in Table 1. The simulation of pesticide runoff from paddy fields to a river was carried out with two types of herbicides such as pretilachlor and mefenacet that have different physicochemical properties among those observed in the field survey. Pretilachlor has high water solubility (50 000 ppb), while mefenacet has relatively low water solubility (4000 ppb). The ability of the model was evaluated by comparing the simulation results with those in the field survey.
Z¼
ðFo;i Fi Þ2 =Fo;i :
The flow rate of river water calculated using these coefficients is presented in Fig. 3, together with the observed one and the rainfall data. The model successfully described the profiles of the observed flow rate of river water. 4.2. Pesticide behavior in a river The application amount and term of pesticides were obtained by means of a questionnaire collected directly from the all farmers in these basins. The environmental conditions of the paddy fields are shown in Table 2. The water depth of the paddy fields was 0.05 m constantly. The thickness of each soil layer was defined as 0.025 m. The soil properties were derived from the references [3,6,13]. To find the surface runoff rate of water from paddy fields to the river, Loff, the surface runoff rate related to the irrigation–runoff process, Lig, must be considered. However, it is difficult to measure Lig, thus Lig was assumed to be 0.10 mm/h, that is, 30% of the maximum irrigation rate (0.33 mm/h) calculated from the power consumption and ability of the pumping facilities in the basin. Table 2 also shows physiochemical
4.1. River flow The required input data for predicting the flow rate of river water are rainfall and evapotranspiration. Hourly rainfall data were obtained from the Yasato Meteorological Station near the field survey area. Evapotranspiration was 2.5 mm/day on rainy days and 5.0 mm/day on other days for Paddy Area [12]; it was 1.0 mm/day on rainy days and 2.0 mm/day on other days for Other Area. The simulation was carried out using these input data based on a day. The coefficients in the tank
Rainfall Rainf allll (mm/ h) (mm/h)
x X i¼1
4. Results and discussion
obse serv rv ed rive r flow. observed river flow
predicted ow pred ted river predicted riverflow flow
20 20
3027
15 10 10 5
00 44
St.2.2 St St.2
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
4/27
Ri ver flow (m 3/s /s)
1
00 44
4/23
3/s) 3/s) River f low flow rate(m (m River
3
22
St.3.3 St St.3
3
22 1
00 44
St.5 St St.5.5
3
22 1
00 6/30 6/30
6/26 6/26
6/22 6/22
6/18 6/18
6/14 6/14
6/10 6/10
6/6 6/6
6/2 6/2
5/29 5/29
5/25 5/25
5/21 5/21
5/17 5/17
5/13 5/13
5/9 5/9
5/5 5/5
5/1 5/1
4/27 4/27
4/23 4/23
Time ((day) Time(day) Fig. 3. River flow at each station and rainfall data at Yasato meteorological station.
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Table 2 Environmental conditions of paddy fields and physicochemical properties of pesticides Environmental conditions of paddy fields
Symbol
Depth of surface water (m) Thickness of each soil (m) Soil bulk density (kg/m3) Porosity of the soil Penetration rate of water (m/s) Surface runoff rate of water from paddy fields to a river per a unit area of paddy fields related to the irrigation–runoff process (mm/h)
hW hS g e Lg
0.05 0.025 1500 0.47 1.2 107
Lig
0.1
Physicochemical properties of pesticides
Symbol
Mefenacet
Pretilachlor
Water solubility (mg/m3) Dissolution rate constant (/s) Volatilization rate (m/s) Degradation rate constant in water (/s) Degradation rate constant in soil (/s) Partition coefficient (m3/kg) Fruendlich exponent Adsorption rate constant (/s) Desorption rate constant (/s) Surface diffusion coefficient (m2/s)
CWS kS KL kdw kds Kf m ksorp kdes Ds
4000 4.6 106 4.0 1013 3.9 107 1.4 106 4.8 102 1.17 1.4 105 2.3 106 8.7 1011
50 000 3.5 106a 6.8 1010 8.2 107b 4.3 107b 5.6 103a 1.15a 1.4 105 2.3 106 8.7 1011
All properties of mefenacet are cited from Ref. [6]. a Measured value. b Cited from Ref. [12]. Values are estimated from Ref. [6].
properties of pesticides that were used in the simulation. These values are cited from the references [3,6,12–14]. Fig. 4 shows, for an example, the simulation results and the data obtained from the field survey on mefenacet and pretilachlor at St. 2, St. 3, and St. 5, together with the application amount and term of the herbicides at each region. The results of mefenacet and pretilachlor were in closer agreement with the field data. The runoff rates of pesticides estimated from the simulation results and the actual runoff rates (observation) are shown in Table 3, with the application amounts collected directly through the all farmers in these regions. The runoff rates were within 9.5–12%. The runoff rate of mefenacet that has relatively low solubility was approximately the same as pretilachlor that has high solubility. This tendency was also pointed out in the field survey in the companion paper [8]. The concentration of pesticides in the river began to increase immediately after application, as can be seen in Fig. 4. This fact will give us a useful information that the stop flowing of paddy water just after application of herbicides is an important way to reduce the loading to aquatic ecosystems. From the simulation results, it is attested that the surface runoff of paddy water actually continued all the time. The simulation results also show the reason why the increase of the concentration of the
pesticides in the river during rainy days was observed in May and not in June. In May, the pesticide runoff from paddy fields markedly increased during rainy days since the runoff of paddy water was raised by rainfall. However, the pesticides hardly flowed out of the paddy fields after June 10th although the rainfall occurred many times during the period. It was demonstrated from the simulation that the pesticides adsorbed onto the paddy soils are hardly released to the paddy water during the period. The simulation results indicated that the behavior of pesticides in paddy fields strongly affects the pesticide runoff profiles.
5. Conclusion From the viewpoint of kinetics, the mathematical model was developed to predict the runoff of pesticides from paddy fields to a river. The developed model was applied to the river basin in a rural region. The model reflected well the runoff profiles of pesticides obtained from the detailed field survey. This emphasizes that the model, taking into consideration the kinetics of pesticides in paddy fields, is capable of estimating and reproducing the actual runoff characteristics of pesticides.
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Mefenacet observed co concentratio entratio n. observed concentration
00 2
44 6
6/30
6/26
6/22
6/18
6/14
6/10
6/
6/2
5/29
5/9
5/5
5/1
St.3
88 00 2
44 6
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
4/27
4/23
St.5 St .5
88 00 2
44 6
Appl ic icat at ionamount am ount ((kg) Application (kg)
St.2 St .2
4/27
88 6/30 6/30
6/26 6/26
6/22 6/22
6/18 6/18
6/14 6/14
6/10 6/10
6/6 6/6
6/2 6/2
5/29 5/29
5/25 5/25
5/21 5/21
5/17 5/17
5/13 5/13
5/9 5/9
5/5 5/5
5/1 5/1
4/27 4/27
4/23 4/23
25 25 20 15 15 10 55 00 25 25 20 15 15 10 55 00 25 25 20 15 15 10 55 00
4/23
Concentra ion Conc ncent rtat ion n(ppb) (ppb) ( pb)
application amount application app ication am ount . predicted pred icted con concent ent r ation . predicted concentration
Time(day)
Fig. 6(b). Time courses of concentration and application amount of mefenacet. applicat io ion n amount amo unt . pre ict ed predict d concent concent r at ion.
obser served co concent ncent r at io ion. n.
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
St.3 St .3
6/30
6/26
6/22
6/18
6/14
6/10
6/6
6/2
5/29
5/25
5/21
5/17
5/13
5/9
5/5
5/1
4/27
4/23
St.5
6/30 6/30
6/26 6/26
6/22 6/22
6/18 6/18
6/14 6/14
6/10 6/10
6/6 6/6
6/2 6/2
5/29 5/29
5/25 5/25
5/21 5/21
5/17 5/17
5/13 5/13
5/9 5/9
5/5 5/5
5/1 5/1
4/27 4/27
4/23 4/23
00 11 22 33 00 11 22 33 00 11 22 33
Appcat lication am ount (kg) g) Appli ion amount (kg)
St.2 St .2
4/27
15 15 10 10 55 00 15 15 10 10 55 00 15 15 10 10 55 00
4/23
Concentration Concent r at ion(ppb) Conce (ppb)
Pretil achlor
Time(day) Time(day)
Fig. 4. Time courses of concentration and application amount of mefenacet and pretilachlor.
Table 3 Predicted and observed runoff rates of pesticides during the field survey Application amount (kg)
Mefenacet Pretilachlor
22.1 6.6
Runoff amount (kg)
Runoff rate (%)
Observation
Simulation
Observation
Simulation
3.2 0.93
2.1 0.79
14.5 14.1
9.5 11.9
References [1] Takagi H, Aizawa T, Kasahara M, Magara Y. Behaviour of pesticides in the water resource from the paddy area. Water Supply 1995;13:119–24. [2] Johnson BR. A simple adsorption/dilution model for rice herbicides. Bull Environ Contam Toxicol 1991;47: 244–50. [3] Li S, Migita J. Pesticide runoff from paddy field and its impact on receiving water. Wat Sci Tech 1992;25(11): 69–76.
[4] Inao K, Kitamura Y. Pesticide paddy field model (PADDY) for predicting pesticide concentrations in water and soil in paddy fields. Pestic Sci 1999;55:38–46. [5] Kibe K, Takahashi M, Kameya T, Urano K. Adsorption rate equation of herbicides in paddy soils. J Pestic Sci 2000;25:234–9 [in Japanese]. [6] Yoshida T, Nakano Y. Behaviour of pesticides in a paddy field with rapid water penetration. Chem Eng Japan 2000;26(6):842–8 [in Japanese]. [7] Nagafuchi O. Study on characteristics and modeling of pesticides runoff from paddy fields. Doctor Thesis, Yamaguchi University, 1998, p. 71–94 [in Japanese].
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[8] Nakano Y, Miyazaki A, Yoshida T, Ono K, Inoue T. A study on pesticide runoff from paddy fields to a river in rural region—1: field survey of pesticide runoff in the Kozakura river, Japan. Water Res, 2004; in press. doi: 10.1016/j.watres.2004.02.013 [9] Sugawara M. On the analysis of runoff structure about several Japanese rivers. Jpn J Geophys 1961;2(4):1–76. [10] Sugawara M. Automatic calibration of the tank model. Hydro Sci Bull 1979;24:375–88. [11] Suimonkenkyukaihen in the Ministry of Construction, 9th ed. Calculation issue of an outflow of water 2, Corporation
of Japan Construction Technical Association, Tokyo; 1987. [12] Takagi H, Inao K, Kitamura Y. Mathematical model and simulation for behavior of pesticides in paddy fields, Proceedings of the 14th Symposium on Environmental Science of Pesticide 1996, p. 65–80. [13] Kanazawa J. Biodegradability of pesticides in water by microbes in activated sludge, soil and sediment. Environ Monit Assess 1987;9:57–70. [14] Tomlin C. The pesticide manual, tenth ed. London: British Crop Protection Council; 1994.