Modeling water temperature in a rice paddy for agro-environmental research

agricultural and forest meteorology 148 (2008) 1754–1766

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Modeling water temperature in a rice paddy for agro-environmental research Tsuneo Kuwagata a,*, Takahiro Hamasaki b, Tsutomu Watanabe c a

National Institute for Agro-Environmental Sciences, Tsukuba 305-8604, Japan National Agricultural Research Center for Hokkaido Region, Sapporo 062-8555, Japan c Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan b

article info

abstract

Article history:

Water temperature in rice paddies (Oryza sativa L.) is one of the most important factors

Received 10 January 2008

affecting the growth and yield of rice, and also influences CH4 emission from paddy fields.

Received in revised form

We developed a simple model of the daily mean water temperature in a rice paddy. The

6 May 2008

model has two steps for evaluating the paddy water temperature. In the first step, the daily

Accepted 19 June 2008

mean water temperature of a non-vegetated water surface (Tw0 ) is evaluated from meteorological data (air temperature, specific humidity, wind speed, solar radiation, and downward longwave radiation) by daily 24-h mean or daytime (nighttime) 12-h mean heat

Keywords:

balance equations. The bulk heat transfer coefficient at the water surface is a key parameter

Crop canopy

for evaluating Tw0 . Next, the daily mean water temperature in a rice paddy ðTw Þ is evaluated

Micrometeorology

by adding a correction term to Tw0 . Here, the correction term is described as a function of the

Rice paddy

leaf area index (LAI), solar radiation, and wind speed, and the formula was determined

Surface energy balance

empirically. The model simulated fairly well the daily mean water temperature of rice

Turbulent exchange process

paddies with root mean square errors of 0.81–0.85 8C.

Water temperature

This study also demonstrated the important result that the influence of a plant canopy on water temperature depends not only on canopy density (LAI), but also on solar radiation and wind speed. Tw was usually lower than Tw0 , but in rice paddies with LAI = 0.5–1.5, Tw was higher than Tw0 under strong wind conditions in sunny weather. These characteristics were incorporated into the model developed in this study. # 2008 Elsevier B.V. All rights reserved.

1.

Introduction

Rice (Oryza sativa L.) is a staple food on which half of the world’s population relies, and is widely cultivated in climatic regions from tropical to cool-temperate. Rice is usually grown under flooded conditions; about three-quarters of global rice production is grown in irrigated flooded fields (IRRI, 2002). The water temperature in a rice paddy is one of the most important factors affecting the growth and yield of rice. Crop growth rate and leaf photosynthesis are influenced by water temperature

at different growth stages (Matsushima et al., 1964; Shimono et al., 2002, 2004), and the risk of spikelet sterility is increased by cold water temperatures (Satake et al., 1988; Shimono et al., 2002, 2005). Because of the importance of water temperature in rice production, rice paddy water temperature must be input into crop growth models for paddy rice (Hasegawa and Horie, 1997; Confalonieri et al., 2005; Shimono et al., 2007a,b). Water temperature in a rice paddy also influences the emission of methane (CH4), which is one of the most important greenhouse gases. CH4 is emitted from rice paddy fields through the plant body (Nouchi et al., 1990, 1994). The rice

* Corresponding author. Fax: +81 29 838 8211. E-mail address: [email protected] (T. Kuwagata). 0168-1923/$ – see front matter # 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2008.06.011

agricultural and forest meteorology 148 (2008) 1754–1766

paddy water temperature affects not only biogeochemical processes related to CH4 production in saturated paddy soils but also the conductance of CH4 through the rice plants (Hosono and Nouchi, 1997; Fumoto et al., 2008). Therefore, precise estimation of the paddy water temperature is very important both for modeling and for estimating CH4 emissions from rice paddy fields worldwide (Fumoto et al., 2008). Several studies have attempted to model water temperature in a rice paddy. Uchijima (1959, 1963) investigated annual variations in water temperature and heat balance in shallow water with no rice plants and evaluated the climatic aspects of seasonal and spatial variations of paddy water temperature in Japan by using a simplified heat balance equation. Because the actual water temperature is influenced by the canopy density of rice plants (Uchijima, 1961), Takami et al. (1989) presented a simple scheme for evaluating the daily mean water temperature under a plant canopy by using a simplified heat balance equation. Similar models have been developed by Maruyama et al. (1998) and Ohta and Kimura (2007) to estimate the daily mean paddy water temperature under various weather conditions. In these three models, the bulk heat transfer coefficient at the water surface was held constant or allowed to vary as a function of canopy density only, and the effect of wind speed on the water temperature was not taken into account, although in rice paddies, the actual water temperature depends also on wind speed. During the last 20–30 years, many integrated models have also been developed for studying the heat balance and micrometeorology of plant canopies (e.g., Norman and Campbell, 1983; Foley et al., 1996; Sellers et al., 1996; Anderson et al., 2000; Watanabe et al., 2004). Some of these models can simulate the microclimate and water temperature in a rice paddy (Inoue, 1985; Kim et al., 2001; Saptomo et al., 2004). These models, however, are not simple; they require data on many model parameters to characterize the thermal and physiological properties of the canopy and soil layers even to evaluate just the daily mean paddy water temperature. Therefore, a new, simple model for evaluating the daily mean water temperature in a rice paddy is needed. In this study, we developed a new, simple model for evaluating the daily mean water temperature in a rice paddy. Using this model, we compared simulation results with field observations for daily mean paddy water temperature, and also investigated the influence of meteorological conditions, such as wind speed, and the leaf area index (LAI) on water temperature.

2.

Materials and methods

2.1.

Concept of the model

Our model for evaluating paddy water temperature is based on heat balance equations for the water surface, and takes into account the effect of the plant canopy on the water temperature. The model consists of two steps. In the first step, the daily mean water temperature of a non-vegetated water surface ðTw0 Þ is evaluated from meteorological data (air temperature, specific humidity, wind speed, solar radiation, and downward longwave radiation) by using heat balance equations. Next, the daily mean

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water temperature in a rice paddy ðTw Þ is evaluated by adding a correction term to Tw0 . The correction term is a function of LAI and meteorological conditions (solar radiation and wind speed) and is determined empirically. The detailed structure of the model is explained in Section 3.4.1, and flow charts outlining the procedure for evaluating Tw and Tw0 are shown in Fig. 10.

2.2.

Basic equations for the non-vegetated water surface

2.2.1. Diurnal variations in the water temperature of the nonvegetated water surface We examined the diurnal variations in water temperature and heat balance of the non-vegetated water surface to determine the method for evaluating Tw0 . For simplicity, we assumed that water temperature was vertically and horizontally uniform in each paddy field, that the soil was homogeneous, and that there was no horizontal heat transfer in the soil. The heat budget for the non-vegetated water surface is given by Kondo (1994) R #  G ¼ H þ lE þ esT4w0 ;

(1)

R #  ð1  rg ÞS # þ eL # ;

(2)

where R# is the downward radiative flux, G is the heat storage of the ground, H is the sensible heat flux, lE is the latent heat flux (E is the rate of evaporation from the water surface (kg m2 s1)), l is the specific latent heat of vaporization (J kg1), and Tw0 is the water temperature of the non-vegetated water surface (K). S# is the solar radiation, L# is the downward longwave radiation, rg is the albedo of the water surface, s is the Stefan–Boltzmann constant (=5.67  108 W m2 K1), and e is the emissivity of the water surface (assumed to be 1.0 in this study). The units of each term in Eq. (1) are W m2 (or MJ m2 d1). The sensible and latent heat fluxes were parameterized by using the bulk formulas (Kondo and Ishida, 1997): H ¼ c p rCH uðTw0  TÞ;

(3)

lE ¼ lrCE uðqsat ðTw0 Þ  qÞ;

(4)

where cp is the specific heat of air at constant pressure (J kg1 K1), r is the density of air (kg m3), u is the wind speed (m s1), T is the air temperature (K), q is the specific humidity (kg kg1), and qsat(Tw0) is the saturated specific humidity at the water temperature Tw0. CH and CE are the bulk transfer coefficients for sensible and latent heat, respectively (CH ffi CE for the water surface). The values of CH and CE depend on both the roughness lengths of the water surface and the thermal stability of the air flow over the water surface (see Appendix A). The heat storage of the ground, G, is divided into two terms: G ¼ Gw þ Gs ; Gw ¼ cw rw Dw

Gs ¼ lg

(5) @Tw0 þ cw rw wp ðTw0  Tw0 Þ; @t

 @Ts  ; @z z¼0

(6)

(7)

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where Gw is the heat storage of the water layer and Gs is the heat flux into the soil. Tw0 is the temperature of the irrigation water (K), cw is the specific heat of water (J kg1 K1), rw is the density of water (kg m3), Dw is the depth of the water layer (m), wp is the inflow rate of irrigation water (m s1), Ts is the soil temperature (K), lg is the heat conductivity of soil (W m1 K1), and z is the depth of the soil (m). If Dw is invariant with time, then wp is consistent with the amount of water loss at depth. Heat conduction in the soil is given by (e.g., Antonopoulos, 2006):   @Ts @ @Ts @Ts lg ¼  cw rw wp ; (8) cg rg @z @t @z @z where t is time, cg is the specific heat of soil (J kg1 K1), rg is the density of soil (kg m3), and wp is the liquid water flux in the soil (m s1, assumed to be invariant with z and positive downward). Eq. (8) can be numerically solved for given initial conditions of the soil temperature profile, Ts(z, t0), and boundary conditions, Ts(0, t) = Tw0(t) and @Ts(zbot, t)/@z = 0 (0  z  zbot, t  t0). Here, zbot is the depth of the lower boundary (bottom) of the soil. The value of zbot was determined by considering soil-layer conditions and the integration time used to solve Eq. (8). Time series of (Tw0, H, lE, Ts) can be evaluated from time series of meteorological conditions (T, q, u, S#, L#) by solving Eqs. (1)–(8).

2.2.2. Daily mean water temperature of the non-vegetated water surface To evaluate the daily mean water temperature of the nonvegetated water surface, the following heat balance and heat transfer equations are used by the model: 4

R # ¼ H þ lE þ esTw0 ;

(9)

H ¼ c p rCH uðTw0  TÞ;

(10)

lE ¼ lrCE uðqsat ðTw0 Þ  qÞ;

(11)

(1971–2000) are 21.0 8C and 79%), and the total precipitation during same period was 353 mm (the normal value is 458 mm). Three test fields were used, each 14 m  18 m. The planting density of the first field (paddy 1) was 11 hills m2 (30 cm  30 cm per hill), and that of the second field (paddy 2) was 25 hills m2 (20 cm  20 cm per hill). There were no plants in the third field (non-vegetated test field). The water depth of each field was controlled at 7–8 cm during the experimental period (early July to late August). Irrigated water stored in a water warming pond flowed continuously into the paddies through channels to minimize horizontal heterogeneity of water temperature in the test fields. The rice cultivar grown in the experiment was Akitakomachi. Germinated seeds were seeded directly (four seeds per hill) into paddies 1 and 2 on 29 May 1997. Data from the three test fields were used to develop the model. The method for evaluating the water temperature of a non-vegetated water surface ðTw0 Þ was established by using the data from the non-vegetated test field. The influence of canopy density on water temperature was examined by comparing the data from the two paddy fields in which rice was grown (paddies 1 and 2) with the data from the nonvegetated test field. The correction term for evaluating the rice paddy water temperature ðTw Þ from Tw0 was determined from this comparison. The influence of planting density on water temperature was also examined by comparing the data between paddies 1 and 2. Another test field (paddy A), located 1.5 km north of the other three test fields, was used to validate the accuracy of the newly developed model. This field was 20 m  50 m, and the planting density near the center of the paddy was 16.7 hills m2 (30 cm  20 cm spacing). Water depth varied from 0 to 10 cm during the experimental period (early July to mid-August). The field was irrigated with water that flowed directly from an irrigation channel, and a water warming pond was not used. Seedlings of the cultivar Akitakomachi were transplanted into the paddy in early June.

2.3.2. where the overbar denotes the daily mean value averaged over 24 h. Note that the daily mean heat storage of the ground, G, is assumed to be zero in Eq. (9). These equations are also used for describing the daytime or nighttime mean (averaged over 12 h) heat balance of the non-vegetated water surface. As discussed in Section 3.2, the values of CH and CE in Eqs. (10) and (11) for the daily mean heat balance are not equal to those used in Eqs. (3) and (4).

2.3.

Experimental design

2.3.1.

Test fields

Field experiments were carried out at the National Agricultural Research Center for Tohoku Region, Morioka, Japan (39845.00 N, 14188.50 E, 170 m MSL) from spring to summer 1997. Morioka is located in northern Japan, where the growth and yield of rice are sometimes damaged by low temperatures during cool summer conditions. In Morioka, the daily mean temperature and humidity, averaged from June to August in 1997, were 21.6 8C and 78% (the normal values over 30 years

Measurements and data

The canopy density of rice plants is represented in the model by the LAI, which is defined as the total area of leaves above a unit area of ground. LAI was measured at 6- to 8-day intervals during the rice-growing season in paddies 1 and 2 and at 3- to 14-day intervals in paddy A. In paddies 1 and 2, a total of 12–24 plant samples from 4 plots were measured. The location of each plot was determined at random for each measurement. In paddy A, which was treated as a single plot, 3–20 plant samples were measured. An automatic area meter (AAM-9; Hayashi Denko Co., Tokyo, Japan) was used to measure leaf area. Daily LAI values were obtained from regression curves (expressed as polynomial [or sigmoid] functions of day of year), which were calculated from the measurement data by the least-squares method. Water temperatures (at the water surface and at 0 and 2 cm above the soil surface) and soil temperatures (at 5 or 6 depths from the surface to 0.35 m depth) were measured in the center of each field with thermocouples (Type-T) with a precision of 0.1 8C. To examine the horizontal uniformity of water temperature in each field, water temperatures

agricultural and forest meteorology 148 (2008) 1754–1766

(2 cm above the soil surface) at two points 4.5–5 m from the center of the field on opposite sides and the temperature of the irrigation water at the water inlet to the field were measured. There were no significant differences among the water temperatures measured at the three depths in the center of each field, and the horizontal differences in water temperature were small in all fields. Therefore, we used the water temperatures measured at 2 cm above the soil surface in the center of each field as the representative value of water temperature. Air temperature and humidity were measured at 1.4 m above the ground (Vaisala HMP35D sensors; housed under an aspirated radiation shield), and wind speed and direction were measured at 2.5 m above the ground with a propeller-vane anemometer (Model 5103; R.M. Young Co., Traverse City, MI, USA). Solar radiation and downward longwave radiation were measured with a pyranometer (MS-801; EKO Instruments Co., Tokyo, Japan) and a pyrgeometer (PIR; Eppley Lab. Inc., Newport, RI, USA), respectively. These sensors were installed next to the three test fields. The albedo of the water surface in all test fields was determined by measuring downward and upward solar radiation with a pair of pyranometers (MS-801) before seeding or transplanting. Its value was 0.05 in all 4 fields. Most data (water and soil temperatures and meteorological data) were collected at 1-min intervals, converted to 10-min averages, and stored in dataloggers (CR10X, CR21X; Campbell Sci. Inc., Logan, UT, USA).

2.4.

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2.4.2. Calculation of daily mean water temperature of the non-vegetated water surface The daily mean water temperature of the non-vegetated water surface was evaluated from the daily mean meteorological data ðT; q; u; S # ; L # Þ by Eqs. (9)–(11). The daytime or nighttime mean (averaged over 12 h) water temperature of the nonvegetated water surface was also evaluated by Eqs. (9)–(11) in the same manner. The calculation was carried out for the period from 8 July to 27 August 1997. During this period, the non-vegetated test field was flooded. The results of the calculation are reported in Section 3.2.

2.4.3.

Influence of canopy density on water temperature

The water temperature in a rice paddy is strongly influenced by the canopy density (LAI) of rice plants, which gradually increases during the growing season. Both the radiative and turbulent environments in the plant canopy vary with canopy density, thereby altering the paddy water temperature (Uchijima, 1961). In this study, we examined the difference in the daily mean water temperature between a paddy ðTw Þ and a non-vegetated water surface ðTw0 Þ for various meteorological conditions by comparing the data from the two test paddy fields (paddies 1 and 2) with the data from the nonvegetated test field. On the basis of the data from the three test fields from 13 July to 26 August 1997, the value of DTw ð  Tw  Tw0 Þ was experimentally parameterized as a function of solar radiation, wind speed, and LAI. During this period, the test fields (paddies 1 and 2) were flooded and covered with the growing rice crop.

Procedures for calculation and analysis

2.4.1. Numerical experiment of water temperature and heat balance of the non-vegetated water surface

3.

Results and discussion

The diurnal variations in water temperature and heat balance of the non-vegetated water surface (the non-vegetated test field in the field experiments) were evaluated by numerically solving Eqs. (1)–(8). For the actual calculation, Eqs. (6)–(8) were transformed into finite-difference equations (CrankNicolson method), which were integrated with Eqs. (1)–(4) with adequate iterations to satisfy all equations. The calculation was carried out for 13 consecutive days (from 0900 JST 22 July to 0900 JST 2 August 1997, where JST is Japan Standard Time). Because there was no rain during this period, the conditions were suitable for analyzing the diurnal variations in water temperature and heat balance. The results of the calculation are described in Section 3.1. The observed meteorological data (T, q, u, S#, L#) in the experimental field were used as input data for the calculation, and the initial soil temperature profile was also based on observed data. The depth of the lower boundary of the soil was set at zbot = 60 cm, and the water depth was set at 7 cm. The soil parameters used were cgrg = 3.60  106 J m3 K1 and lg = 1.0 W m1 K1, which were measured experimentally in soil samples. For simplicity, the liquid water flux in the soil was assumed to be wp = 0 mm day1, and the temperature of the irrigation water, Tw0 , was assumed to be same as that of the non-vegetated water surface, Tw0; the latter assumption was confirmed by measuring Tw0 . The albedo of the water surface was set at rg = 0.05, the measured value.

We present and discuss our results in four parts. First, in Section 3.1, we analyze the characteristics of water temperature and heat balance of the non-vegetated water surface on the basis of field observations and the numerical experiment using the heat balance equations. Next, on the basis of the results reported in Section 3.1, we introduce two alternative methods for evaluating the daily mean water temperature of a non-vegetated water surface ðTw0 Þ (Section 3.2). Then, in Section 3.3, we examine the influence of canopy density on water temperature to parameterize the difference in the daily mean water temperature between paddy and non-vegetated water surface. Finally, we present our model of the daily mean water temperature in a rice paddy ðTw Þ in Section 3.4.

3.1. Water temperature and heat balance of the nonvegetated water surface 3.1.1.

Water and soil temperature

Fig. 1 shows the observed and calculated diurnal variations of water temperature in the non-vegetated test field for the 13 consecutive days from 0900 JST 22 July to 0900 JST 2 August 1997. The water temperature was always higher than the air temperature, with the maximum difference of up to about 10 8C reached around noon each day. The water temperatures calculated with the heat balance equations simulated the observed diurnal variations fairly well. The root mean square error (RMSE) for the calculated water temperature (over 30-

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Fig. 1 – Diurnal variations in water temperature of the non-vegetated test field during 13 consecutive days. There was no rain, and the water depth was controlled at 7 cm during this period. The solid line indicates water temperatures simulated by using heat balance equations, and the short dashed line indicates water temperatures measured at the center of the field (2 cm above the soil surface). The long dashed line indicates air temperature. DOY is day of year.

min intervals) was 0.57 8C. The daily mean water and soil temperatures are shown in Fig. 2. The differences in daily mean water and air temperatures ranged from 2 to 4 8C. The daily mean water and soil temperatures, determined from the 30-min-interval data calculated using the heat balance equations, are also mostly consistent with the observations. However, the calculated daily mean soil temperatures at a depth of 25 cm are somewhat (0.4–1.1 8C) higher than observations after DOY 208, presumably owing mainly to the assumption that wp = 0 mm day1 in the calculation.

Fig. 2 – Daily mean water and soil temperatures of the nonvegetated test field (11 consecutive days). The calculations were made using heat balance equations. The daily mean soil temperatures at the depths of 6, 12, and 25 cm below the soil surface are shown. The broken line indicates the daily mean air temperature.

3.1.2.

Heat balance at the water surface

The heat balance equation, Eq. (9), which is used by the model to evaluate the daily mean water temperature of a nonvegetated water surface, does not include the heat storage of the ground, G (i.e., the model assumes that the daily, daytime, or nighttime mean value of G is zero). To confirm that this assumption is valid, we examined the characteristics of the heat balance in the non-vegetated test field. As shown in Figs. 1 and 2, calculations based on the heat balance equations were able to simulate the observed diurnal variations of water and soil temperatures fairly well, except for the soil temperature at a depth of 25 cm. Fortunately, the discrepancy in the soil temperature at this deep level had little effect on the water temperature and heat budget simulated from the heat balance equations. Therefore, these results confirm that we can use the results of the heat budget calculated from the heat balance equations for the present purpose. Fig. 3 shows the simulated results of the diurnal variation in the heat budget components of the non-vegetated test field during the first half of the 13-consecutive-day period. Here, the heat budget is described as Rnet = H + lE + G; that is, the net radiative flux Rnet is the sum of the sensible heat flux H, the latent heat flux lE, and the heat storage of the ground G. Both G and lE showed large diurnal variations. The daily maximum of G, in the late morning, was positive, whereas the daily minimum, in the early evening, was negative. The daily maximum of lE occurred around noon, and lE became nearly zero at midnight. H was much smaller in magnitude than G or lE, and its daily maximum occurred around noon. The daily mean heat budget over the non-vegetated test field (11 consecutive days) is shown in Fig. 4. Rnet was nearly equal to the sum of H and lE, and G was negligible. That is, more than 83% of Rnet was due to lE, and H contributed 10–22% of Rnet . In spite of large diurnal variation in G, the value of G was very small, ranging from 11 to 10 W m2 each day. Thus, G was confirmed to be negligible when considering the daily mean heat balance at the non-vegetated water surface, supporting the use of Eq. (9), which assumes G to be 0. The behavior of G evaluated here is similar to that observed in a Phragmites canopy in a prairie wetland (Burba et al., 1999). Next, we examined the contribution of G to the daytime (or nighttime) heat balance averaged over 12 h. The 12-h mean value of G depended on the starting time of day used to

agricultural and forest meteorology 148 (2008) 1754–1766

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Fig. 3 – Diurnal variation in heat budget components of the non-vegetated test field (the first half of the 13-consecutive-day period in Fig. 1), calculated from heat balance equations. Here, G is the heat storage of the ground, H is the sensible heat 4 . flux, lE is the latent heat flux, and net radiative flux Rnet is defined as R #  sTw0

determine the daytime (nighttime) average (Fig. 5). When daytime was defined as from 0900 to 2100 JST and nighttime was defined as from 0000 to 0900 and from 2100 to 2400 JST of the same day (that is, the nighttime consisted of the two discrete periods), then the contribution of G to both the daytime and nighttime mean heat balances was negligible. We could therefore use Eq. (9) as both the daytime and nighttime

Fig. 4 – Daily mean heat budget in the non-vegetated test field calculated from the heat balance equations (11 consecutive days). The overbar denotes the daily mean value.

Fig. 5 – The 12-h mean heat budget in the non-vegetated test field as a function of the starting time of day used to determine the daytime (nighttime) averages (averaged over 11 days). If the stating time of day was set at 2100 JST, heat budget was averaged from 0000 to 0900 and from 2100 to 2400 JST of the same day. The results are based on calculations using the heat balance equations. LST is local standard time.

mean heat balance equations by adopting these definitions of the daytime and nighttime periods.

3.2. Modeling the daily mean water temperature of a nonvegetated water surface We employed two alternative methods for evaluating the daily mean water temperature of a non-vegetated water surface Tw0 . In the first method (Model 1), the daytime (0900–2100 JST) and nighttime (0000–9000 and 2100–0000 JST) mean water temperatures, (Tw0)D and (Tw0)N, were calculated by using Eqs. (9)–(11) to calculate the 12-h mean heat balances, and the daily mean water temperature was evaluated as the average of (Tw0)D and (Tw0)N. The bulk transfer coefficients CH (=CE) in Eqs. (10) and (11) were evaluated following the Monin– Obukhov similarity theory (M–O theory, see Appendix A) by using the mean meteorological conditions during the daytime or nighttime. In the second method (Model 2), the daily mean water temperature was calculated directly by using equations Eqs. (9)–(11) to calculate the 24-h mean heat balance. The bulk transfer coefficients for Model 2 were parameterized as shown below. Fig. 6(a) shows the bulk transfer velocities ðCH uÞ of the non-vegetated water surface (the non-vegetated test field) for the daytime and nighttime mean heat balances. These values were evaluated from the daytime and nighttime 12-h mean meteorological data on the basis of M–O theory (Model 1). The daytime values of CH are larger than the nighttime values because of more unstable atmospheric conditions during the daytime. Fig. 6(b) shows the bulk transfer velocities for the daily 24-h mean heat balance. The values of CH u were estimated by two different methods: either they were calculated by using Eqs. (9)–(11) and the measured daily mean water temperatures (crosses), or they were evaluated on the basis of M–O theory (open circles) from the daily mean meteorological conditions. The values estimated by the first method were not only larger than those determined by the second method but also larger than the daytime values of CH evaluated on the basis of M–O theory (Fig. 6a). It is obvious that the relationship between CH u and u estimated from the measured daily mean water temperatures (the long dashed line in Fig. 6) should be used

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Fig. 7 – Seasonal changes in the daily mean water temperature of the non-vegetated water surface (the nonvegetated test field) calculated using the newly developed models: (a) Model 1 and (b) Model 2. The broken line indicates air temperature. Fig. 6 – Bulk transfer velocities ðCH uÞ of the non-vegetated water surface (the non-vegetated test field). (a) Daytime and nighttime mean values evaluated by using Monin– Obukhov similarity theory (M–O theory), (b) daily mean values evaluated on the basis of M–O theory (open circles), and those estimated from the daily mean water temperatures measured for S # > 120 W m2 (crosses). The long dashed line in (a) is same as that in (b).

for calculating Tw0 if we use the daily 24-h mean heat balance equations for evaluating Tw0 (Model 2). The larger CH u values for the daily mean heat balance equations can be explained by the non-linear effect of the heat balance equations. This effect is discussed in detail in Appendix B. Fig. 7 shows seasonal changes in the daily mean water temperature of the non-vegetated water surface (the nonvegetated test field) calculated by using Model 1 (a) and Model 2 (b). The empirical relationship between CH u and u (CH u ¼ a þ bu, a = 0.0017 m s1, b = 0.00218, where u¯ is the daily mean wind speed at a height of 2.5 m above the ground) obtained from the measured daily mean water temperatures is used in Model 2. Both models simulated the daily mean water temperature fairly well. The RMSE for the calculated water temperature was 0.57 8C (Model 1) or 0.65 8C (Model 2). However, Model 1 simulated Tw0 poorly when we changed the starting and ending times of the daytime (nighttime) period from those defined above (not shown).

3.3.

Influence of canopy density on the water temperature

The water temperature of a rice paddy is strongly influenced by the canopy density (LAI) of the rice plants, which gradually increases during the growing season (Uchijima, 1961; Yoshimoto et al., 2005; Ohta and Kimura, 2007), but the relationships

between water temperature and LAI have not been quantified in detail previously. Fig. 8 shows the observed relationships between water temperature and LAI. Under sunny weather conditions (solar radiation S #  10 MJ m2 d1 ), the daily mean water temperature depended on wind speed as well as on LAI. Under strong wind conditions (daily mean, u  1:7 m s1 at a height of 2.5 m above the ground) and sun, the water temperature of the rice paddy ðTw Þ was 0–1 8C higher than that of the non-vegetated water surface ðTw0 Þ for LAI < 2.0, whereas Tw was lower for LAI  2.0. Under light wind ðu < 1:7 m s1 Þ and sun, Tw decreased monotonously with increasing LAI. In contrast, with cloudy weather ðS # < 8 MJ m2 d1 Þ, Tw and Tw0 did not significantly differ regardless of LAI. The temperature difference between the water and air was also smaller under cloudy conditions. The mean value of Tw  T was 3.59 8C for S #  10 MJ m2 d1 , and 1.84 8C for S # < 8 MJ m2 d1 . It should be noted that Fig. 8 shows water temperatures measured in both paddies 1 and 2. During the experimental period, LAI ranged from 0.15 to 2.44 in paddy 1 and from 0.26 to 3.25 in paddy 2. Although the planting density in paddy 2 (25 hills m2) was more than twice that in paddy 1 (11 hills m2), there was no significant difference in the quantitative relationships between ðTw  Tw0 Þ and LAI between the two paddies, suggesting that the water temperature in a rice paddy does not depend on the planting density. The plant canopy has three effects on the water temperature in a rice paddy (Kuwagata et al., 1998): (1) incident shortwave (solar) radiation at the water surface is reduced through absorption of solar radiation by the leaf canopy, (2) incident longwave radiation at the water surface is increased by the longwave radiation emitted from the canopy (equivalent to the greenhouse effect), and (3) turbulent transfer between the water surface and air is reduced in the canopy layer. The first effect tends to cause Tw to decrease, but the

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1

f cw ðXÞ ¼ 0:17f½ðX3=2 þ 1Þ

 1 þ Xg;

f ss ðXÞ ¼ 2:1f½3:5ðX þ 0:1Þ5=2 þ 1 f cs ðXÞ ¼ 0:0; WðXÞ ¼

B1 ¼

B2 ¼

 0:99g  1:05X;

(15) (16)

1 ; ½1 þ 1000 expðXjXjÞ

pffiffiffi 3 ; ðSs  Sc Þ

C1 ¼ B1 Sc þ

1

(14)

pffiffiffi 3;

pffiffiffi 3 ; ðus  uw Þ

C2 ¼ B2 uw þ

pffiffiffi 3;

(17)

(18)

(19) (20)

(21)

where S # (MJ m2 d1) is the daily mean solar radiation, u (m s1) is the daily mean wind speed at a height of 2.5 m Fig. 8 – Observed relationships between water temperature and LAI, where Tw is the daily mean water temperature of the rice paddy and Tw0 that of the non-vegetated water surface. (a) Sunny conditions (solar radiation I10 MJ mS2 dS1), and (b) cloudy conditions (<8 MJ mS2 dS1). u is the daily mean wind speed at a height of 2.5 m above the ground. Data from both paddies 1 and 2 (13 July–26 August 1997) were used.

second and third effects lead to an increase in Tw . The higher Tw values for LAI < 2.0 under strong wind conditions in sunny weather can be explained by the distinct reduction of turbulent transfer from its level at LAI = 0 (the third effect), despite a small reduction in the total incident (shortwave + longwave) radiation, whereas the reduction of the incident shortwave radiation (the first effect) is dominant for LAI  2.0 under the same weather conditions. Under light wind, the reduction of turbulent transfer (the third effect) is weakened, because turbulent transfer due to forced convection is even weaker when LAI = 0. For these reasons, Tw was lower than Tw0 for all values of LAI under light wind and sunny conditions. The observed characteristics of the water temperature shown in Fig. 8 could be simulated by a heat balance model of a plant canopy (Kuwagata et al., 1998). The influence of the plant canopy on the water temperature thus depends not only on canopy density (LAI) but also on solar radiation and wind speed. The value of DTw ð  Tw  Tw0 Þ can be expressed as DTw ð CÞ ¼ ½WðB1 S # þ C1 Þ  f sw ðLAIÞ þ ð1  WðB1 S # þ C1 ÞÞ  f cw ðLAIÞ  ð1  WðB2 u þ C2 ÞÞ þ ½WðB1 S # þ C1 Þ  f ss ðLAIÞ þ ð1  WðB1 S # þ C1 ÞÞ  f cs ðLAIÞ  WðB2 u þ C2 Þ; 1

f sw ðXÞ ¼ 0:95f½ðX3=2 þ 1Þ

 1 þ Xg;

(12) (13)

Fig. 9 – Comparison of DTw ð  Tw  Tw0 Þ values calculated by the empirical formulas and observed values of DTw (abscissa: observation data; ordinate: calculated data). Data are the same as those shown in Fig. 8. Results for solar radiation: (a) S #  9 MJ m2 d1 ; (b) S # < 9 MJ m2 d1 .

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above the ground, Ss = 15 MJ m2 d1, Sc = 7 MJ m2 d1, us = 2.2 m s1, and uw = 1.2 m s1. In Eq. (12), DTw ffi fsw (8C) when S # > Ss and u < uw , DTw ffi fcw (8C) when S # < Sc and u < uw , DTw ffi fss (8C) when S # > Ss and u > us , and DTw ffi fcs (8C) when S # < Sc and u > us . These formulas were derived empirically from the observation data shown in Fig. 8. We then compared the DTw values calculated by these empirical formulas with observed DTw values (Fig. 9) for all data from 13 July to 26 August 1997. These formulas simulated the observation data fairly well both for S #  9 MJ m2 d1 and for S # < 9 MJ m2 d1 ; the RMSE of the calculated DTw was 0.26 8C. Therefore, the empirical formulas for DTw (Eqs. (12)– (21)) can be used to evaluate the daytime mean water temperature of a rice paddy Tw from the water temperature of a non-vegetated water surface Tw0 , which is calculated using the heat balance equations, Eqs. (9)–(11).

equations is evaluated empirically by 1=3 Cˆ H u ¼ Cˆ E u ¼ max½a þ bu; cf ðTw0  TÞ ;

(22)

where a = 0.0017 m s1, b = 0.00218, cf = 0.0012 m s1 K1/3, and u (m s1) is the daily mean wind speed at a height of 2.5 m above the ground. (2) Evaluation of the daily mean water temperature in a rice paddy (ðTw Þ) (Models 1 and 2) Tw is evaluated by adding the correction term, DTw (Eqs. (12)–(21)), to Tw0 .

3.4. Modeling daily mean water temperature in a rice paddy

Here, as was explained in Section 3.3, the effect of the plant canopy on the water temperature is experimentally parameterized in DTw. For the evaluation of Tw , Tw should not be less than its minimum value TwðminÞ , which is theoretically determined from the heat balance equations. Here, TwðminÞ is given by

3.4.1.

TwðminÞ ¼ min½Tw0 ; TwðinfÞ ;

Model description

Fig. 10 shows the procedures for evaluating the daily mean water temperature in a rice paddy, Tw . The steps for evaluating Tw are as follows: (1) Evaluation of the daily mean water temperature for LAI = 0 ðTw0 Þ. (Model 1) The daytime (0900–2100 JST) and nighttime (0000-0900 and 2100-2400 JST) mean water temperatures, (Tw0)D and (Tw0)N, are calculated by using Eqs. (9)–(11) to calculate the 12-h mean heat balances, and the daily mean water temperature Tw0 is evaluated as the average of (Tw0)D and (Tw0)N. The bulk transfer coefficient CH (=CE) is evaluated on the basis of M–O theory. (Model 2) The daily mean water temperature Tw0 is calculated by using Eqs. (9)–(11) to calculate the 24-h mean heat balance. The bulk transfer coefficient Cˆ H ð¼ Cˆ E Þ for the 24-h mean

(23)

where TwðinfÞ is the equilibrium value of Tw for LAI ! 1. The value of TwðinfÞ can be approximately evaluated from the daily mean heat balance equations, Eqs. (9)–(11) and (22), by sub4 stituting L # ¼ sT , S # ¼ 0, and u ¼ 0 into them. Note that Tw0 is less than TwðinfÞ under the specific conditions of strong wind without sunshine. Finally, Tw is evaluated by Tw ¼ max½Tw0 þ DTw ; TwðminÞ :

(24)

The advantage of these models is that Tw can be evaluated from only the 12-h or 24-h mean meteorological data and the simplified heat balance equations. Information about the properties of the soil and the water layer, such as the specific heat of the soil and the water depth, is not needed to calculate Tw . Definitions of the daytime and nighttime periods used in Model 1 should be changed according to the difference between local standard time (LST) and local solar time (LSoT).

Fig. 10 – Flow charts showing the procedure for evaluating the daily mean water temperature in a rice paddy, Tw . (a) Model 1, (b) Model 2. Met. Data: meteorological data (T, q, u, S#, L#) averaged over 12 h (Model 1) or 24 h (Model 2).

agricultural and forest meteorology 148 (2008) 1754–1766

For example, LSoT in the Kyushu region of Japan is about 1 h later than that in the Tohoku region, although LST (= JST) is the same in both regions. Therefore, in the Kyushu region, daytime should be set as the period from 1000 to 2200 JST and nighttime as the period from 0000 to 1000 JST and 2200 to 2400 JST.

3.4.2.

Model validation

We examined the performance of the models by using data from paddy A. During the period from 2 July to 18 August 1997, the field was irrigated. Fig. 11 shows the seasonal changes in the daily mean water temperature of paddy A. The difference between water and air temperatures gradually decreased with the growth of the rice. Both models (Models 1 and 2) simulated the daily mean rice paddy water temperature fairly well; the RMSE of the calculated Tw was 0.85 8C (Model 1) or 0.81 8C (Model 2). The RMSE values roughly equal those reported for other simple models (Takami et al., 1989; Maruyama et al., 1998; Ohta and Kimura, 2007). The advantage of our models is that they take into account the effect of wind speed on the water temperature. These results also demonstrate that the performance of the present models was good even though the water depth in paddy A varied from 0 to 10 cm during the growing period. Therefore, without using any information on water depth, the present model simulated fairly well the daily mean water temperature of a rice paddy in which the water depth varied. This result confirmed that the daily water temperature is insensitive to water depth. The accuracy of the calculated values of Tw did not differ significantly between Models 1 and 2. Model 2 has the advantage of simplicity, but it is necessary to check whether the empirical formula for the bulk transfer coefficient (Eq. (22)) used in Model 2 is applicable in other areas. The applicability in other areas of the empirical formulas used for calculating DTw should also be checked.

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The preliminary version of our model (Model 2) has already been used in a rice growth model (Shimono et al., 2007b), and also for simulating methane emission from rice paddy fields by a process-based biogeochemistry model (Fumoto et al., 2008). The results of these studies suggest that our model can simulate paddy water temperatures in other areas of Japan and China fairly well. We will examine the applicability of our models in other areas in another paper.

4.

Conclusions

(1) The diurnal variation in the water temperature of a nonvegetated water surface was simulated fairly well by using heat balance equations. The simulated results suggest that the contribution of the heat storage of the ground (G) was negligible for calculation of not only the daily mean but also the daytime (or nighttime) mean heat balances at the non-vegetated water surface when daytime was defined as the period from 0900 to 2100 JST and nighttime as the period from 0000 to 0900 JST and 2100 to 2400 JST of the same day (Tohoku region). (2) The bulk heat transfer coefficient, which we were able to use for evaluating the daily mean water temperature of the non-vegetated water surface from the daily mean heat balance equations, was larger than that estimated on the basis of M–O theory because of the non-linearity of the heat balance equations. (3) The influence of the plant canopy on the water temperature depended on not only LAI but also solar radiation and wind speed. The daily mean water temperature in the rice paddy ðTw Þ was usually lower than that of the nonvegetated water surface ðTw0 Þ. However, in a rice paddy with LAI = 0.5–1.5, Tw was higher than Tw0 under strong wind conditions in sunny weather. On the other hand, the water temperature in the rice paddy did not depend on planting density. These characteristics are taken into account by the newly developed model for determining Tw . (4) A simple two-step model for determining the daily mean water temperature Tw in a rice paddy was presented. In the first step, Tw0 is evaluated from meteorological data on the basis of the daily 24-h mean or the daytime (nighttime) 12h mean heat balance equations. Next, Tw is evaluated by adding a correction term to Tw0 . The correction term is a function of LAI, solar radiation, and wind speed, and its formula was determined empirically. The model simulated the observed data fairly well, with RMSE of 0.81–0.85 8C.

Acknowledgements

Fig. 11 – Seasonal changes in the daily mean water temperature of a rice paddy (paddy A) calculated using the newly developed models ((a) Model 1, (b) Model 2) compared with observation data. The broken line indicates air temperature.

The authors are grateful to Dr. Kiyoshi Ozawa of the Japan International Research Center for Agricultural Sciences, Dr. Mari Murai-Hatano of the National Agricultural Research Center for Tohoku Region, Dr. Youichi Torigoe of the National Agricultural Research Center for Western Region, Dr. Toshihiro Hasegawa of the National Institute of Agro-Environmental Sciences, and Dr. Masumi Okada and Dr. Hiroyuki Shimono of the Faculty of Agriculture, Iwate University, for valuable

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discussions and useful advice. The authors also thank Dr. Ryoji Sameshima of the National Agricultural Research Center for Tohoku Region for providing the crop information for the test fields, and the support staff of the National Agricultural Research Center for Tohoku Region for their assistance during the field experiments.

Appendix A. The bulk transfer coefficients for a non-vegetated water surface

Appendix B. Theoretical consideration of the bulk transfer coefficients for the daily mean heat balance equations An approximated solution of the heat balance equations (Eqs. (1)–(4)) for calculating the water temperature of the nonvegetated water surface is given by Tw0  T ¼ F  R;

(A.7)

1

On the basis of Monin–Obukhov similarity theory (M–O theory, Monin and Obukhov, 1954), the bulk transfer coefficients for a non-vegetated water surface in Eqs. (3) and (4) are given by (Kondo, 1975; Kondo and Ishida, 1997) CH ¼ max½k2 ½C M ðza1 ; z0 ; LÞ1 ½C H ðza2 ; zT ; LÞ1 ; cf DT1=3 ;

(A.1)

CE ¼ max½k2 ½C M ðza1 ; z0 ; LÞ1 ½C E ðza2 ; zq ; LÞ1 ; cf DT1=3 ;

(A.2)

F  K1  ½rCH uðc p þ lDÞ þ 4sT3  ;

(A.8)

R  R #  esT4  lrCH u½qsat ðTÞ  q  G;

(A.9)

where the approximations qsat ðTw0 Þ ’ qsat ðTÞ þ D  ðTw0  TÞ and sT4w0 ’ T4 þ 4sT3 ðTw0  TÞ ðDðTÞ  @qsat ðTÞ=@TÞ are made, and it is assumed that e = 1.0 and CH = CE, respectively. Hereafter, the daytime mean value of any variable Y is described as (which is equivalent to Y in the text), and

   and (  )0 are defined as

and DT  Tw0  T;

where k (=0.4) is the von Ka´rma´n constant; CM, CH, and CE are the integrated forms of the dimensionless shear functions for momentum, sensible heat, and water vapor, respectively; and cf is the coefficient for the transfer under conditions of free convection (m s1 K1/3). Furthermore, L is the Monin–Obukhov length (m), za1 is the height (above the ground) at which wind speed is measured, za2 is the height at which air temperature and specific humidity are measured, and z0, zT, and zq are the roughness lengths of the water surface for momentum, sensible heat, and water vapor, respectively. The Monin–Obukhov length is defined by L¼

Q0 u3 kgH=ðc p rÞ

YðX1 ; X2 ; . . .Þ   Yð < X1 > ; < X2 > ; . . .Þ;

(A.10)

Y0  Y  < Y > ;

(A.11)

(A.3)

(A.4)

;

where Y is expressed as a function of X1, X2, . . ., and X1, X2, . . . correspond to meteorological variables. Averaging Eq. (A.7) over 24 h yields: < Tw0  T > ¼ f  < F > < R > ;

(A.12)

< F0 R0 > :

(A.13)

f ¼ 1 þ

Furthermore, Eq. (A.12) can be rewritten as < Tw0  T > ¼ f K  1 R  ;

(A.14)

K  ¼ r < CH u > ðc p þ lDð < T > ÞÞ þ 4s < T > 3 ;

(A.15)

1

where u is the friction velocity (m s ), Q0 is the reference potential temperature (K), and g is the acceleration due to gravity (m s2). It should be noted that the influence of water vapor on static stability is not taken into account by Eq. (A.4). The friction velocity u can be expressed as (Kondo, 1975) u2 ¼ CM u2 ;

(A.5)

CM ¼ k2 ½C M ðza1 ; z0 ; LÞ2 ;

(A.6)

where CM is the bulk transfer coefficient for momentum. The formulas for CM, CH, and CE are summarized in previous papers (Kondo, 1975, 1994; Kondo and Ishida, 1997). The roughness lengths of the water surface for calculating CM, CH, and CE were set at z0 = 0.06 mm, and zT = zq = 0.16 mm, respectively (Kondo, 1975). The coefficient cf for the water surface was set at 0.0012 m s1 K1/3 (Kondo and Ishida, 1997).

R  ¼ ð < R # >  es < T > 4 Þ  lr < CH u > ðqsat ð < T > Þ  < q > Þ;

f ¼ f 1 f 2 f ;

(A.16)

(A.17)

f1 

K ; < F > 1

(A.18)

f2 

;

R

(A.19)

where = 0 is assumed. In the case of f = 1, Eqs. (A.14)– (A.16) are equivalent to an approximated solution of the heat balance equations (Eqs. (9)–(11)) for the daily mean water temperature of the non-vegetated water surface. However, under ordinary meteorological conditions, f 6¼ 1. As discussed below, the non-linear term /() in Eq. (A.13) affects the value of f.

agricultural and forest meteorology 148 (2008) 1754–1766

Next, we estimate the value of f by using the meteorological data in the present study (51 days, 8 July–27 August 1997). For simplicity, the meteorological data for each day are divided into two data sets: daytime (0900–2100 JST) and nighttime (0000-0900 and 2100-2400 JST) means. Using these two data sets, the right-hand sides of Eqs. (A.13), (A.18), and (A.19) are evaluated for each day. The results are summarized as follows: f  ¼ 0:50  0:98 ðmean : 0:81Þ  1  A y;

(A.20)

f 1 ¼ 1:00  1:24 ðmean : 1:06Þ  ð1  A1 yÞ1 ;

(A.21)

f 2 ¼ 0:81  1:05 ðmean : 0:93Þ  1  A2 y;

(A.22)

f ¼ 0:55  0:98 ðmean : 0:81Þ  1  Ay;

(A.23)

y1 

ðCH uÞN ; ðCH uÞD

(A.24)

where (Y)D and (Y)N are the daytime and nighttime mean values of Y, respectively, and A*, A1, A2, A are positive numerical constants. Under ordinary conditions, 0  y < 1 ((CHu)N  (CHu)D). The values of f*, f11, and f2 become smaller when daytime CHu values are much larger than nighttime values. As for f* (Eq. (A.13)), the ordinary conditions of ((F0 )D < 0, (R0 )D > 0) and ((F0 )N > 0, (R0 )N < 0) lead to < F0 R0 >/() < 0, resulting in f* < 1 ( > 0 and > 0 under ordinary conditions). On the other hand, f1  f2  1 because of the increase in f1 with decreasing f2. Thus, we reach the final result of f  f* < 1. In Eq. (A.14), the values of both K  1 and R  decrease with increasing < CH u > . To obtain correct values of from Eqs. (A.14)–(A.16) for f = 1, we therefore have to use larger values of < CH u > than those estimated by using M– O theory.

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