## Abstract

Many meteorological and air-quality models require land characteristics as inputs. A field experiment was conducted to study the surface energy budget of a rice paddy in Taiwan. During the day, the energy balance ratio measured by an eddy covariance (EC) system was found to be 95% after considering the photosynthetic and local advected heat fluxes. The observations by the EC system suggest that the Bowen ratio was about 0.18 during the daytime. The EC system also measured the daytime absorbed carbon dioxide flux. The equivalent photosynthetic energy flux was about 1% of the net solar radiation. A reference table describing the land characteristics of rice paddies for use in meteorological and air-quality models is listed that shows that the albedo and the Bowen ratio measured over rice paddies were lower than those listed in many state-of-the-art models. This study proposes simulating latent heat flux by assigning proper values for canopy resistance rather than by assigning constant values for Bowen ratio or surface moisture availability. The diurnal pattern of the canopy resistance of the rice paddy was found to be “U” shaped. Daytime canopy resistance was observed to be 87 s m^{−1}, and a high canopy resistance (∼900 s m^{−1}) should be assigned during nighttime periods.

## 1. Introduction

Many state-of-the-art meteorological and air-quality models, such as the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5; Grell et al. 1995), the Weather Research and Forecasting (WRF) Model (Dudhia et al. 2005), the American Meteorological Society–Environmental Protection Agency Regulatory Model (AERMOD; USEPA 2004), and the Comprehensive Air Quality Model with Extensions (CAMx; ENVIRON 2006), require land characteristics such as albedo, Bowen ratio, surface moisture availability, and area heat capacity for the calculations of mixing length, stability class, dry deposition, and surface energy components (Kitada and Regmi 2003). However, many of the reference tables describing the characteristics of agricultural land covers in these models were derived from sites in western countries that are largely based on values typical for cereal crops, such as winter wheat and corn, that dominate both the U.S. and west European agricultural sector.

In south and east Asia, rice is the major food staple and major crop (Simmonds et al. 1999). For example, in Taiwan, 42% of plain terrain (elevation <200 m above sea level)—12% of land—is utilized for rice paddies (TWCOA 2006). Rice is very different from other crops, in that it is grown under flooded conditions over most of the growing season. The fact that it is flooded substantially affects surface energy balance components over a rice paddy relative to other nonirrigated crops, or even crops that are irrigated only at certain times during the growing season (Terjung et al. 1989). In addition, more than 80% of freshwater resource development projects in Asia are used for irrigation, and about half of the total irrigation water is used for rice production (Bhuiyan 1992). The water-fed rice paddy field may modify the surface energy budget, water cycle, runoff, groundwater storage (Wu et al. 2001), and possibly climate (Simmonds et al. 1999) of the region. For accurately quantifying the water usage of a rice paddy, better knowledge of the mass, momentum, and energy exchange between rice paddies and the atmosphere is therefore necessary.

Observations of the energy exchange between rice paddies and the atmosphere are still sparse. There have been only a few studies in the United States (Campbell et al. 2001), China (Gao et al. 2003), and Japan (Harazono et al. 1998; Leuning et al. 2000; Yoshimoto et al. 2005). To the author’s knowledge, no study in Taiwan has been reported. This study, therefore, tries to report data observed at a rice paddy site in Taiwan. However, in this country it is very difficult to find a site with sufficient fetch where the horizontal heterogeneity can be neglected, because of the presence of buildings, roads, and trees near most rice paddy sites. Moreover, many field experiments show that the surface energy budget fails to close, such as in Gao et al. (2003), in the International Rice Experiment (Harazono et al. 1998), and at many of a global network of micrometeorological flux measurement sites that measure the exchanges of carbon dioxide, water vapor, and energy between the biosphere and atmosphere (FLUXNET) sites (e.g., Wilson et al. 2002a, b; Meyers and Hollinger 2004). They indicate that there is a general lack of closure at most sites, with energy balance ratios (EBRs) ranging from 70% to 95%. More careful treatments of horizontally advected fluxes and minor flux terms are therefore needed.

The purposes of this study are to 1) evaluate the surface energy closure by incorporating more energy exchange components between a rice paddy and the atmosphere, and 2) determine the characteristics of rice paddies that can be used for meteorological and air-quality models. Section 2 describes the characteristics of the experimental site. Section 3 presents the method and the instrumentation used in this study. Section 4 shows the observed results of the surface energy components, carbon dioxide (CO_{2}) flux, and evapotranspiration from the rice paddy. Sections 5 and 6 report the land characteristics of the rice paddy and compare with other study sites. Conclusions are made in section 7.

## 2. Method

The surface energy budget is based on the fundamental principle of conservation of energy. It can be shown that the sum of surface latent heat and sensible heat flux should be equivalent to all other energy sinks and sources (e.g., Wilson et al. 2002b), as illustrated in Fig. 1 as

with

where *V* is the available heat flux for turbulent heat fluxes at the surface. It is defined as the sum of *R _{n}* −

*G*−

*S*−

*W*−

*F*. Here,

*R*is the net radiation (positive downward);

_{n}*G*is the ground heat flux measured by the heat flux plate sensors (positive downward);

*S*is the soil heat storage between the soil surface and the depth of the heat flux plate sensors (e.g., Tsuang 2005);

*W*is the heat storage in the paddy water;

*C*is the canopy heat storage between the land surface and the height of the eddy covariance system (e.g., Garratt 1992);

*A*is the local advected heat flux (Brutsaert 1982; Guo and Schuepp 1994);

*F*is the photosynthetic energy flux (positive downward); LE

*is the latent heat flux at the canopy height (positive upward);*

_{c}*H*is the sensible heat flux at the canopy height (positive upward);

_{c}*H*is surface sensible heat flux; LE is surface latent heat flux;

*R*is the incoming solar radiation (positive downward);

_{s}*R*

_{sr}is the reflected solar radiation (positive upward),

*R*

_{ld}is the atmospheric longwave radiation (positive downward);

*R*

_{lu}is the terrestrial longwave radiation (positive upward);

*C*

_{CO2}is the energy required for each mole of CO

_{2}fixed by photosynthesis (=422 kJ g mole

^{−1}; Nobel 1999);

*M*

_{CO2}is the molecular weight of CO

_{2};

*F*

_{CO2}is the flux of CO

_{2}measured by the eddy covariance (EC) system (plus upward);

*ρ*,

_{g}*ρ*, and

_{a}*ρ*are density of the wet soil, the air, and the water, respectively;

_{w}*c*and

_{p}*c*are specific heat capacity of the air and the wet soil, respectively;

_{g}*L*is the latent heat of vaporization;

_{υ}*θ*is potential temperature;

*q*is specific humidity;

*T*and

_{g}*T*are soil temperature and water temperature, respectively;

_{w}*z*is the depth from the land surface to the heat flux plate sensor;

_{g}*h*is the height of the EC system installation;

_{c}*z*is the depth of water in paddies; and

_{w}*u*and

*υ*are wind components in

*x*direction and

*y*direction, respectively.

Surface sensible heat flux *H* and surface latent heat flux LE can be parameterized (e.g., Brutsaert 1982; Garratt 1992) as

### a. Examination of energy balance closure

Energy balance closure is examined using three methods in this study. The first method is to derive regression coefficients from the ordinary least squares (OLS) relationship between the hourly sums of the turbulence heat fluxes (LE + *H*) and the available heat flux (*V*; Wilson et al. 2002b). Note that the OLS regression is technically valid only if there are no random errors in the independent variable. The second method is to evaluate the EBR (Wilson et al. 2002b) between the sum of the turbulence heat fluxes (LE + *H*) and the available heat flux (*V*) over a specific time period, that is,

The third method is to quantify the discrepancy between the available heat flux (*V*) and turbulence heat flux (LE + *H*). The discrepancy provides information about whether the turbulence heat flux observed by the EC system could be overestimated or underestimated. The residual heat flux *R* of the energy closure is defined as

where the residual heat flux should be equal to zero when the surface energy budget is closed.

### b. Bowen ratio, canopy resistance, and surface moisture availability

Once surface sensible heat and latent heat fluxes are obtained, its Bowen ratio can be determined according to its definition (e.g., Brutsaert 1982) as

In addition, adopting the concept of resistance to heat and vapor transferred to the atmosphere, the surface sensible latent heat fluxes can be determined (Monteith 1965) as

where *r _{a}* is aerodynamic resistance for heat,

*r*is canopy resistance for evapotranspiration,

_{c}*T*is the skin temperature of paddy surface,

_{s}*T*is air temperature,

_{a}*q**(

*T*) is the saturated specific humidity at

_{s}*T*, and

_{s}*q*is specific humidity of air. By rearranging Eqs. (13) and (14),

_{a}*r*and

_{a}*r*can be determined as

_{c}In addition, once aerodynamic resistance is determined, the potential latent heat flux PE can be determined from Eq. (14) by setting *r _{c}* = 0 (e.g., Grell et al. 1995) as

Surface moisture availability *m* is defined as the ratio between actual and potential evapotranspiration (Grell et al. 1995). As a result, surface moisture availability can be determined as

## 3. Characteristics of rice paddy and site description

The study site is located at the Taiwan Agricultural Research Institute (TARI) (24°01′N, 120°41′E, 50 m above sea level) in the Taichung basin in central Taiwan (Fig. 2). The purpose of the institute is to improve the cultivation technique for agricultural products, investigate plant pathology, and conduct research in the field of agricultural micrometeorology. Soil at the experimental site was predominantly loam, of which the volumetric heat capacity *ρ _{g}c_{g}* is set at 2.99 × 10

^{6}J m

^{−3}K

^{−1}for wet soil (Hillel 1982).

In central Taiwan, there are two growing seasons for rice paddies—one beginning in February and the other in July. From sowing to harvest, it usually takes 120 days for the first rice crop and 100 days for the second rice crop. The rice (Japonica rice cultivar Tainung 67) was transplanted to the study site on 8 March 2005 and was harvested at the end of June 2005 (Fig. 3). The rice was cultivated following the rules of “precision agriculture,” set up by TARI. Flux measurements were carried out from 5 April to 19 May 2005, which was from about the maximum tillering stage to the end of the booting stage. During the experimental period the canopy height increased about from 26.1 to 73.7 cm. The rice field was flooded throughout the entire experiment. The depth of the water layer during the flooded period ranged from 2 to 6 cm. The distance between rice plants was 30 cm × 15 cm. Several patches of similar rice paddies composed a rectangular paddy field, about 0.45 km in the north–south direction × 0.2 km in the east–west direction. The experiment site was almost completely surrounded by farmlands (CTCI 2003).

An EC system and a micrometeorology station were set up at nearly the center of the paddy field. The measured items included incoming solar radiation, reflected solar radiation, atmospheric longwave radiation, terrestrial longwave radiation, atmospheric pressure, wind speed and direction, air temperature, relative humidity, soil temperature, and ground heat flux. The results are shown in Fig. 4. During the study period, wind directions alternated between day and night. It is likely part of a valley–mountain wind system, regularly observed in the basin (Tsai and Tsuang 2005).

Carbon dioxide flux, sensible heat flux, and latent heat flux were measured directly from an EC system. The EC system consists of a three-dimensional sonic anemometer (CSAT3; Campbell Scientific, Inc.) to measure the fluctuations of wind velocity components (i.e., *u*, *υ*, and *w*) and virtual temperature, a fine-wire thermocouple (FW05) to measure the fluctuations of air temperature, and an open-path CO_{2}/H_{2}O fast-response infrared gas analyzer (LI7500; Li-Cor, Inc.) to measure fluctuations in CO_{2} concentration and water vapor density. The open-path analyzer with a 0.125-m-span open path was installed at the same height as the sonic anemometer with a horizontal separation of about 0.20 m. All sensors were mounted on a mast at a height of 5 m above ground level. All of the signals of the sensors were sampled at 20 Hz and were averaged over 10-min periods. Note that the ratio of the fetch to the measurement height of a fingerprint area is about 28 (Horst 1999; Tsai and Tsuang 2005). That is, the minimum fetch required for the flux measurements from the rice paddy by the EC system is 140 m. Note that the EC system was mounted at 5-m height. Because the rice paddy was about 0.45 km in the north–south direction × 0.2 km in the east–west direction, it implies that the fetch of the rice paddy was sufficient for either the north or south wind direction, but less sufficient for either the east or west wind direction.

A Solar Infrared Radiation Station (SIRS) system was used in this study to measure each component of the radiation balance. The SIRS consisted of four individual sensors, including both upward and downward pyranometers (PSPs), and both upward and downward pyrgeometers (PIRs), manufactured by the Epply Laboratory, Inc. Each component of this system was mounted on a mast at a height of 5 m above ground level. In addition, a net radiation sensor Q*7.1 [made by Radiation and Energy Balance Systems (REBS)] was also used to double check the net radiation determined from the SIRS.

Ground heat flux *G* was obtained using the mean value of two soil heat flux plate sensors (REBS’ HFT-3.ls), buried at a depth of 8 cm. The soil temperature between the soil heat flux plate sensors and the surface was measured using the averaging soil thermocouple probe (TCAV), which consisted of four thermocouple junctions divided into two groups and buried at depths of 3 and 6 cm, respectively. The distance between the two groups in the same level was 1 m. The mean values of TCAV served as the mean soil temperature (*T _{g}*) between the instruments and the surface.

## 4. Surface energy components

Figure 5 shows the daily variation of each surface energy component during the study period. During the experiment, there were three overcast periods (12–17 April, 26–29 April, and 6–15 May 2005). It can be seen that during the overcast periods, the magnitudes of solar radiation, latent heat flux, sensible heat flux, and CO_{2} flux were much lower than in partial cloud or clear-sky days. Note that there were gaps in the figure for various reasons. The LI7500 eddy covariance system failed under rainy and foggy conditions, and there were several rain events before the end of the measuring period. Hence, data of latent heat flux and CO_{2} flux under these conditions have been discarded. Soil temperature was not measured until 11 April. A pyrgeometer battery failed during the gaps. During the period from 16 to 25 April 2005, there was no rainfall, the data were more complete, and the winds were northern or southern dominated (Fig. 4). From these two wind directions, the fetch of the rice paddy was sufficient at the measurement height of the EC system. Therefore, only data during this period were used for detailed analysis and to derive the characteristics of the rice paddy.

The net radiation measured by the SIRS was slightly lower than that measured by the Q*7.1 with the bias at −25 W m^{−2}, the RMSE at 46 W m^{−2}, and the correlation coefficient at 0.99. The sensible heat flux derived from the perturbation of virtual temperature observed by CSAT3 was slightly higher than that of temperature observed by the FW05 thermocouple with the bias at 1 W m^{−2}, the RMSE at 6 W m^{−2}, and the correlation coefficient at 0.95. Observations from the SIRS and CSAT3 were used in the rest of the paper. Note that the SIRS is generally considered to be the standard. This implies that using the other combinations (Q*7.1 plus FW05) would increase the residual heat flux by 26 W m^{−2}.

Figure 6 shows the diurnal composite of each energy component during the period. Ranging from 0 to 600 W m^{−2}, *R _{n}*,

*R*,

_{s}*R*

_{ld}, and

*R*

_{lu}belong to the highest magnitude group. LE

*belongs to the second highest group ranging from −50 to 500 W m*

_{c}^{−2}. The magnitude of

*H*was lower than that of LE

_{c}*and close to those of heat storage components*

_{c}*S*and

*W*, and ground heat flux

*G*;

*A*,

*C*, and

*F*belong to the lowest group ranging from −5 to 10 W m

^{−2}. Note that the magnitude of the residual heat flux

*R*is close to

*W*. Table 1 summarizes the results and expresses each budget component as a ratio of available heat flux. During the daytime, net radiation was the dominant contributor to the surface and latent heat flux was the main receiver from the surface. During the nighttime, ground heat flux and soil heat storage were the dominant energy contributors, and net radiation and latent heat flux were the major receivers.

The rice paddy during the experiment was filled with water ranging from 2 to 6 cm deep. The wet soil storage is determined according to Eq. (3). The paddy water heat storage is determined according to Eq. (4). During the day, the ground heat flux, the soil heat storage, and the paddy water storage consisted of 12%, 16%, and 7% of available heat flux, respectively (Table 1).

Table 2 and Fig. 7 show the EBRs and the regression coefficients from the OLS relationship between the sums of the turbulence heat fluxes (LE + *H*), against the available heat flux (*V*) of various corrections. It can be seen that both the EBRs and the regression coefficients of the OLS relationship become closer to 1 after each correction. The corrections include 1) coordinate rotation correction (e.q. Wilczak et al. 2001), 2) Webb correction (Webb et al. 1980), 3) canopy heat storage correction, 4) advected heat flux correction, and 5) photosynthetic energy correction.

### a. Coordinate rotation correction

The latent heat flux and the sensible heat flux observed from the EC system can be hindered because of the tilt of the instrument and the slope of the terrain. Over flat terrain, the long-term mean vertical velocity should be zero. Under the assumption of the mean vertical velocity being zero, two-axis coordinate rotation is applied to all EC estimates to correct the nonzero vertical velocity according to Wilczak et al. (2001). After the coordinate rotation correction, the sensible heat flux decreased slightly but latent heat flux increased by about 8%. As a result, the daytime EBR and the slope of OLS relationships increased by 7% and 0.07, respectively (Table 2).

### b. Webb correction

Webb et al. (1980) showed that the eddy flux of heat should be corrected for density fluctuations in calculating the fluxes of water vapor and CO_{2}. Therefore, the corrections for the effects of density fluctuations, owing to the transfer of sensible heat on the water vapor and CO_{2} fluxes, were carried out.

After turbulence heat fluxes were corrected according to Webb et al. (1980) for the effect of density fluctuations, the daytime EBR improved by 2% and the slope of OLS relationship increased by 0.04 (Table 2).

### c. Photosynthetic heat flux (F), canopy heat storage (C), and advected heat flux (A) corrections

The photosynthetic heat flux, canopy storage, and local advected heat flux are usually neglected in the energy budget equation (e.g., Harazono et al. 1998; Twine et al. 2000; Wilson et al. 2002a; Gao et al. 2003). Nonetheless, at the study site, these three minor terms were examined.

As described by Meyers and Hollinger (2004), an estimate of the energy used in photosynthesis is obtained from the energy that is required to break the bonds of the reactants and those in forming glucose and oxygen, that is, 6H_{2}O + 6CO_{2} ⇒ 6O_{2} + C_{6}H_{12}O_{6}. The solar energy stored in the bonds of carbohydrate is about 422 kJ of energy per mole of CO_{2} fixed by photosynthesis. This constant is used to compute the photosynthetic energy from the CO_{2} flux measured by the EC system (Nobel 1999), as described in Eq. (7). During the day, the photosynthetic heat flux consists of 2% of the available heat flux (Table 1). This ratio is close to that of Oke (1987); he suggested the photosynthesis is typically on the order of 1%–2% of the available heat flux. The EBR increased by 0.02 after the incorporation of the photosynthetic heat flux during the daytime. In addition, the slope of OLS increased by about 0.02 after the correction (Table 2).

The canopy heat storage term is the rate of energy storage per unit area between the surface and the height (*h _{c}* = 5 m) where the sensible and latent heat fluxes were measured by the EC system. The canopy heat storage is determined according to Eq. (5). During the day, the canopy heat storage term consisted of 0.4% of available heat flux (Table 1). The EBR increased by 0.004 after the incorporation of the term during the daytime. In addition, the slope of the OLS relationship increased by 0.008 after the correction (Table 2).

The heterogeneity of temperature and wetness of the land surface will generate horizontal transports of heat and moisture, the so-called local advection, when wind flows cross it (Brutsaert 1982). In this study, there are a few buildings and trees distributed around the study area (Fig. 3). Therefore, local advection heat flux was estimated using Eq. (6), which is the simplified, steady-state, two-dimensional, mean thermodynamic equation. The upwind numerical scheme is used for the calculation of advected heat flux (e.g., Griebel et al. 1998). The horizontal temperature (specific humidity) gradients are determined using the temperatures (specific humidities) interpolated at locations 1 km north, south, east, and west from the study site. The inverse-distance-weighting technique (Scire et al. 2000; Tsuang 2003a) was used for the interpolation from nearby stations. There were nine meteorological stations located within 15 km from the study site (Fig. 2). These stations are maintained with routine quality assurance and quality control. During the day, the local advected heat flux consisted of 0.8% of available heat flux (Table 1). The EBR increased by 0.008 after the incorporation of the term during the daytime. In addition, the slope of the OLS relationship increased by 0.001 after the correction (Table 2).

## 5. Land characteristics of rice paddies

The daytime EBR of this study is as high as 95%, which is higher than previous studies over rice paddies (e.g., Gao et al. 2003). Therefore, parameters derived from the experimental data may be of value for determining mass, momentum, and energy exchange rates between rice paddies and the atmosphere. Major characteristics of the study site are listed in Table 3, along with characteristics of other rice paddy sites reported in literature. The derived parameters listed in the table include albedo, Bowen ratio, aerodynamic resistance, canopy resistance, surface moisture availability, surface emissivity, and area heat capacity.

### a. Albedo

The albedo (the ratio between reflected solar radiation and incoming solar radiation at the site), was observed to vary from 0.07 to 0.19. The majority of this variation is due to a strong diurnal variation in albedo, as shown in Fig. 8. Note that over a water body, it is well known that the albedo is a function of solar zenith angle (e.g., Arya 2001). The relationship between the albedo *α* and solar zenith angle *z* at this rice paddy site is determined to be

The above equation has a correlation coefficient at 0.75 and RMSE at 0.015. Because a few meteorological models use a single solar zenith angle–independent value for albedo of a given land type, it may introduce errors for net solar radiation estimation during the sunrise and sunset periods. The represented albedo at the site is determined to be 0.09, which is the ratio between the accumulated reflected solar radiation and the accumulated incoming solar radiation during the study period. This value lies in the range between soil and water (Arya 2001). The value of 0.09 is close to that of other rice paddies (Gao et al. 2003), ranging from 0.08 to 0.17, but is lower than the value of 0.14 used in AERMOD and the value of 0.18 used in both MM5 and WRF (Table 3).

### b. Surface emissivity

Surface emissivity ɛ is the ratio of radiation emitted by a surface and the theoretical radiation of a blackbody. It is defined (e.g., Brutsaert 1982) as

where *σ* is the Stefan–Boltzmann constant and *T _{s}* is the land skin temperature (K). Nonetheless, it is very difficult to measure

*T*, especially for a rice paddy, which consists of the skin temperature of rice itself, exposed wet soil, and exposed water surface. However, from Eq. (13), it can be inferred that the signs of “

_{s}*T*−

_{s}*T*” should be the same as those of surface sensible heat fluxes. Rearranging the above equation, we can determine

_{a}*T*from the observed terrestrial longwave radiation

_{s}*R*

_{lu}as

Figure 9a shows that the upward sensible heat flux occurs from 0600 to 1700 LT. From Eq. (13), it can be inferred that *T _{s}* −

*T*should be positive during the same period. Figure 9b shows

_{a}*T*−

_{s}*T*with

_{a}*T*calculated using various values for the emissivity. It can be seen that by choosing a surface emissivity of 0.86, the positive period of

_{s}*T*−

_{s}*T*coincided with the positive period of the observed sensible heat flux. In addition, the simulated diurnal range of the skin temperature was reasonable when compared with those of observed surface air temperature and soil temperature (Fig. 9c). Note that it is well known that the diurnal range of skin temperature is larger than those of surface air temperature and soil temperature (e.g., Carslaw and Jaeger 1959; Tsuang 2003b; Prigent et al. 2003; Aires et al. 2004). Furthermore, daytime

_{a}*T*should be higher than the temperatures of surface air and subsurface soil, but nighttime

_{s}*T*should be lower than those temperatures. Using the other values for the emissivity, the positive period of

_{s}*T*−

_{s}*T*was less similar to that of the sensible heat flux. Nonetheless, there was still about 18% of the data for which the signs of

_{a}*T*−

_{s}*T*were not the same as those of the sensible heat fluxes (Fig. 9d). The value of 0.86 for the emissivity was lower than the values of 0.92 used in MM5 and WRF, and the value of 0.96 assumed in Gao et al. (2003; Table 3).

_{a}### c. Bowen ratio

The Bowen ratio is determined according to Eq. (12) using the surface sensible heat flux and the surface latent heat flux observed by the EC system and modified according to Eqs. (18) and (19) (Fig. 10). During the daylight hours, the mean value of the ratio was 0.18, with a standard deviation of 0.05 (Tables 3 and 4). This value was slightly higher than those of other rice paddies (Gao et al. 2003; Harazono et al. 1998), ranging from 0.07 to 0.15, but lower than the value of 0.30 used in AERMOD. During the nights the Bowen ratio became negative, but had extremely high standard deviations when both components of the surface sensible and latent heat fluxes were smaller than the residual heat flux. Therefore, the eddy covariance may not be able to measure the ratio between the fluxes correctly during the nights (Wilson et al. 2002b).

### d. Surface moisture availability

Surface moisture availability is used in meteorological models (MM5 and WRF) for determining the actual evapotranspiration rate from the potential evapotranspiration rate. It can be calculated according to Eq. (18) from the derived aerodynamic resistance and the canopy resistance. The results are shown in Fig. 10. The highest composite mean of 0.68 occurred in the early afternoon when canopy resistance reached its minimum, and the lowest value of 0.05 occurred during the night when canopy resistance reached its maximum (Fig. 10). In general, the daytime values were higher than the value of 0.5 as prescribed in MM5 and WRF (Table 3), but the nighttime values were lower than 0.5. The daytime mean was 44 ± 8%, which is significantly higher than the value of 34 ± 7% observed in Harazono et al. (1998; Tables 3 and 4).

### e. Aerodynamic and canopy resistances for evapotranspiration

Figure 11 shows both the aerodynamic and canopy resistance, determined according to Eqs. (15) and (16) based on atmospheric variables observed at the site, respectively. The diurnal patterns of both resistances were “U” shaped. The minimum values occurred around local noon when solar radiation reached its maximum, and the maximum values occurred during the night from 1900 to 0700 LT. These are reasonable. During the night, the atmosphere is stable, causing higher aerodynamic resistance, and the stomata are closed, causing a higher canopy resistance. At local noon, the atmosphere is the most unstable, causing a lower aerodynamic resistance, and the stomata are fully opened, causing a lower canopy resistance. In the early afternoon, canopy resistance reached its minimum of 40 s m^{−1}; during the night the resistance could potentially be higher than 1000 s m^{−1}. The range of daily daytime canopy resistance was between 60 and 143 s m^{−1} (Table 4). These values were close to those for rice paddies in Yoshimoto et al. (2005), ranging from 50 to 200 s m^{−1}, and close to those in Harazono et al. (1998), ranging from 78 to 100 s m^{−1}.

### f. Area heat capacity

Area heat capacity is used in meteorological models (MM5 and WRF) for determining land skin temperature. It can be determined, as long as land skin temperature and surface ground heat flux *G _{s}* are available (Tsuang 2005), as

where *G _{s}* ≡

*G*+

*S*+

*A*;

*ρ*,

_{s}*c*, and

_{s}*k*are the density (kg m

_{s}^{−3}), specific heat (J kg

^{−1}K

^{−1}), and heat diffusion coefficient (m

^{2}s

^{−1}) of land surface, respectively; and

*ω*is the earth’s angular velocity (=2

*π*/24 h

^{−1}). In addition,

*ρ*

_{s}

*c*

_{s}

*k*

_{s}/

*ω*is defined as the area heat capacity of a land surface (A. Arakawa and Y. Mintz 1974, personal communication).

Figure 12 shows the time series of *G _{s}*(

*t*) and ∂

*T*(

_{s}*t*− 3 h)/∂

*t*and the

*x*–

*y*plot between them from 16 to 25 April 2005. Using the OLS relationship, the area heat capacity

*ρ*

_{s}

*c*

_{s}

*k*

_{s}/

*ω*was determined to be 278 700 ± 9500 J m

^{−2}K

^{−1}and

*ρ*

_{s}

*c*

_{s}

*k*

_{s}was determined to be 2376 J m

^{−2}K

^{−1}s

^{−1/2}with a correlation coefficient of 0.88. The area heat capacity was slightly higher than the value of 2.5 × 10

^{5}J m

^{−2}K

^{−1}as prescribed in MM5 and WRF (Table 3). The value of

*ρ*

_{s}

*c*

_{s}

*k*

_{s}was slightly larger than that of wet loam at 2189 J m

^{−2}K

^{−1}s

^{−1/2}but is lower than that of water at 5926 J m

^{−2}K

^{−1}s

^{−1/2}(Tsuang 2005). This is reasonable because the derived value was between those of water and wet loam, and close to that of wet loam. Note that the surface of rice paddy consists of paddy water fraction, exposed wet loam fraction, and rice plant surface fraction; the representative value should be close to the harmonic average of these fractions (Tsuang 2005).

## 6. Discussion

From the above discussions, it can be seen that except for the Bowen ratio and surface moisture availability, the land characteristics measured in this study are close to those observed in other rice paddies. Table 4 lists data observed in Japan (Harazono et al. 1998) and Taiwan (this study) during the daytime period (from 0800 to 1800 LT). From the table, it can be seen that values of both the Bowen ratio and surface moisture availability at the Japanese site were statistically significantly lower than those of the Taiwanese site. The mean Bowen ratio at the Japanese site was 0.08 ± 0.05, while that at the Taiwanese site was 0.18 ± 0.05; the mean surface moisture availability at the Japanese site was 34 ± 7%, while that at the Taiwanese site was 44 ± 8%. It would be interesting to know which site value is more representative for rice paddy. On the other hand, their daytime canopy resistances were close to each other. The mean daytime canopy resistance at the Japanese site was 91 ± 9 s m^{−1}, while that at the Taiwanese site was 82 ± 23 s m^{−1}. Their difference was not statistically significant.

The canopy resistances between the Japanese and the Taiwanese sites were not statistically significantly different. Using the mean daytime canopy resistance of the two sites (the Japanese site and the Taiwanese site) of 87 s m^{−1}, the surface moisture availability can be determined from Eq. (18), and the Bowen ratio can be determined (e.g., Jarvis et al. 1976; Wilson et al. 2002a) as

where *r*_{i} is climatological resistance and *B*_{eq} is the equilibrium Bowen ratio when evaporation is at thermodynamic equilibrium under the conditions *r _{c}* =

*r*= 0. They are defined as

_{i}The above equation shows that *B*_{eq} decreases with air temperature because ∂*q**/∂*T* increases with air temperature.

Table 5 and Fig. 13 show the calculated Bowen ratio and surface moisture availability for each day at the two paddy sites during the daytime periods when setting daytime canopy resistance at the mean of the two sites. It can be seen that at the two sites, the general trends of the Bowen ratio and surface moisture availability are well captured with correlation coefficients of 0.86 and 0.88, respectively. This implies that the differences of the Bowen ratio and surface moisture availability between the Japanese and the Taiwanese sites were not because of their difference in canopy resistance, but because of their differences in the other variables listed in Eqs. (18) and (23). At the Japanese site, the wind speeds were higher than the Taiwanese site, creating lower aerodynamic resistances. Note that the mean wind speed at the Japanese site was 2.6 ± 0.7 m s^{−1}, while that at the Taiwanese site was 1.9 ± 0.3 m s^{−1}. As a result, the surface moisture availability became lower, according to Eq. (18). At the Japanese site, the air temperatures were higher, causing higher ∂*q**/∂*T*. Note that the mean air temperature at the Japanese site was 32.2 ± 0.3°C, while that at the Taiwanese site was 26.9 ± 0.9°C. As a consequence, the Bowen ratios were lower at the Japanese site, according to Eq. (23). Therefore, it can be inferred that the discrepancies of the Bowen ratio and surface moisture availability at the Japanese and the Taiwanese sites were mainly due to the difference in meteorological conditions during their study periods, not difference in their canopy resistances. The same conclusion has been found for other land types (Wilson et al. 2002a).

With respect to surface sensible and latent heat fluxes, they can be determined if any one of the Bowen ratio, canopy resistance, or surface moisture availability variables is known. For partitioning sensible and latent heat fluxes, it will be interested to understand which of the following parameterization is more accurate: 1) the constant Bowen ratio method, as used in AERMOD, 2) the constant canopy resistance method, as suggested by Monteith (1965), or 3) the constant surface moisture availability method, as used in MM5 and WRF. If the values of available heat flux and Bowen ratio are available, surface sensible and latent heat fluxes can be determined as

If surface moisture availability is known, canopy resistance can be determined by rearranging Eq. (18) as

In addition, if the Bowen ratio is known, canopy resistance can be determined by rearranging Eq. (22) as

Figure 14 and Table 5 show comparisons of surface sensible heat flux and surface latent heat flux between calculations and observations. The calculations use the mean characteristics of the Japanese site and the Taiwanese sites for the simulation. The following three methods are conducted: 1) calculation using a constant daytime Bowen ratio of 0.13, 2) calculation using constant daytime canopy resistance at 87 s m^{−1}, and 3) calculation using constant daytime surface moisture availability at 0.39. From the table, it can be seen that among the three methods, the constant canopy resistance method is preferred because it has the lowest RMSE and the highest correlation coefficient for the simulations of surface sensible heat flux and surface latent heat flux.

Nonetheless, canopy resistance for a rice paddy in fact is not a constant; it depends on transpiration resistance in rice stomata and evaporation resistance within the rice canopy for paddy water to evaporate (Tsuang and Tu 2002). For example, it can be seen that on 17–18 April 2005 at the Taiwanese study site, both the Bowen ratio and the surface moisture availability are not well reproduced by setting the canopy resistance at 87 s m^{−1} (Fig. 13). For the entire study period, on 17 April the solar radiation was the weakest, whereas on 18 April the solar radiation was the strongest. It is well known that transpiration resistance decreases with solar radiation (Blondin 1988). Therefore, during the 2 days the canopy resistances were departed from the mean daytime value at 87 s m^{−1}. A further study on the mechanisms of canopy resistance of rice paddy is suggested.

## 7. Conclusions

A field measurement was conducted to examine the surface energy balance closure over rice paddies at the study site using the eddy covariance system. The observed energy components are listed in Tables 1 and 2. It can be seen that the energy balance ratios and the regression coefficients of the OLS relationship become closer to 1 after the corrections of the 1) coordinate rotation correction, 2) Webb et al. (1980) correction, 3) canopy heat storage correction, 4) advected heat flux correction, and 5) photosynthetic energy correction. The EBR reached 95% and the residual heat flux decreased to 12 W m^{−2} during the day. Observations from the SIRS and CSAT3 are used for the evaluation. Other combination of instruments might increase the residual heat flux by 26 W m^{−2}.

Major characteristics observed at the rice paddy are listed in Table 3. Major differences between observations and model default values are for albedo, Bowen ratio, surface moisture availability, surface emissivity, and area heat capacity. The albedo was observed at 0.09, the surface emissivity was observed at 0.86, and the area heat capacity was observed at 2.8 × 10^{5} J m^{−2} K^{−1}. These values are suggested to replace the default values in meteorological or air-quality models for rice paddies. For choosing a proper value of aerodynamic roughness for rice paddy in the aforementioned models, please refer to Tsai and Tsuang (2005) for details. It is expected that the climate in rice paddy–dominated regions, simulated by a model that adopts our suggestions, would become hotter and more humid than before this cultivation, because the albedo and Bowen ratio measured over rice paddies are lower than those of cultivated land, as listed in many air-quality and meteorological models. Nonetheless, nonlinearity in the modeling system may be against the inference.

On the other hand, this study does not suggest using the constant Bowen ratio or surface moisture availability measured in this study to replace the default values in the models because those value are air temperature and wind speed dependent, respectively. Alternatively, this study suggests simulating sensible and latent heat fluxes by assigning proper values for canopy resistance (Monteith 1965). The error and correlation simulated by this suggestion are found to be better than those simulated by setting either the Bowen ratio or surface moisture availability to be constant. The representative daytime canopy resistance at two rice paddy sites was observed to be 87 s m^{−1}. During the nighttimes, a high canopy resistance (∼900 s m^{−1}) should be assigned. Nonetheless, daytime canopy resistance varies with solar radiation. A further study on the mechanisms of canopy resistance of rice paddy could advance the current suggestions.

## Acknowledgments

This work is supported by NSC/Taiwan under Contracts NSC94-2211-E-005-039, NSC95-EPA-Z-005-001, NSC 95-2111-M-005-001, and the MOE/Taiwan under the ATU plan. We are also indebted to many students in our laboratory for helping with the instrumentation and the experiment. Thanks are given to Dr. D. J. Liu and Noel Dallow for proofreading and to the editor A. DeGaetano and three anonymous reviewers for enriching the manuscript significantly.

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## Footnotes

*Corresponding author address:* Ben-Jei Tsuang, Department of Environmental Engineering, National Chung Hsing University, 250 Kuokang Road, Taichung 402, Taiwan. Email: tsuang@nchu.edu.tw