# Estimating Rice Panicle Temperature with Three-Layer Model

Authors: Yanyan Wang; Hiroki Oue; Zhijun Luo; Ming Chen; Shiyu Liu; Chunhuo Zhou; Xiaowu He
Journal: Advances in Meteorology
 (2020)

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## Abstract

Rice panicle temperature (Tp) is a key factor for studying high temperature impacts on spikelet sterility. Comparing with measuring Tp by hand, a Tp simulation model could obtain Tp data readily. The two-layer energy budget model which divides the soil layer and canopy layer was widely used to predict rice canopy temperature (Tc), but panicle existed mostly in the upper layer canopy, and we have proved that Tc was different from the upper layer canopy temperature (Tc1), and the upper layer must be separated from the whole canopy for the purpose of estimating Tp. Thus, we developed the three-layer model, contained upper canopy layer with panicle (50–100 cm), lower rice canopy layer (10–40 cm), and water surface layer (≤10 cm) to estimate Tp with general meteorological and vegetation growth data. There were two steps to estimate Tp. The first step was calculating Tc1 and lower layer canopy temperature (Tc2) by solving heat balance equations with canopy resistances. And the second step was estimating Tp with following parameters: (a) the inclination factors of leaves and panicles (F1, F2, and Fp) which were decided by fitting the calculated transmissivity of downward solar radiation (TDSR) to the measured TDSR, (b) the aerodynamic resistance between the panicle and atmosphere (rap) denoted by wind speed, (c) the panicle resistance for transpiration (rp) denoted by days after heading, and (d) air temperature and humidity at the panicle’s height (Tac1 and eac1) calculated from the resistances of the pathways of sensible and latent heat fluxes in accordance with Ohm’s law. The model simulated fairly well the Tc1, Tc2, and Tp with root mean square errors (RMSEs) of 0.76°C, 0.75°C, and 0.81°C, respectively, where RMSE of measured Tp and predicted Tp by integrated micrometeorology model for panicle and canopy temperature (IM2PACT) including two-layer model was 1.27°C. This model was validated well by two other rice cultivars, and thus, it demonstrated the three-layer model was a new feasible way to estimate Tp.


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## Body

## 1. Introduction

With increasing concerns about global warming, the impacts of higher temperature on rice production have become a major focus in many rice-producing countries in tropical, subtropical, and temperate regions [1–9]. In China, extreme high temperature in 2003 caused about 5 million tonnes of rice yield loss [10], while unusual temperatures (>40°C) in many areas of Kanto and Tokai regions of Japan resulted in 25% spikelet sterility in 2007 [11].Rice panicle is most sensitive to high temperature during the flowering stage [12–16]. It has been proved that high temperature prevents anther dehiscence and decreases basal pore length of the anther, resulting in low numbers of germinating pollen grains on the stigma, and thus, it causes spikelet sterility [7, 12, 15, 17–22].Effect of high temperature on spikelet sterility has been studied under different conditions. Matsui et al. [23] reported that spikelet fertility was significantly damaged when daily maximum air temperature exceeded 35°C. Abeysiriwardena et al. [24] revealed high temperature condition (35°C day/30°C night) induced complete grain sterility when relative humidity (RH) was 85–95%. Contrary to the results above, [25, 26] demonstrated spikelet sterility of rice did not occur seriously even daily maximum Ta was over 40°C in Australia during the 2004–2006 growing seasons because the strong transpirational cooling by low relative humidity (<20%) brought panicle temperature (Tp) 6.8°C lower than Ta. But spikelet sterility occurred frequently in Jianghan Basin, China, where Ta was not so high, since Tp was 4.0°C higher than Ta under high solar radiation with high RH (>80%) and low wind speed (u < 1 m s−1) conditions [27]. Therefore, Tp instead of Ta is a key factor for high temperature impact study. As measuring Tp was a time-consuming and laborious work, a Tp simulation model was needed to obtain Tp data readily.Until now, only limited information has been reported about panicle temperature models. Sheehy et al. [28] developed a Tp model with air temperature and thermal burden. Oue et al. [29] measured Tp in every 10 cm rice canopy layer in the CO2 ambient and CO2 elevated plots during the daytime in Wuxi, China, and developed a heat balance model of Tp based on the measured stomatal conductance. To date, the whole canopy temperature (Tc) predicted by the two-layer model has been used to calculate the long-wave radiations to the panicle as shown in the integrated micrometeorology model for panicle and canopy temperature (IM2PACT) [30]. However, panicle exists mostly in the upper layer canopy, and we have proved that Tc is different from the upper layer canopy temperature (Tc1), and the upper layer must be separated from the whole canopy for the purpose of estimating Tp, whereas the multilayer model [31] required many vertical profiles of micrometeorological environments and fluxes of momentum, and heat and vapor within and above a vegetation, making it unusable to predict Tp with insufficient data.Therefore, the objectives of this paper are (1) to develop a three-layer model to calculate panicle temperature based on general meteorological and vegetation growth data and (2) to compare the performance to estimateTp by three-layer model and Tp by IM2PACT [30] including two-layer model.


## 2. Materials and Methods

### 2.1. Measurements in the Rice Paddy Field

The experimental paddy field was located in the Ehime University Senior High School, Matsuyama, Japan (33°50′N, 132°47′E). The Japonica type rice (cultivar Akitakomachi) was transplanted with 20 × 30 cm spacing on May 27, 2014, and then harvested on September 8, 2014.The global solar radiation (St), downward long-wave radiation (Ld), and upward long-wave radiation (Lu) above the rice canopy were detected using pyranometer CNR-4 (Kipp & Zonen, the Netherlands) at 2.0 m height from the ground. To measure soil heat flux (G), a soil heat plate CHF-HDP01 (Campbell Scientific Inc., Logan, UT, USA) was buried in the soil surface. Air temperature (Ta) and relative humidity (RH) were observed using ventilated psychrometers HMP-45A (Vaisala Inc., Helsinki, Finland), first mounted at 0.6 m and 1.0 m of a 2.5 m tower, and then lifted to 1.0 m and 1.5 m on July 28, respectively, when rice plant was 81 cm in height. Three-cup anemometers 014A (MetOne, USA) were mounted as the same heights of psychrometers to measure the wind speed (u). Downward and upward long-wave radiations beneath the rice canopy were both measured with PRI-01 (Prede, Japan) sensors. Water surface temperature (Tw) or ground surface temperature (Tg) was measured with the thermocouple sensor. All data were sampled per 10 s; then, they were averaged and recorded per 10 min using a data logger CR23x (Campbell Scientific Inc., Logan, UT, USA).Three stubs of rice were taken to measure the upper layer canopy temperature (Tc1), the lower layer canopy temperature (Tc2), and the panicle temperature (Tp) per 2 or 3 h in the daytime using an infrared thermometer THI-500 (Tasco, Japan). The solar radiation within rice canopy was measured with a line type pyranometer PCM200 (Prede, Japan) in the center between stubs in parallel and perpendicular directions, of which the average was calibrated from the solar radiation measured with CNR-4 (Kipp & Zonen, the Netherlands) at 2.0 m. The transmissivity of downward solar radiation (TDSR) refers to the ratio of the St in the rice canopy in every 10 cm to that above the rice canopy. Subsequently, the average TDSRs from 50 cm to 100 cm and from 10 cm to 40 cm were set as the upper and lower layer rice canopy TDSRs, respectively. TDSRs were measured from 10 cm to the top of the canopy per 10 cm and 1.2 m (above the rice canopy). The canopy temperature, Tp, and solar radiation within canopy data were recorded using ZR-RX 20 portable multilogger (Omron, Japan). At the heading and the flowering stage, irrigation was performed in the paddy field at 5-day interval. Besides, 8 cm depth irrigation water decreased to 0 through evaporation and infiltration in one and a half days. At the ripening stage, there was almost no water.Plant area density (PAD) was sampled three rice plants at the interval of one week. The taken three rice plants were cut at intervals of 10 cm, split into components of leaves, stems, and panicles, respectively, and then scanned. Lastly, the area of each part (projected area for panicle) was calculated using ImageJ software. Water depth (dw) was measured per two or three hours in the daytime. Water surface evaporation (Eg) beneath the rice canopy was measured with the lysimeter (length × width × depth: 60 × 20 × 30 cm) and recorded twice (8:30 and 18:30) per day.


### 2.2. Estimating Panicle Temperature (Tp) with Three-Layer Model

The input data of the three-layer model to estimateTp include (a) hourly radiations, (b) temperature, humidity, and wind speed, (c) water surface data, and (d) vegetation growth data. Tp was estimated in two steps. The first step was calculating Tc1 and Tc2 by solving heat balance equations with canopy resistances and the second step was estimating Tp with calculated Tc1 and Tc2.The schematic of the aerodynamic resistance and upper and lower layer canopy resistances of one-layer and three-layer models is illustrated in Figure1. The schematic diagram illustrating the method for estimation Tc1, Tc2, and Tp by the three-layer model is shown in Figure 2. And the input parameters required for the calculation in the model are shown in Table 1.Figure 1
A schematic representation of the aerodynamic resistance and upper and lower canopy resistances of (a) one-layer and (b) three-layer models. LET was the latent heat flux for the whole canopy (W m−2), Ts was the surface temperature of the paddy field (°C), ra was the aerodynamic resistance to the transfer of sensible heat between the whole rice canopy and water surface (s m−1), rcg was the total canopy resistance consists of rice canopy resistance and water surface resistance (s m−1), LEp was the latent heat flux on a panicle (W m−2), LEc1 was the latent heat flux between upper layer rice canopy and atmosphere (W m−2), LEc2 was the latent heat flux between lower layer rice canopy and atmosphere (W m−2), LEg was the latent heat flux between water surface beneath the rice canopy and atmosphere (W m−2), Tp was the panicle temperature (°C), Tc1 was the upper layer canopy temperature (°C), Tc2 was the lower layer canopy temperature (°C), Tg was the water temperature (°C), rap was the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (s m−1), rac1 was the aerodynamic resistance to the transfer of sensible heat between upper layer rice canopy and atmosphere (s m−1), rac2 was the aerodynamic resistance to the transfer of sensible heat between lower layer rice canopy and atmosphere (s m−1), rag was the aerodynamic resistance to the transfer of sensible heat between water surface and atmosphere (s m−1), rp was the panicle transpiration resistance (s m−1), rc1 was the upper layer canopy resistance (s m−1), rc2 was the lower layer canopy resistance (s m−1), and rg was albedo of water surface (s m−1).
(a)
(b)Figure 2
A schematic diagram illustrating the method for estimating upper and lower layer canopy temperatures (Tc1 and Tc2) and panicle temperature (Tp). The grey rounded rectangles denote input data, and the grey diamonds denote output data.Table 1
Input parameters required for the calculation in the three-layer model.
Symbol
Name
Unit
Forcing parameters
R
n
Net radiation for the whole canopy
W m−2
G
Soil heat flux
W m−2
L
d
Downward long-wave radiation for the whole canopy
W m−2
L
u
Upward long-wave radiation for the whole canopy
W m−2
T
a
Air temperature
°C
e
a
Water vapor pressure of the air
hPa
u
Wind speed
m s−2
Ground characteristics
T
w
Water temperature
°C
d
w
Water depth
m
LE
g
Latent heat flux between water surface beneath canopy and atmosphere
W m−2
Canopy characteristics
a
1
Green leaf and yellow leaf area index in the upper canopy layer
m2 m−3
a
2
Green leaf and yellow leaf area index in the lower canopy layer
m2 m−3
PAR
Photosynthetically active radiation
μ mol m−2 s−1
g
s
Stomatal resistance
cm s−1
Note:gs was referred to Oue’s literature [32]; other data were observed.In the one-layer model, the rice canopy and water surface were set as a whole, and energy budget in a paddy field was expressed as follows:(1)Rn=LET+H+G+δW,(2)δW=CwdwTwt+1−Twtδt,where Rn was the net radiation (W m−2), LET was the latent heat flux (W m−2), H was the sensible heat flux (W m−2) for the whole canopy, and δW was the change of storage energy in the water surface (W m−2) calculated by equation (2) based on the measured water temperatures and water depth. LET was calculated by the Bowen ratio method (equation 3(a)) with air temperatures and water vapor pressure of air at two different heights, and H was calculated by equation (1). Aerodynamic resistance between the whole rice canopy and water surface (ra) and the total canopy resistance that consists of rice canopy resistance and water surface resistance (rcg) was calculated by equations (3b) and (3c):(3a)LET=Rn−G1+Bo,(3b)H=cpρTs−Tara,(3c)LET=cpρesatTs−eaγra+rcg,where cp was the specific heat capacity of the air at constant pressure (J g−1 °C−1), ρ was the air density (kg m−3), Ts was the surface temperature of the paddy field (°C), esat(Ts) was the saturation-specific humidity at Ts (hPa), and ea was the specific humidity of the air (kg kg−1).T
s was the surface temperature of the paddy field (°C) calculated based on the upward long-wave radiation (Lu) and downward long-wave radiation (Ld), as expressed in the following equation:(4)Lu=εsσTs4+1−εsLd,where εs was the surface emissivity set as 0.97 in this study.Based on the data of measuredG, δW, LE, and H were calculated by equation (1), and Ts was obtained by equation (4). Subsequently, ra was obtained by equation (3b), and lastly rcg was calculated by equation (3c) based on the data of measured Ta, ea, and LET.In the three-layer model, net radiation (Rn) sums the net radiation absorbed by upper canopy layer (Rnc1), the net radiation absorbed by lower canopy layer (Rnc2), and the net radiation absorbed by water surface layer (Rng):(5)Rn=Rnc1+Rnc2+Rng.The energy budget equations for water surface were written from the following equations:(6)Rng=Hg+LEg+G+δW,(7a)LEg=cpρesatTg−eaγrag+rg,(7b)Hg=cpρTg−Tarag,where Hg was the sensible heat flux between water surface beneath canopy and atmosphere (W m−2) LEg was the latent heat flux between water surface beneath canopy and atmosphere (W m−2) obtained from the water surface evaporation by the lysimeter, Tg was the ground surface temperature (°C) (assumed Tg = Tw in the model), esat(Tg) was the saturation-specific humidity at Tg (hPa), γ was the psychrometric constant (kPa °C−1), rag was calculated by equation (7a) based on the measured LEg and Tg first, Hg was calculated by equation (7b), and then Rng, Rnc1 + Rnc2 were calculated by equations (5) and (6), respectively.The energy budget equations for upper canopy layer (50–100 cm) and lower canopy layer (10–40 cm) were written from equations (8) to (10c):(8)Rnc1+Rnc2=Hc1+LEc1+Hc2+LEc2,(9a)Hc1+Hc2=H−Hg,(9b)Hc1=cpρTc1−Tarac1,(9c)Hc2=cpρTc2−Tarac2,(10a)LEc1+LEc2=LET−LEg,(10b)LEc1=cpρesatTc1−eaγrc1+rac1,(10c)LEc2=cpρesatTc2−eaγrc2+rac2,where LEc1 and LEc2 were the latent heat flux between upper and lower layer canopy and atmosphere (W m−2), respectively. Hc1 and Hc2 were the sensible heat flux between upper and lower layer canopy and atmosphere (W m−2), respectively. Tc1 was the upper layer canopy temperature (°C), Tc2 was the lower layer canopy temperature (°C), esat(Tc1) and esat(Tc2) were the saturation-specific humidity at Tc1 and Tc2 (hPa), rac1 and rac2 were aerodynamic resistances to the transfer of sensible heat between upper and lower layer canopy and atmosphere (s m−1), respectively, rc1 and rc2 were the upper and lower layer canopy resistances (s m−1), respectively.For the aerodynamic resistances, the association ofra, rag, rac1, and rac2 was expressed in the following equation:(11)1ra=1rag+1rac1+1rac2.In this study,rc1 and rc2 were calculated by stomatal resistance (gs), green leaf and yellow leaf area index in the upper rice canopy layer (a1), and green leaf and yellow leaf area index in the lower rice canopy layer (a2), as expressed in equations (12a) and (12b). Because gs was not measured in the experimental paddy field in 2014, gs developed by Oue [32] was adopted (values as shown in Table 2), as expressed in equation (13):(12a)rc1=1gsa1,(12b)rc2=1gsa2,(13)gs=msPAR+gsmax−gsmin2ns+gsmin−12ns×msPAR+gsmax−gsmin2−4msPARgsmax−gsminns1/2,where gs was the stomatal conductance (cm s−1), ms and ns were parameters, PAR was photosynthetically active radiation (μ mol m−2 s−1), gsmax was the maximum of stomatal conductance (cm s−1), and gsmin was the minimum of stomatal conductance (cm s−1).Table 2
m
s and gsmax in the gs model.
Date
Canopy layer
VPD (hPa)
m
s (cm s−1)/(μ mol m−2 s−1)
g
s
max (cm s−1)
August 6
Upper
∼18
0.00247
1.500
18∼
0.00170
0.500
Lower
∼10
0.002405
1.500
10∼15
0.002095
1.200
15∼
0.001925
0.800
August 13
Upper
∼8
0.00780
0.820
8∼
0.01246
0.410
Lower
∼8
0.009935
0.515
8∼
0.00833
0.470
August 27
Upper
∼9
0.00282
0.500
9∼
0.00195
0.400
Lower
∼10
0.003155
0.900
10∼11
0.00261
0.750
11∼
0.00213
0.450
September 4
Upper
∼16
0.003475
0.550
16∼
0.000445
0.400
Lower
∼15
0.001315
0.400
15∼16
0.00123
0.400
∼16
0.00615
0.400
Note: VPD is vapor pressure deficit,gs is the stomatal conductance (cm s−1), gsmax is the maximum of stomatal conductance (cm s−1), gsmin is the minimum of stomatal conductance (cm s−1), and ms and ns are parameters.With the calculatedrc1 and rc2, Tc1, Tc2, rac1, and rac2 were calculated by equations (8)–(10c).The net radiation input to a panicle (Rin) sums shortwave and long-wave radiation absorbed by the panicle (W m−2), as expressed in equation (14a). Ll and La were long-wave radiations from a leaf surface adjacent to the panicle and from the atmosphere (W m−2), respectively. Sd and Sf were downward direct and diffused shortwave radiations (W m−2), respectively, and θ was the solar zenith angle (°), Fp was the inclination factor of panicle, and df was the diffusivity factor for radiation. Besides, the heat balance in the panicle layer was written as equation (14b).(14a)Rin=1−0.35FpsecθSd+2dfSf+FpdfLl+La,(14b)Rin=2FpdfσTp4+H+pLEp,(15a)Ll=σTc14+Ld−σTc14exp−F1a1df,(15b)La=σTc24+σTg4−σTc24exp−F2a2df+σTc14+σTc24−σTc14exp−F1a1df,where F1 and F2 were the inclination factors of upper and lower layer rice canopy, respectively. F1, F2, and Fp were decided by fitting the calculated transmissivity of downward solar radiation (TDSR) to the measured TDSR (Figure 3).Figure 3
Vertical profiles of transmissivity of downward solar radiation (TDSR) within the rice canopy in every 10 cm in the paddy field on August 7, 2014 (a–e). (a) 8:50, (b) 10:50, (c) 12:40, (d) 14:50, and (e) 16:40.
(a)
(b)
(c)
(d)
(e)Besides,Hp and LEp were sensible and latent heat fluxes on a panicle (W m−2), which were written as follows:(16a)Hp=cpρTp−Tac1rap,(16b)LEp=cpρesatTp−eTac1γrap+rp,(17)Tc1−Tac1rc1=Tac1−Tarac1.Moreover,Tac1 was the air temperature at panicle’s height (°C) which was calculated by the transposition of equation (17) as shown in equation (18a), and likewise, eac1 was the absolute humidity at panicle’s height (hPa) calculated as expressed in equation (18b):(18a)Tac1=rac1Tc1+rc1Tarc1+rac1,(18b)eac1=rac1Tc1+rc1earc1+rac1,where rap, the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (s m−1), denoted the parameter of wind speed (Section 3.3.2), and then rp, panicle transpiration resistance (s m−1), denoted the parameter of days after the heading stage (Section 3.3.3). Lastly, Tp was calculated by combining equations from equations (14a) to (18b).The average value of measured panicle temperature from 50 cm to 100 cm was set as the measuredTp, which was compared with the Tp using the three-layer model and by IM2PACT [30] including the two-layer model.


### 2.3. Statistical Analysis of Models

The measured and calculatedTc1, Tc2, and Tp were compared by using error analysis and linear regression. Root mean squared error (RMSE), mean absolute error (MAE), and the standard deviation (SD) [33–35] were adopted to evaluate measured and calculated Tc1, Tc2, Tc, and Tp by the models.


### 2.4. Three-Layer Model Validation

We planted rice (cultivar Hinohikari) from June 21 to November 20, 2015, and rice (cultivar Nikomaru) from June 21 to November 27, 2015, in the same paddy field. PAD of two cultivars was both measured from July 9 to October 14, 2015. Other meteorological instruments were set as same as 2014. Six images were taken to getTc and Tp by infrared thermometer FLIR-i5 (FLIR systems, USA) at different heights every two or three hours during daytime.


## 2.1. Measurements in the Rice Paddy Field

The experimental paddy field was located in the Ehime University Senior High School, Matsuyama, Japan (33°50′N, 132°47′E). The Japonica type rice (cultivar Akitakomachi) was transplanted with 20 × 30 cm spacing on May 27, 2014, and then harvested on September 8, 2014.The global solar radiation (St), downward long-wave radiation (Ld), and upward long-wave radiation (Lu) above the rice canopy were detected using pyranometer CNR-4 (Kipp & Zonen, the Netherlands) at 2.0 m height from the ground. To measure soil heat flux (G), a soil heat plate CHF-HDP01 (Campbell Scientific Inc., Logan, UT, USA) was buried in the soil surface. Air temperature (Ta) and relative humidity (RH) were observed using ventilated psychrometers HMP-45A (Vaisala Inc., Helsinki, Finland), first mounted at 0.6 m and 1.0 m of a 2.5 m tower, and then lifted to 1.0 m and 1.5 m on July 28, respectively, when rice plant was 81 cm in height. Three-cup anemometers 014A (MetOne, USA) were mounted as the same heights of psychrometers to measure the wind speed (u). Downward and upward long-wave radiations beneath the rice canopy were both measured with PRI-01 (Prede, Japan) sensors. Water surface temperature (Tw) or ground surface temperature (Tg) was measured with the thermocouple sensor. All data were sampled per 10 s; then, they were averaged and recorded per 10 min using a data logger CR23x (Campbell Scientific Inc., Logan, UT, USA).Three stubs of rice were taken to measure the upper layer canopy temperature (Tc1), the lower layer canopy temperature (Tc2), and the panicle temperature (Tp) per 2 or 3 h in the daytime using an infrared thermometer THI-500 (Tasco, Japan). The solar radiation within rice canopy was measured with a line type pyranometer PCM200 (Prede, Japan) in the center between stubs in parallel and perpendicular directions, of which the average was calibrated from the solar radiation measured with CNR-4 (Kipp & Zonen, the Netherlands) at 2.0 m. The transmissivity of downward solar radiation (TDSR) refers to the ratio of the St in the rice canopy in every 10 cm to that above the rice canopy. Subsequently, the average TDSRs from 50 cm to 100 cm and from 10 cm to 40 cm were set as the upper and lower layer rice canopy TDSRs, respectively. TDSRs were measured from 10 cm to the top of the canopy per 10 cm and 1.2 m (above the rice canopy). The canopy temperature, Tp, and solar radiation within canopy data were recorded using ZR-RX 20 portable multilogger (Omron, Japan). At the heading and the flowering stage, irrigation was performed in the paddy field at 5-day interval. Besides, 8 cm depth irrigation water decreased to 0 through evaporation and infiltration in one and a half days. At the ripening stage, there was almost no water.Plant area density (PAD) was sampled three rice plants at the interval of one week. The taken three rice plants were cut at intervals of 10 cm, split into components of leaves, stems, and panicles, respectively, and then scanned. Lastly, the area of each part (projected area for panicle) was calculated using ImageJ software. Water depth (dw) was measured per two or three hours in the daytime. Water surface evaporation (Eg) beneath the rice canopy was measured with the lysimeter (length × width × depth: 60 × 20 × 30 cm) and recorded twice (8:30 and 18:30) per day.


## 2.2. Estimating Panicle Temperature (Tp) with Three-Layer Model

The input data of the three-layer model to estimateTp include (a) hourly radiations, (b) temperature, humidity, and wind speed, (c) water surface data, and (d) vegetation growth data. Tp was estimated in two steps. The first step was calculating Tc1 and Tc2 by solving heat balance equations with canopy resistances and the second step was estimating Tp with calculated Tc1 and Tc2.The schematic of the aerodynamic resistance and upper and lower layer canopy resistances of one-layer and three-layer models is illustrated in Figure1. The schematic diagram illustrating the method for estimation Tc1, Tc2, and Tp by the three-layer model is shown in Figure 2. And the input parameters required for the calculation in the model are shown in Table 1.Figure 1
A schematic representation of the aerodynamic resistance and upper and lower canopy resistances of (a) one-layer and (b) three-layer models. LET was the latent heat flux for the whole canopy (W m−2), Ts was the surface temperature of the paddy field (°C), ra was the aerodynamic resistance to the transfer of sensible heat between the whole rice canopy and water surface (s m−1), rcg was the total canopy resistance consists of rice canopy resistance and water surface resistance (s m−1), LEp was the latent heat flux on a panicle (W m−2), LEc1 was the latent heat flux between upper layer rice canopy and atmosphere (W m−2), LEc2 was the latent heat flux between lower layer rice canopy and atmosphere (W m−2), LEg was the latent heat flux between water surface beneath the rice canopy and atmosphere (W m−2), Tp was the panicle temperature (°C), Tc1 was the upper layer canopy temperature (°C), Tc2 was the lower layer canopy temperature (°C), Tg was the water temperature (°C), rap was the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (s m−1), rac1 was the aerodynamic resistance to the transfer of sensible heat between upper layer rice canopy and atmosphere (s m−1), rac2 was the aerodynamic resistance to the transfer of sensible heat between lower layer rice canopy and atmosphere (s m−1), rag was the aerodynamic resistance to the transfer of sensible heat between water surface and atmosphere (s m−1), rp was the panicle transpiration resistance (s m−1), rc1 was the upper layer canopy resistance (s m−1), rc2 was the lower layer canopy resistance (s m−1), and rg was albedo of water surface (s m−1).
(a)
(b)Figure 2
A schematic diagram illustrating the method for estimating upper and lower layer canopy temperatures (Tc1 and Tc2) and panicle temperature (Tp). The grey rounded rectangles denote input data, and the grey diamonds denote output data.Table 1
Input parameters required for the calculation in the three-layer model.
Symbol
Name
Unit
Forcing parameters
R
n
Net radiation for the whole canopy
W m−2
G
Soil heat flux
W m−2
L
d
Downward long-wave radiation for the whole canopy
W m−2
L
u
Upward long-wave radiation for the whole canopy
W m−2
T
a
Air temperature
°C
e
a
Water vapor pressure of the air
hPa
u
Wind speed
m s−2
Ground characteristics
T
w
Water temperature
°C
d
w
Water depth
m
LE
g
Latent heat flux between water surface beneath canopy and atmosphere
W m−2
Canopy characteristics
a
1
Green leaf and yellow leaf area index in the upper canopy layer
m2 m−3
a
2
Green leaf and yellow leaf area index in the lower canopy layer
m2 m−3
PAR
Photosynthetically active radiation
μ mol m−2 s−1
g
s
Stomatal resistance
cm s−1
Note:gs was referred to Oue’s literature [32]; other data were observed.In the one-layer model, the rice canopy and water surface were set as a whole, and energy budget in a paddy field was expressed as follows:(1)Rn=LET+H+G+δW,(2)δW=CwdwTwt+1−Twtδt,where Rn was the net radiation (W m−2), LET was the latent heat flux (W m−2), H was the sensible heat flux (W m−2) for the whole canopy, and δW was the change of storage energy in the water surface (W m−2) calculated by equation (2) based on the measured water temperatures and water depth. LET was calculated by the Bowen ratio method (equation 3(a)) with air temperatures and water vapor pressure of air at two different heights, and H was calculated by equation (1). Aerodynamic resistance between the whole rice canopy and water surface (ra) and the total canopy resistance that consists of rice canopy resistance and water surface resistance (rcg) was calculated by equations (3b) and (3c):(3a)LET=Rn−G1+Bo,(3b)H=cpρTs−Tara,(3c)LET=cpρesatTs−eaγra+rcg,where cp was the specific heat capacity of the air at constant pressure (J g−1 °C−1), ρ was the air density (kg m−3), Ts was the surface temperature of the paddy field (°C), esat(Ts) was the saturation-specific humidity at Ts (hPa), and ea was the specific humidity of the air (kg kg−1).T
s was the surface temperature of the paddy field (°C) calculated based on the upward long-wave radiation (Lu) and downward long-wave radiation (Ld), as expressed in the following equation:(4)Lu=εsσTs4+1−εsLd,where εs was the surface emissivity set as 0.97 in this study.Based on the data of measuredG, δW, LE, and H were calculated by equation (1), and Ts was obtained by equation (4). Subsequently, ra was obtained by equation (3b), and lastly rcg was calculated by equation (3c) based on the data of measured Ta, ea, and LET.In the three-layer model, net radiation (Rn) sums the net radiation absorbed by upper canopy layer (Rnc1), the net radiation absorbed by lower canopy layer (Rnc2), and the net radiation absorbed by water surface layer (Rng):(5)Rn=Rnc1+Rnc2+Rng.The energy budget equations for water surface were written from the following equations:(6)Rng=Hg+LEg+G+δW,(7a)LEg=cpρesatTg−eaγrag+rg,(7b)Hg=cpρTg−Tarag,where Hg was the sensible heat flux between water surface beneath canopy and atmosphere (W m−2) LEg was the latent heat flux between water surface beneath canopy and atmosphere (W m−2) obtained from the water surface evaporation by the lysimeter, Tg was the ground surface temperature (°C) (assumed Tg = Tw in the model), esat(Tg) was the saturation-specific humidity at Tg (hPa), γ was the psychrometric constant (kPa °C−1), rag was calculated by equation (7a) based on the measured LEg and Tg first, Hg was calculated by equation (7b), and then Rng, Rnc1 + Rnc2 were calculated by equations (5) and (6), respectively.The energy budget equations for upper canopy layer (50–100 cm) and lower canopy layer (10–40 cm) were written from equations (8) to (10c):(8)Rnc1+Rnc2=Hc1+LEc1+Hc2+LEc2,(9a)Hc1+Hc2=H−Hg,(9b)Hc1=cpρTc1−Tarac1,(9c)Hc2=cpρTc2−Tarac2,(10a)LEc1+LEc2=LET−LEg,(10b)LEc1=cpρesatTc1−eaγrc1+rac1,(10c)LEc2=cpρesatTc2−eaγrc2+rac2,where LEc1 and LEc2 were the latent heat flux between upper and lower layer canopy and atmosphere (W m−2), respectively. Hc1 and Hc2 were the sensible heat flux between upper and lower layer canopy and atmosphere (W m−2), respectively. Tc1 was the upper layer canopy temperature (°C), Tc2 was the lower layer canopy temperature (°C), esat(Tc1) and esat(Tc2) were the saturation-specific humidity at Tc1 and Tc2 (hPa), rac1 and rac2 were aerodynamic resistances to the transfer of sensible heat between upper and lower layer canopy and atmosphere (s m−1), respectively, rc1 and rc2 were the upper and lower layer canopy resistances (s m−1), respectively.For the aerodynamic resistances, the association ofra, rag, rac1, and rac2 was expressed in the following equation:(11)1ra=1rag+1rac1+1rac2.In this study,rc1 and rc2 were calculated by stomatal resistance (gs), green leaf and yellow leaf area index in the upper rice canopy layer (a1), and green leaf and yellow leaf area index in the lower rice canopy layer (a2), as expressed in equations (12a) and (12b). Because gs was not measured in the experimental paddy field in 2014, gs developed by Oue [32] was adopted (values as shown in Table 2), as expressed in equation (13):(12a)rc1=1gsa1,(12b)rc2=1gsa2,(13)gs=msPAR+gsmax−gsmin2ns+gsmin−12ns×msPAR+gsmax−gsmin2−4msPARgsmax−gsminns1/2,where gs was the stomatal conductance (cm s−1), ms and ns were parameters, PAR was photosynthetically active radiation (μ mol m−2 s−1), gsmax was the maximum of stomatal conductance (cm s−1), and gsmin was the minimum of stomatal conductance (cm s−1).Table 2
m
s and gsmax in the gs model.
Date
Canopy layer
VPD (hPa)
m
s (cm s−1)/(μ mol m−2 s−1)
g
s
max (cm s−1)
August 6
Upper
∼18
0.00247
1.500
18∼
0.00170
0.500
Lower
∼10
0.002405
1.500
10∼15
0.002095
1.200
15∼
0.001925
0.800
August 13
Upper
∼8
0.00780
0.820
8∼
0.01246
0.410
Lower
∼8
0.009935
0.515
8∼
0.00833
0.470
August 27
Upper
∼9
0.00282
0.500
9∼
0.00195
0.400
Lower
∼10
0.003155
0.900
10∼11
0.00261
0.750
11∼
0.00213
0.450
September 4
Upper
∼16
0.003475
0.550
16∼
0.000445
0.400
Lower
∼15
0.001315
0.400
15∼16
0.00123
0.400
∼16
0.00615
0.400
Note: VPD is vapor pressure deficit,gs is the stomatal conductance (cm s−1), gsmax is the maximum of stomatal conductance (cm s−1), gsmin is the minimum of stomatal conductance (cm s−1), and ms and ns are parameters.With the calculatedrc1 and rc2, Tc1, Tc2, rac1, and rac2 were calculated by equations (8)–(10c).The net radiation input to a panicle (Rin) sums shortwave and long-wave radiation absorbed by the panicle (W m−2), as expressed in equation (14a). Ll and La were long-wave radiations from a leaf surface adjacent to the panicle and from the atmosphere (W m−2), respectively. Sd and Sf were downward direct and diffused shortwave radiations (W m−2), respectively, and θ was the solar zenith angle (°), Fp was the inclination factor of panicle, and df was the diffusivity factor for radiation. Besides, the heat balance in the panicle layer was written as equation (14b).(14a)Rin=1−0.35FpsecθSd+2dfSf+FpdfLl+La,(14b)Rin=2FpdfσTp4+H+pLEp,(15a)Ll=σTc14+Ld−σTc14exp−F1a1df,(15b)La=σTc24+σTg4−σTc24exp−F2a2df+σTc14+σTc24−σTc14exp−F1a1df,where F1 and F2 were the inclination factors of upper and lower layer rice canopy, respectively. F1, F2, and Fp were decided by fitting the calculated transmissivity of downward solar radiation (TDSR) to the measured TDSR (Figure 3).Figure 3
Vertical profiles of transmissivity of downward solar radiation (TDSR) within the rice canopy in every 10 cm in the paddy field on August 7, 2014 (a–e). (a) 8:50, (b) 10:50, (c) 12:40, (d) 14:50, and (e) 16:40.
(a)
(b)
(c)
(d)
(e)Besides,Hp and LEp were sensible and latent heat fluxes on a panicle (W m−2), which were written as follows:(16a)Hp=cpρTp−Tac1rap,(16b)LEp=cpρesatTp−eTac1γrap+rp,(17)Tc1−Tac1rc1=Tac1−Tarac1.Moreover,Tac1 was the air temperature at panicle’s height (°C) which was calculated by the transposition of equation (17) as shown in equation (18a), and likewise, eac1 was the absolute humidity at panicle’s height (hPa) calculated as expressed in equation (18b):(18a)Tac1=rac1Tc1+rc1Tarc1+rac1,(18b)eac1=rac1Tc1+rc1earc1+rac1,where rap, the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (s m−1), denoted the parameter of wind speed (Section 3.3.2), and then rp, panicle transpiration resistance (s m−1), denoted the parameter of days after the heading stage (Section 3.3.3). Lastly, Tp was calculated by combining equations from equations (14a) to (18b).The average value of measured panicle temperature from 50 cm to 100 cm was set as the measuredTp, which was compared with the Tp using the three-layer model and by IM2PACT [30] including the two-layer model.


## 2.3. Statistical Analysis of Models

The measured and calculatedTc1, Tc2, and Tp were compared by using error analysis and linear regression. Root mean squared error (RMSE), mean absolute error (MAE), and the standard deviation (SD) [33–35] were adopted to evaluate measured and calculated Tc1, Tc2, Tc, and Tp by the models.


## 2.4. Three-Layer Model Validation

We planted rice (cultivar Hinohikari) from June 21 to November 20, 2015, and rice (cultivar Nikomaru) from June 21 to November 27, 2015, in the same paddy field. PAD of two cultivars was both measured from July 9 to October 14, 2015. Other meteorological instruments were set as same as 2014. Six images were taken to getTc and Tp by infrared thermometer FLIR-i5 (FLIR systems, USA) at different heights every two or three hours during daytime.


## 3. Results and Discussion

### 3.1. General Meteorological Conditions

From July 18 to September 8, the daily average global solar radiation (St) was 262 W m−2, the average air temperature (Ta) was 25°C, while the highest Ta was 35°C on July 26, 2014. The average relative humidity (RH) was 81%, and the average wind speed (u) at 1.0 m reached 0.5 m s−1. The total precipitation, the total evapotranspiration, and the daily evapotranspiration were 670 mm, 567 mm, and 5 mm, respectively.


### 3.2. Plant Area Density (PAD)

Panicles’ height ranges from 50 cm to 100 cm, and this part of the rice plant was set as the upper canopy layer. There was no panicle on July 18, and the heading was observed on July 25 (Figure4). The average of the measured green leaf and yellow leaf area index in the upper layer rice canopy (a1) ranged from 50 cm to 100 cm, which reached its peak on August 8 (2.5) and then decreased. However, green leaf and yellow leaf area index in the lower layer rice canopy (a2) decreased from 3 on July 25 to 1.5 on August 8, 2014.Figure 4
Observed vertical profiles of plant area density (PAD) in the rice paddy field from July 18 to August 15, 2014. (a) July 18, (b) July 25, (c) August 1, (d) August 8, and (e) August 15.
(a)
(b)
(c)
(d)
(e)


### 3.3. Modeling Parameter Results

#### 3.3.1. ParametersF1, F2, and Fp

From August 5 to September 7 in the ripening stage, there was a little diurnal variation of rice morphology.F
1 was smaller than F2 because the transmissivity of solar radiation was larger in the upper layer, and the leaf area index of the upper layer canopy (a1) was also bigger than that in the lower layer (a2). For example, a1 was 2.5 and a2 was 1.5 on August 8. F1 and F2 were larger in the morning and afternoon than those at noon, respectively. This was because of the different solar radiation altitudes: in the morning and afternoon, the solar altitude was low, and the solar radiation in the upper layer was large after cutting off, and at noon, the solar radiation was the highest, and the solar radiation in the upper layer was smaller after cutting off. This was dependent on the morphology of canopy: leaves stood upright from 60 cm to 100 cm in the upper layer. In the lower layer, in the morning and afternoon, the solar radiation coming diagonally would be cut off by leaves, while at noon, the solar radiation coming from overhead would not be largely cut off, thereby leading to the smaller F1 and F2 during this period.F
p was important after the ripening stage, when the panicles hung their heads and cover the top of the canopy [36]. Fp variation was similar to that of F1 from morning to afternoon because of the similar form of panicles and leaves.F
1 and F2 were smaller than the leaf inclination factor (F) in the ripening stage published by Maruyama et al. [37]. To estimate the radiation exchange processes in the rice canopy, the hourly variation of F1, F2, and Fp should be considered for accuracy.


#### 3.3.2. Aerodynamic Resistance between the Panicle and Atmosphere (rap)

Table3 lists the aerodynamic resistance between the panicle and atmosphere (rap) and meteorological data when rp was set as 0: there was rain before, or dew was found in the morning (August 5, 7, 18, 26, and 28).Table 3
r
ap in the rice paddy field.
Date
Time
T
p (°C)
T
ac1 (°C)
u (m s−1)
r
ap (s m−1)
August 5
8:30
26.8
27.8
0.4
18.1
August 7
8:30
26.8
28.4
0.6
10.9
August 18
8:30
26.3
26.9
0.6
10.9
August 26
9:30
26.1
27.6
1.7
6.2
August 28
8:30
24.7
25.1
0.6
12.4
Note:rap is the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere, Tp is the panicle temperature, Tac1 is the air temperature at the panicle’s height, and u is the wind speed.As a result of correlation analysis between the meteorological conditions (St, Ta, RH, and u) and rap, it was found that rap was primarily affected by u with the correlation coefficient of −0.93. This is consistent with the results reported by Yan and Oue [38], which suggested that u at 2.0 m from the ground was the major factor affecting ra, rag, and rac (aerodynamic resistance between the rice canopy and atmosphere). The association between u (0.35 m s−1 < u < 1.75 m s−1) and rap on the same days is shown in Figure 5(a), as expressed below:(19)rap=6.7551u.Figure 5
Relationship between wind speed (u) and aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (rap) in the rice paddy field on August 5, 7, 18, 26, and 28, 2014 (a). Change of panicle transpiration resistance (rp) against the days after heading (DAH) in the rice paddy field on August 12, 18, 19, and 31 and September 2, 2014 (b).
(a)
(b)The friction of the panicle-atmosphere surface could be weakened by the wind speed, and the transport of heat and water vapor between panicle and atmosphere was primarily attributed to molecular diffusion.Since from August 5 to September 7, the plant height and PAD only had little difference, and the effect of the canopy structure was not considered forrap in this study.


#### 3.3.3. Panicle Resistance for Transpiration (rp)

Based on the measured averageTp from 50 cm to 100 cm and rap calculated by Eq. (19), rp can be calculated by equations (16a) and (16b). Five days under large St, high Ta and low RH conditions meaning strong transpiration (August 12, 18, 19, and 31 and September 2) were selected to analyze the influence of rp (Table 4).Table 4
r
p in the rice paddy field.
Date
Time
DAH
S
t (W m−2)
T
a (°C)
u (m s−1)
RH (%)
r
p (s m−1)
August 12
14:30
18
773
29
1.4
70
5.3
August 18
11:10
24
662
31
1.2
68
5.4
August 19
10:30
25
748
33
1.6
60
5.6
August 31
13:00
37
711
29
1.4
65
13.3
September 2
11:30
39
761
29
1.1
67
19.6
Note: DAH is days after heading,St is solar radiation, Ta is the air temperature, RH is the relative humidity, u is the wind speed, and rp is the panicle transpiration resistance.Correlations between days after heading (DAH), meteorological conditions (St, Ta, u, and RH), and rp suggest that DAH was the major influencing factor, with the correlation coefficient of 0.92. Besides, the changes of rp against the DAH in the rice paddy field are shown in Figure 5(b). rp increased asymptotically with the rise in DAH, and their relationship was expressed as follows:(20)rp=1.295exp0.0652DAH.Thus far, though there was rare information aboutrp, few researchers have measured the transpirational conductance gp (=1/rp) in rice paddy fields. Our results showed a similar variation but smaller values compared with those of cultivar “Wuxiangjing 9” reported by Oue et al. [29], in which gp decreased with the increase in DAH from 0 to 9 under both ambient CO2 and free air CO2 enrichment condition.This new useful method was presented in this study to denoterp as a parameter by DAH, while some other methods were reported. In the integrated micrometeorology model for panicle and canopy temperature (IM2PACT) developed by Yoshimoto et al. [30], gp denotes the parameter of the relative humidity in the vicinity of panicle (RHac), which was not easily and accurately measured with the ordinary ventilated psychrometers. Based on the measurements of rice varieties at the time of flowering, Fukuoka et al. [39] presented three regression equations of gp as a function of vapor pressure deficit (VPD).


### 3.4. ModelingTp

The differences betweenTc1 and Tc2 were presented by Wang et al. [40]. The average values of measured canopy temperature from 50 cm to 100 cm and from 10 cm to 40 cm were set as the measured Tc1 and Tc2, which were then compared with the modelled ones, as shown in Figures 6(a) and 6(b). The root mean square errors (RMSE) of modelled Tc1 and Tc2 were 0.76°C and 0.75°C. Besides, the difference between modelled and measured Tc1 and Tc2 ranged from −1.69°C to 1.35°C and from −1.50°C to 1.61°C, respectively. According to results of the 2-tailed t-test statistical analysis, the modelled Tc1 and Tc2 values were not significantly different from the measured values at the 0.05 probability level.Figure 6
Comparisons between the measured and modelled upper layer canopy temperature (Tc1) (a) and lower layer canopy temperature (Tc2) (b) in the rice paddy field from August 5 to September 7, 2014.
(a)
(b)In this study, we setTc = (Tc1 × a1 + Tc2 × a2)/(a1 + a2), and measured Tc was compared with that estimated by the two-layer model developed by Yan and Oue [38], as shown in Figure 7(a). RMSE of Tc by our three-layer model was 0.63°C, smaller than that by the two-layer model (1.21°C).Figure 7
Comparison ofTc by the three-layer model and the two-layer model (a) and Tp by the three-layer model and IM2PACT (b) in the rice paddy field from August 5 to September 7, 2014.
(a)
(b)As shown in Figure7(b), RMSE of Tp estimated by the three-layer model was 0.81°C, smaller than that estimated by IM2PACT (1.27°C) including the two-layer model. Better agreements between the measured and modelled Tp by the three-layer model than that by IM2PACT were obtained, particularly under high Ta conditions as shown in Table 5. This was because (1) Tc1 instead of Tc was used to predict Tp, since modelled Tc1 could be 3°C different with modelled Tc; (2) F1, F2, and Fp were determined by fitting the calculated TDSR to the measured TDSR, F1, F2, and Fp varied with time because of the different solar radiation altitudes: rather than set to be constant; and (3) rp denotes the parameter of measured Tp by DAH which considering transpiration cooling instead of the RHac.Table 5
T
p estimated by three-layer model and by IM2PACT [30].
Date
Time
S
t (W m−2)
T
a (°C)
RH (%)
T
c (°C)
T
c1 (°C)
T
p by IM2PACT (°C)
T
p by three-layer model (°C)
MeaTp (°C)
August 5
9:00
212
28
80
26.7
26.2
28.9
26.6
26.8
August 5
14:00
201
30
71
28.1
26.9
27.6
26.9
27.0
August 11
11:00
671
27
73
28.9
25.5
27.0
25.2
25.7
August 18
9:00
235
27
84
26.3
25.8
26.7
26.2
26.3
August 18
12:00
599
31
68
26.8
29.5
27.4
28.4
28.4
August 18
15:00
485
32
68
28.5
26.7
29.7
28.8
28.7
August 19
9:00
477
32
66
28.2
26.1
29.8
28.5
28.9
August 19
14:00
745
32
66
28.5
30.5
28.6
29.6
30.1
August 19
16:00
541
33
59
28.5
28.9
28.5
29.3
29.1
August 20
17:00
188
29
77
28.3
26.4
28.9
27.8
27.7
August 20
18:00
80
29
78
27.7
25.1
27.2
26.5
26.6
August 26
12:00
474
29
67
27.6
26.5
25.7
27.4
27.0
August 26
15:00
442
30
69
28.2
26.4
30.3
27.5
28.1
September 3
15:00
86
29
70
27.2
25.2
29.1
26.5
27.1
September 6
10:00
474
29
71
26.7
24.9
28.1
25.7
26.7
September 6
16:00
93
28
76
29.3
28.8
27.8
30.1
29.3
Note: Mea means measured.RMSE ofTp estimated by the three-layer model for rice (cultivar Hinohikari) was 0.93°C, and RMSE of Tp estimated by the three-layer model for rice (cultivar Hinohikari) was 0.89°C. Error analysis statistics of the comparison between measured and calculated canopy and panicle temperatures by models is shown in Table 6.Table 6
Error analysis statistics of the comparison between measured and calculated canopy and panicle temperatures by models.
Temperature
RMSE (°C)
MAE (°C)
SD (°C)
T
c estimated by three-layer model
0.73
0.81
0.64
T
c estimated by two-layer model
1.21
1.56
1.25
T
c1 estimated by three-layer model
0.76
0.75
0.74
T
c2 estimated by three-layer model
0.75
0.63
0.98
T
p estimated by three-layer model
0.81
0.7
0.67
T
p estimated by IM2PCT
1.27
0.95
0.76
Note:Tc is the canopy temperature (°C); two-layer model is developed by Yan and Oue [38]; Tc1 and Tc2 are the upper and lower layer canopy temperatures, respectively; Tp is the panicle temperature (°C); IM2PACT is integrated micrometeorology model for panicle and canopy temperature developed by Yoshimoto et al. [30]; RMSE is the root mean square error, MAE is the mean absolute error, and SD is the standard deviation.


## 3.1. General Meteorological Conditions

From July 18 to September 8, the daily average global solar radiation (St) was 262 W m−2, the average air temperature (Ta) was 25°C, while the highest Ta was 35°C on July 26, 2014. The average relative humidity (RH) was 81%, and the average wind speed (u) at 1.0 m reached 0.5 m s−1. The total precipitation, the total evapotranspiration, and the daily evapotranspiration were 670 mm, 567 mm, and 5 mm, respectively.


## 3.2. Plant Area Density (PAD)

Panicles’ height ranges from 50 cm to 100 cm, and this part of the rice plant was set as the upper canopy layer. There was no panicle on July 18, and the heading was observed on July 25 (Figure4). The average of the measured green leaf and yellow leaf area index in the upper layer rice canopy (a1) ranged from 50 cm to 100 cm, which reached its peak on August 8 (2.5) and then decreased. However, green leaf and yellow leaf area index in the lower layer rice canopy (a2) decreased from 3 on July 25 to 1.5 on August 8, 2014.Figure 4
Observed vertical profiles of plant area density (PAD) in the rice paddy field from July 18 to August 15, 2014. (a) July 18, (b) July 25, (c) August 1, (d) August 8, and (e) August 15.
(a)
(b)
(c)
(d)
(e)


## 3.3. Modeling Parameter Results

### 3.3.1. ParametersF1, F2, and Fp

From August 5 to September 7 in the ripening stage, there was a little diurnal variation of rice morphology.F
1 was smaller than F2 because the transmissivity of solar radiation was larger in the upper layer, and the leaf area index of the upper layer canopy (a1) was also bigger than that in the lower layer (a2). For example, a1 was 2.5 and a2 was 1.5 on August 8. F1 and F2 were larger in the morning and afternoon than those at noon, respectively. This was because of the different solar radiation altitudes: in the morning and afternoon, the solar altitude was low, and the solar radiation in the upper layer was large after cutting off, and at noon, the solar radiation was the highest, and the solar radiation in the upper layer was smaller after cutting off. This was dependent on the morphology of canopy: leaves stood upright from 60 cm to 100 cm in the upper layer. In the lower layer, in the morning and afternoon, the solar radiation coming diagonally would be cut off by leaves, while at noon, the solar radiation coming from overhead would not be largely cut off, thereby leading to the smaller F1 and F2 during this period.F
p was important after the ripening stage, when the panicles hung their heads and cover the top of the canopy [36]. Fp variation was similar to that of F1 from morning to afternoon because of the similar form of panicles and leaves.F
1 and F2 were smaller than the leaf inclination factor (F) in the ripening stage published by Maruyama et al. [37]. To estimate the radiation exchange processes in the rice canopy, the hourly variation of F1, F2, and Fp should be considered for accuracy.


### 3.3.2. Aerodynamic Resistance between the Panicle and Atmosphere (rap)

Table3 lists the aerodynamic resistance between the panicle and atmosphere (rap) and meteorological data when rp was set as 0: there was rain before, or dew was found in the morning (August 5, 7, 18, 26, and 28).Table 3
r
ap in the rice paddy field.
Date
Time
T
p (°C)
T
ac1 (°C)
u (m s−1)
r
ap (s m−1)
August 5
8:30
26.8
27.8
0.4
18.1
August 7
8:30
26.8
28.4
0.6
10.9
August 18
8:30
26.3
26.9
0.6
10.9
August 26
9:30
26.1
27.6
1.7
6.2
August 28
8:30
24.7
25.1
0.6
12.4
Note:rap is the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere, Tp is the panicle temperature, Tac1 is the air temperature at the panicle’s height, and u is the wind speed.As a result of correlation analysis between the meteorological conditions (St, Ta, RH, and u) and rap, it was found that rap was primarily affected by u with the correlation coefficient of −0.93. This is consistent with the results reported by Yan and Oue [38], which suggested that u at 2.0 m from the ground was the major factor affecting ra, rag, and rac (aerodynamic resistance between the rice canopy and atmosphere). The association between u (0.35 m s−1 < u < 1.75 m s−1) and rap on the same days is shown in Figure 5(a), as expressed below:(19)rap=6.7551u.Figure 5
Relationship between wind speed (u) and aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (rap) in the rice paddy field on August 5, 7, 18, 26, and 28, 2014 (a). Change of panicle transpiration resistance (rp) against the days after heading (DAH) in the rice paddy field on August 12, 18, 19, and 31 and September 2, 2014 (b).
(a)
(b)The friction of the panicle-atmosphere surface could be weakened by the wind speed, and the transport of heat and water vapor between panicle and atmosphere was primarily attributed to molecular diffusion.Since from August 5 to September 7, the plant height and PAD only had little difference, and the effect of the canopy structure was not considered forrap in this study.


### 3.3.3. Panicle Resistance for Transpiration (rp)

Based on the measured averageTp from 50 cm to 100 cm and rap calculated by Eq. (19), rp can be calculated by equations (16a) and (16b). Five days under large St, high Ta and low RH conditions meaning strong transpiration (August 12, 18, 19, and 31 and September 2) were selected to analyze the influence of rp (Table 4).Table 4
r
p in the rice paddy field.
Date
Time
DAH
S
t (W m−2)
T
a (°C)
u (m s−1)
RH (%)
r
p (s m−1)
August 12
14:30
18
773
29
1.4
70
5.3
August 18
11:10
24
662
31
1.2
68
5.4
August 19
10:30
25
748
33
1.6
60
5.6
August 31
13:00
37
711
29
1.4
65
13.3
September 2
11:30
39
761
29
1.1
67
19.6
Note: DAH is days after heading,St is solar radiation, Ta is the air temperature, RH is the relative humidity, u is the wind speed, and rp is the panicle transpiration resistance.Correlations between days after heading (DAH), meteorological conditions (St, Ta, u, and RH), and rp suggest that DAH was the major influencing factor, with the correlation coefficient of 0.92. Besides, the changes of rp against the DAH in the rice paddy field are shown in Figure 5(b). rp increased asymptotically with the rise in DAH, and their relationship was expressed as follows:(20)rp=1.295exp0.0652DAH.Thus far, though there was rare information aboutrp, few researchers have measured the transpirational conductance gp (=1/rp) in rice paddy fields. Our results showed a similar variation but smaller values compared with those of cultivar “Wuxiangjing 9” reported by Oue et al. [29], in which gp decreased with the increase in DAH from 0 to 9 under both ambient CO2 and free air CO2 enrichment condition.This new useful method was presented in this study to denoterp as a parameter by DAH, while some other methods were reported. In the integrated micrometeorology model for panicle and canopy temperature (IM2PACT) developed by Yoshimoto et al. [30], gp denotes the parameter of the relative humidity in the vicinity of panicle (RHac), which was not easily and accurately measured with the ordinary ventilated psychrometers. Based on the measurements of rice varieties at the time of flowering, Fukuoka et al. [39] presented three regression equations of gp as a function of vapor pressure deficit (VPD).


## 3.3.1. ParametersF1, F2, and Fp

From August 5 to September 7 in the ripening stage, there was a little diurnal variation of rice morphology.F
1 was smaller than F2 because the transmissivity of solar radiation was larger in the upper layer, and the leaf area index of the upper layer canopy (a1) was also bigger than that in the lower layer (a2). For example, a1 was 2.5 and a2 was 1.5 on August 8. F1 and F2 were larger in the morning and afternoon than those at noon, respectively. This was because of the different solar radiation altitudes: in the morning and afternoon, the solar altitude was low, and the solar radiation in the upper layer was large after cutting off, and at noon, the solar radiation was the highest, and the solar radiation in the upper layer was smaller after cutting off. This was dependent on the morphology of canopy: leaves stood upright from 60 cm to 100 cm in the upper layer. In the lower layer, in the morning and afternoon, the solar radiation coming diagonally would be cut off by leaves, while at noon, the solar radiation coming from overhead would not be largely cut off, thereby leading to the smaller F1 and F2 during this period.F
p was important after the ripening stage, when the panicles hung their heads and cover the top of the canopy [36]. Fp variation was similar to that of F1 from morning to afternoon because of the similar form of panicles and leaves.F
1 and F2 were smaller than the leaf inclination factor (F) in the ripening stage published by Maruyama et al. [37]. To estimate the radiation exchange processes in the rice canopy, the hourly variation of F1, F2, and Fp should be considered for accuracy.


## 3.3.2. Aerodynamic Resistance between the Panicle and Atmosphere (rap)

Table3 lists the aerodynamic resistance between the panicle and atmosphere (rap) and meteorological data when rp was set as 0: there was rain before, or dew was found in the morning (August 5, 7, 18, 26, and 28).Table 3
r
ap in the rice paddy field.
Date
Time
T
p (°C)
T
ac1 (°C)
u (m s−1)
r
ap (s m−1)
August 5
8:30
26.8
27.8
0.4
18.1
August 7
8:30
26.8
28.4
0.6
10.9
August 18
8:30
26.3
26.9
0.6
10.9
August 26
9:30
26.1
27.6
1.7
6.2
August 28
8:30
24.7
25.1
0.6
12.4
Note:rap is the aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere, Tp is the panicle temperature, Tac1 is the air temperature at the panicle’s height, and u is the wind speed.As a result of correlation analysis between the meteorological conditions (St, Ta, RH, and u) and rap, it was found that rap was primarily affected by u with the correlation coefficient of −0.93. This is consistent with the results reported by Yan and Oue [38], which suggested that u at 2.0 m from the ground was the major factor affecting ra, rag, and rac (aerodynamic resistance between the rice canopy and atmosphere). The association between u (0.35 m s−1 < u < 1.75 m s−1) and rap on the same days is shown in Figure 5(a), as expressed below:(19)rap=6.7551u.Figure 5
Relationship between wind speed (u) and aerodynamic resistance to the transfer of sensible heat between panicle and atmosphere (rap) in the rice paddy field on August 5, 7, 18, 26, and 28, 2014 (a). Change of panicle transpiration resistance (rp) against the days after heading (DAH) in the rice paddy field on August 12, 18, 19, and 31 and September 2, 2014 (b).
(a)
(b)The friction of the panicle-atmosphere surface could be weakened by the wind speed, and the transport of heat and water vapor between panicle and atmosphere was primarily attributed to molecular diffusion.Since from August 5 to September 7, the plant height and PAD only had little difference, and the effect of the canopy structure was not considered forrap in this study.


## 3.3.3. Panicle Resistance for Transpiration (rp)

Based on the measured averageTp from 50 cm to 100 cm and rap calculated by Eq. (19), rp can be calculated by equations (16a) and (16b). Five days under large St, high Ta and low RH conditions meaning strong transpiration (August 12, 18, 19, and 31 and September 2) were selected to analyze the influence of rp (Table 4).Table 4
r
p in the rice paddy field.
Date
Time
DAH
S
t (W m−2)
T
a (°C)
u (m s−1)
RH (%)
r
p (s m−1)
August 12
14:30
18
773
29
1.4
70
5.3
August 18
11:10
24
662
31
1.2
68
5.4
August 19
10:30
25
748
33
1.6
60
5.6
August 31
13:00
37
711
29
1.4
65
13.3
September 2
11:30
39
761
29
1.1
67
19.6
Note: DAH is days after heading,St is solar radiation, Ta is the air temperature, RH is the relative humidity, u is the wind speed, and rp is the panicle transpiration resistance.Correlations between days after heading (DAH), meteorological conditions (St, Ta, u, and RH), and rp suggest that DAH was the major influencing factor, with the correlation coefficient of 0.92. Besides, the changes of rp against the DAH in the rice paddy field are shown in Figure 5(b). rp increased asymptotically with the rise in DAH, and their relationship was expressed as follows:(20)rp=1.295exp0.0652DAH.Thus far, though there was rare information aboutrp, few researchers have measured the transpirational conductance gp (=1/rp) in rice paddy fields. Our results showed a similar variation but smaller values compared with those of cultivar “Wuxiangjing 9” reported by Oue et al. [29], in which gp decreased with the increase in DAH from 0 to 9 under both ambient CO2 and free air CO2 enrichment condition.This new useful method was presented in this study to denoterp as a parameter by DAH, while some other methods were reported. In the integrated micrometeorology model for panicle and canopy temperature (IM2PACT) developed by Yoshimoto et al. [30], gp denotes the parameter of the relative humidity in the vicinity of panicle (RHac), which was not easily and accurately measured with the ordinary ventilated psychrometers. Based on the measurements of rice varieties at the time of flowering, Fukuoka et al. [39] presented three regression equations of gp as a function of vapor pressure deficit (VPD).


## 3.4. ModelingTp

The differences betweenTc1 and Tc2 were presented by Wang et al. [40]. The average values of measured canopy temperature from 50 cm to 100 cm and from 10 cm to 40 cm were set as the measured Tc1 and Tc2, which were then compared with the modelled ones, as shown in Figures 6(a) and 6(b). The root mean square errors (RMSE) of modelled Tc1 and Tc2 were 0.76°C and 0.75°C. Besides, the difference between modelled and measured Tc1 and Tc2 ranged from −1.69°C to 1.35°C and from −1.50°C to 1.61°C, respectively. According to results of the 2-tailed t-test statistical analysis, the modelled Tc1 and Tc2 values were not significantly different from the measured values at the 0.05 probability level.Figure 6
Comparisons between the measured and modelled upper layer canopy temperature (Tc1) (a) and lower layer canopy temperature (Tc2) (b) in the rice paddy field from August 5 to September 7, 2014.
(a)
(b)In this study, we setTc = (Tc1 × a1 + Tc2 × a2)/(a1 + a2), and measured Tc was compared with that estimated by the two-layer model developed by Yan and Oue [38], as shown in Figure 7(a). RMSE of Tc by our three-layer model was 0.63°C, smaller than that by the two-layer model (1.21°C).Figure 7
Comparison ofTc by the three-layer model and the two-layer model (a) and Tp by the three-layer model and IM2PACT (b) in the rice paddy field from August 5 to September 7, 2014.
(a)
(b)As shown in Figure7(b), RMSE of Tp estimated by the three-layer model was 0.81°C, smaller than that estimated by IM2PACT (1.27°C) including the two-layer model. Better agreements between the measured and modelled Tp by the three-layer model than that by IM2PACT were obtained, particularly under high Ta conditions as shown in Table 5. This was because (1) Tc1 instead of Tc was used to predict Tp, since modelled Tc1 could be 3°C different with modelled Tc; (2) F1, F2, and Fp were determined by fitting the calculated TDSR to the measured TDSR, F1, F2, and Fp varied with time because of the different solar radiation altitudes: rather than set to be constant; and (3) rp denotes the parameter of measured Tp by DAH which considering transpiration cooling instead of the RHac.Table 5
T
p estimated by three-layer model and by IM2PACT [30].
Date
Time
S
t (W m−2)
T
a (°C)
RH (%)
T
c (°C)
T
c1 (°C)
T
p by IM2PACT (°C)
T
p by three-layer model (°C)
MeaTp (°C)
August 5
9:00
212
28
80
26.7
26.2
28.9
26.6
26.8
August 5
14:00
201
30
71
28.1
26.9
27.6
26.9
27.0
August 11
11:00
671
27
73
28.9
25.5
27.0
25.2
25.7
August 18
9:00
235
27
84
26.3
25.8
26.7
26.2
26.3
August 18
12:00
599
31
68
26.8
29.5
27.4
28.4
28.4
August 18
15:00
485
32
68
28.5
26.7
29.7
28.8
28.7
August 19
9:00
477
32
66
28.2
26.1
29.8
28.5
28.9
August 19
14:00
745
32
66
28.5
30.5
28.6
29.6
30.1
August 19
16:00
541
33
59
28.5
28.9
28.5
29.3
29.1
August 20
17:00
188
29
77
28.3
26.4
28.9
27.8
27.7
August 20
18:00
80
29
78
27.7
25.1
27.2
26.5
26.6
August 26
12:00
474
29
67
27.6
26.5
25.7
27.4
27.0
August 26
15:00
442
30
69
28.2
26.4
30.3
27.5
28.1
September 3
15:00
86
29
70
27.2
25.2
29.1
26.5
27.1
September 6
10:00
474
29
71
26.7
24.9
28.1
25.7
26.7
September 6
16:00
93
28
76
29.3
28.8
27.8
30.1
29.3
Note: Mea means measured.RMSE ofTp estimated by the three-layer model for rice (cultivar Hinohikari) was 0.93°C, and RMSE of Tp estimated by the three-layer model for rice (cultivar Hinohikari) was 0.89°C. Error analysis statistics of the comparison between measured and calculated canopy and panicle temperatures by models is shown in Table 6.Table 6
Error analysis statistics of the comparison between measured and calculated canopy and panicle temperatures by models.
Temperature
RMSE (°C)
MAE (°C)
SD (°C)
T
c estimated by three-layer model
0.73
0.81
0.64
T
c estimated by two-layer model
1.21
1.56
1.25
T
c1 estimated by three-layer model
0.76
0.75
0.74
T
c2 estimated by three-layer model
0.75
0.63
0.98
T
p estimated by three-layer model
0.81
0.7
0.67
T
p estimated by IM2PCT
1.27
0.95
0.76
Note:Tc is the canopy temperature (°C); two-layer model is developed by Yan and Oue [38]; Tc1 and Tc2 are the upper and lower layer canopy temperatures, respectively; Tp is the panicle temperature (°C); IM2PACT is integrated micrometeorology model for panicle and canopy temperature developed by Yoshimoto et al. [30]; RMSE is the root mean square error, MAE is the mean absolute error, and SD is the standard deviation.


## 4. Conclusions

Rice panicle temperature (Tp) is a key factor for studying high temperature impacts on spikelet sterility. Comparing with measuring Tp by hand, a Tp simulation model could obtain Tp data readily. We developed the three-layer model to estimate Tp and compared the performance to estimate Tc by three-layer model and Tc by two-layer model developed by Yan and Oue [38]; and to compare the performance to estimate Tp by three-layer model and Tp by IM2PACT [30]. RMSE of Tc by our three-layer model was 0.63°C, smaller than that by the two-layer model (1.21°C). RMSE of Tp estimated by the three-layer model was 0.81°C, smaller than that estimated by IM2PACT (1.27°C).However, from July 9 to September 8, 2014, there was 29 rainy days, on whichTc1, Tc2, and Tp measurement could not be performed, thereby leading to the reduction of measured data. The highest Ta was 34.64°C on July 26, 2014, and Tc1 and Tp higher than 35.0°C could not be observed, so our model was not used for extreme temperature. Furthermore, the three-layer model simulated fairly well the Tc1, Tc2, and Tp with root mean square errors of 0.76°C, 0.75°C, and 0.81°C, and it was validated well by two other rice cultivars, and thus, it demonstrated that the three-layer model was a new feasible way to estimate Tp. In the future, we will measure stomatal resistance (gs) in the rice paddy field and analyze the microclimate observational results in the elevated carbon dioxide concentration experiments [41] with different land use [42] to predict Tp.



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*Source: 6468909-2020-03-20.xml*