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Modeling

Modeling the Effects of Water Temperature on Rice Growth and Yield under a Cool Climate

I. Model Development

^a Faculty of Agriculture, Iwate University, 3-18-8 Ueda, Iwate, 020-8550, Japan
^b Department of Global Resources, National Institute for Agro-Environmental Sciences, 3-1-1 Kannondai, Tsukuba, 305-8604, Japan
^c Graduate School of Agriculture, Hokkaido University, N9, W9, Kita-ku, Sapporo, 060-8589, Japan

^* Corresponding author (shimn{at}iwate-u.ac.jp)

	ABSTRACT

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION DISCUSSION CONCLUSION REFERENCES

 
For paddy rice (Oryza sativa L.), water temperature (T_w) is a major determinant of growth and yield. In rice paddies, T_w is higher than the air temperature (T_a), and this difference significantly affects production, especially in cool climates. However, there is no model to evaluate the effects of T_w on rice yield. To simulate temporal and regional differences in rice productivity under such climates, we developed a simple mechanistic growth model that accounts for the effects of T_w based on the results of previous field trials. The rate of crop ontogenetic change was linearly related with T_w before the heading stage. Leaf area was expressed as a function of leaf emergence and tillering, and leaf senescence was expressed as function of ontogenetic change and spikelet fertility. Radiation use efficiency was less affected by T_w than by leaf area, and its change with respect to ontogenetic changes was expressed using nonlinear functions. Spikelet fertility, which strongly determines grain yield, was expressed as function of cumulative cooling degree-days (below a threshold temperature), water depth, and the height of developing panicles. This model covered the major processes that are affected by T_w, and can be used for evaluating the role of T_w on rice growth and yield under a cool climate.

Abbreviations: DAT, days after transplanting • DVI, developmental index • DVR, developmental rate • HU_t, heat units for tiller number • LAI, leaf area index • LN, leaf number on the main culm • RPW, ratio of panicle weight to total biomass • RTN, relative tiller number • RUE, radiation use efficiency • T_w, water temperature • T_a, air temperature • TLNI, total leaf number index

Received for publication November 25, 2006.

Modeling the Effects of Water Temperature on Rice Growth and Yield under a Cool Climate

I. Model Development

^a Faculty of Agriculture, Iwate University, 3-18-8 Ueda, Iwate, 020-8550, Japan
^b Department of Global Resources, National Institute for Agro-Environmental Sciences, 3-1-1 Kannondai, Tsukuba, 305-8604, Japan
^c Graduate School of Agriculture, Hokkaido University, N9, W9, Kita-ku, Sapporo, 060-8589, Japan

^* Corresponding author (shimn{at}iwate-u.ac.jp)

Received for publication November 25, 2006.
For paddy rice (Oryza sativa L.), water temperature (T_w) is a major determinant of growth and yield. In rice paddies, T_w is higher than the air temperature (T_a), and this difference significantly affects production, especially in cool climates. However, there is no model to evaluate the effects of T_w on rice yield. To simulate temporal and regional differences in rice productivity under such climates, we developed a simple mechanistic growth model that accounts for the effects of T_w based on the results of previous field trials. The rate of crop ontogenetic change was linearly related with T_w before the heading stage. Leaf area was expressed as a function of leaf emergence and tillering, and leaf senescence was expressed as function of ontogenetic change and spikelet fertility. Radiation use efficiency was less affected by T_w than by leaf area, and its change with respect to ontogenetic changes was expressed using nonlinear functions. Spikelet fertility, which strongly determines grain yield, was expressed as function of cumulative cooling degree-days (below a threshold temperature), water depth, and the height of developing panicles. This model covered the major processes that are affected by T_w, and can be used for evaluating the role of T_w on rice growth and yield under a cool climate.

Abbreviations: DAT, days after transplanting • DVI, developmental index • DVR, developmental rate • HU_t, heat units for tiller number • LAI, leaf area index • LN, leaf number on the main culm • RPW, ratio of panicle weight to total biomass • RTN, relative tiller number • RUE, radiation use efficiency • T_w, water temperature • T_a, air temperature • TLNI, total leaf number index

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION DISCUSSION CONCLUSION REFERENCES

 
RICE IS A MAJOR CROP around the world, with 0.6 billion Mg produced annually (IRRI, 2002), most of which is cultivated under irrigated conditions. Irrigated areas account for about half of the harvested area of rice, but contribute three-quarters of global rice production (IRRI, 2002). Yield under irrigated conditions especially under flooding condition is higher than under nonirrigated conditions because flooding provides enough water to prevent constraints on leaf transpiration as well as different temperature environments (vertical stratification) above and below the water surface. In paddies, the temperature of the flood water (T_w) is generally higher than the T_a as a result of solar heating. Tanaka (1962) monitored T_a and T_w in paddy fields at Aomori (40°49' N), in northern Japan, and showed that the maximum and minimum T_w were higher than T_a by as much as 10 and 5°C, respectively. The resulting large difference between T_w and T_a plays an important role in maintaining productivity under flooded conditions, particularly under a cool climate where low temperatures may limit growth.

Although T_a affects leaf temperatures (i.e., the site of photosynthesis above the water surface), T_w affects the temperature of the shoot base, where the shoot meristem is found, and the temperature of the rooting zone, both of which lie below the water. Matsushima et al. (1964) performed a factorial experiment on rice plants with combinations of T_w and T_a ranging from 16 to 36°C and showed that T_w is more influential than T_a in determining yield before the mid-reproductive growth stage. Takamura et al. (1960) also found that T_w was relatively more important than T_a in terms of leaf emergence during the tillering stage. These results suggest that T_w is more influential than T_a. In actual rice cultivation, water management is the most important practice to prevent yield losses under unusually low temperatures (Sakai, 1949; Satake et al., 1988), since deep flooding (deeper than 15 cm) will keep panicles warm for longer than in shallow water. Toriyama and Inoue (1984) analyzed the site-to-site differences in yield loss in northern Japan during a year with a cool summer, and observed that, under similar T_a conditions, differences in T_w were a main cause of the differences among sites. In addition, Sameshima (2004) measured the developmental stage of field-grown rice over several years in northern Japan, and showed that differences among years in the developmental stage at a given date could not be explained well by T_a because the relationship between T_w and T_a differed among years due to the difference in solar radiation. Thus, to understand the causes of regional and temporal yield variations under a cool climate, the effects of T_w and T_a must be evaluated separately.

The effects of T_w on yield result from the integration of various physiological responses. Low T_w, particularly during vegetative growth, slowed the emergence of new leaves and of tillering, and decreased leaf expansion, resulting in decreased canopy interception of radiation and decreased dry matter production (Shimazaki et al., 1963; Shimono et al., 2002). Low T_w during reproductive growth also limited pollen development and decreased fertility, resulting in a decrease in the harvest index (Satake et al., 1988; Shimono et al., 2002). Process-based growth models are a powerful tool for synthesizing and quantifying growth and yield responses. A number of researchers have attempted to model the effects of T_a on rice growth and yield (Iwaki, 1975; Horie, 1987; Kropff et al., 1995; Hasegawa and Horie, 1997), with varying degrees of success, but there have been no attempts to model the effects of T_w separately from those of T_a. A T_w–based model may be able to highlight the effects of the T_w – T_a difference on rice productivity and identify the cause of yield differences among sites under a cool climate. Moreover, the model may help to more accurately predict the effects of future global warming on rice production. Mean T_a is predicted to increase by 3°C in average (range 1–6°C) from the current level by the end of this century as a result of increased atmospheric concentrations of greenhouse-effect gases (IPCC, 2002). Previous predictions of the effect of greenhouse warming on rice yield have used T_a–based growth models (Horie et al., 1995; Kropff et al., 1995). But, given the differences between T_a and T_w in paddy fields, particularly under cool climates, and given the importance of T_w that has been reported in the literature, research is necessary to determine whether a T_w–based model would provide superior results.

The objective of the present series studies was thus to evaluate the impact of T_w on rice production under the cool climate of Hokkaido, the northernmost island of Japan, located from 41.3 to 45.5°N and the coolest rice-producing area in the world, under current and future climates. For that purpose, in this paper we determined the appropriate functions in the responses of rice plants to T_w in the various processes described below, determined these functions and developed a dynamic rice growth model for evaluating the effects of T_w on growth and yield, and tested the model using independent data sets not used for model development.

	MODEL DESCRIPTION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION DISCUSSION CONCLUSION REFERENCES

 
Overview
The model described in this paper accounts for the following effects of T_w. First, T_w principally determines the rate of crop ontogenetic change before the heading stage (i.e., while shoot meristem of the rice plant is below the surface of the water), and this rate ultimately determines the growth duration. A quantitative expression of the crop's developmental stage is also important to allow for the age-dependent changes in plant growth parameters such as partitioning of dry matter. The T_w is also a major determinant of tillering and leaf emergence rates, both of which strongly affect the development of leaf area and ultimately of radiation capture by the canopy. Therefore, in modeling leaf area and canopy radiation capture, the effects of T_w on tillering and leaf emergence are taken into consideration.

Conversion of light energy into dry matter involves physiological processes such as photosynthesis and respiration. However, radiation use efficiency (RUE), which is defined as the quantity of dry matter accumulated per unit of intercepted radiation, was found to be relatively unaffected by T_w, even though RUE changed with developmental stage (Shimono et al., 2002). By determining the time-course of RUE throughout the crop growth period, dry matter accumulation under variable levels of T_w can be simply expressed using canopy radiation capture and RUE, as has been done in many other simplified process models (e.g., Horie, 1987; Muchow et al., 1990; Amir and Sinclair, 1991; Hammer et al., 1995).

Grain yield can be estimated from dry matter accumulation and its partitioning to the panicles. Dry matter partitioning to panicles is dramatically influenced by spikelet fertility, which is sensitive to the thermal conditions under which the panicles develop. Because the developing panicles are initially submerged, and then emerge from the water surface as the stem elongates, both T_w and T_a affect spikelet fertility (Enomoto, 1936; Sakai, 1949; Tanaka, 1962; Matsushima et al., 1964; Tsunoda, 1964; Satake et al., 1988). A model describing these effects, developed in a previous study (Shimono et al., 2005), incorporates the effects of both T_w and T_a on spikelet fertility.

Database
Model development and testing required T_w data as an input. In total, we used 24 data sets obtained from a 4-yr field experiment (1996–1999) involving cool irrigation treatments that imposed different levels of T_w on rice plants at different growth stages. The T_w gradient was produced by the distance from the cold water source using solar heating. The study was conducted at Hokkaido University, Sapporo, Japan (43°04' N, 141°20' E), and was described by Shimono et al. (2002). In addition to temperature data, each data set included the dates of panicle initiation and heading, dry weight of each organ without roots (leaf, leaf sheath plus stem, panicle), stem number, leaf number on the main stem, spikelet fertility, and grain yield. Of these 24 data sets, five were randomly selected from each T_w treatment and used to independently test the accuracy of prediction, and the remaining 19 data sets were used for model development.

The following management practices and T_w treatments were used. Seedlings of ‘Kirara 397’, the most common cold-climate cultivar in this part of Japan, were transplanted into a paddy field in late May. All treatment areas received equal amounts of basal fertilizer (a single application of N = 9.6 g m^–2, P = 4.2 g m^–2, and K = 6.0 g m^–2), which was incorporated into the plow layer before flooding. The T_w treatments were applied during three growth periods in each year: vegetative growth (16–21 days after transplanting [DAT] to panicle initiation), reproductive growth (from panicle initiation to full heading), and early grain-filling (0–20 d after full heading). Three levels of T_w (low, middle, and high) were established for each growth stage, and the difference in T_w between the low- and high-temperature treatments ranged from 3.6 to 6.7°C, versus a range of 2.6 to 5.3°C between the middle- and high-temperature treatments. The treatments are denoted as follows: High, a control without a cool T_w treatment; Low-Vegetative and Middle-Vegetative, low and middle T_w treatments during the vegetative growth period, respectively; Low-Reproductive and Middle-Reproductive, low and middle T_w treatments during the reproductive growth period, respectively; and Low-Grain Filling and Middle-Grain Filling, low and middle T_w treatments during the early grain-filling period, respectively. Additionally, water at the middle T_w was applied continuously to a plot during all three growth periods; this treatment was designated as Middle-Continuous.

Parameterization of the Growth Model
Developmental Stage
Rice development is markedly delayed by low temperatures. To determine the effects of T_w on the rate of crop ontogenetic change, we examined the relationship between T_w and the average developmental rate (DVR) (Horie and Nakagawa, 1990), which is defined as the reciprocal of the growth duration (i.e., 1/growth duration, d^–1) for the vegetative growth period (from transplanting to panicle initiation, Eq. [1]) and the reproductive growth period (from panicle initiation to heading, Eq. [2]). Field data showed that the average DVR was linearly correlated with T_w values ranging from 18 to 22°C during the vegetative growth period and ranging from 17 to 25°C during the reproductive growth period; in contrast, no significant relation between DVR and T_a was observed during either growth period (Fig. 1 ). This indicates that T_w is the major determinant of DVR before heading and that T_a plays only a minor role. From heading to maturity, T_a was used to determine the rate of development because panicles were fully exposed to air during this period. The following formulas were used to express the effects of temperature on DVR.

View larger version (26K): [in this window] [in a new window]   Fig. 1. Relationships between developmental rate (DVR) and air temperature and water temperature (Tw) from transplanting (TP) to panicle initiation (PI) and from PI to heading (HD) for ‘Kirara 397’ rice from 1997 to 1999. *** P < 0.001; * P < 0.05; ns, not significant.

[1]

From panicle initiation to heading:

[2]

From heading to maturity:

[3]

In addition, a developmental index (DVI) is defined:

[4]

where T_bv and T_br are the base temperatures below which rice ontogenetic change stops (°C), and HU_v, HU_r, and HU_g are heat units representing the accumulated temperatures required for completion of each growth period (°C d). From the relationships given in Fig. 1, the estimated parameter values were T_bv = 10.0°C, T_br = 2.84°C, HU_v = 805°C d, and HU_r = 568°C d. The number of heat units for the grain-filling stage (HU_g) was set to 1000°C d after Terashima (2002). The DVI(t) and DVR_i are the developmental indices at the ith DAT and the developmental rate at the ith DAT, respectively. The DVI is defined as 0 at seedling emergence, 1 at panicle initiation, 2 at heading, and 3 at maturity as done by Nakagawa and Horie (1995), and is calculated on a daily basis. The DVI at transplanting (DVI_tp) was calculated by dividing the number of leaves on the main culm at transplanting by the number at panicle initiation, and assuming that the number of leaves increased linearly with increasing developmental stage before panicle initiation (Goto and Hoshikawa, 1988).

Leaf Number, Tiller Number, and Leaf Area Development
Leaf number and tiller number (including the main culm) are the major determinants of leaf area development. Several methods have been proposed for modeling the effects of temperature on the leaf area dynamics of rice (Iwaki, 1975; Horie, 1987; Kropff et al., 1995; Hasegawa and Horie, 1997), but none have accounted for the components of leaf growth such as increased numbers of leaves and tillers.

Leaf number on the main culm (LN) on a given day varied with respect to T_w during the vegetative and reproductive growth periods (Fig. 2a ). The rate of leaf emergence decreased at lower T_w during the vegetative growth period (from 16–21 to 34–47 DAT), but the final leaf number was similar in all treatments. Low T_w during the reproductive growth period (from 34–42 to 69–74 DAT) also lowered the rate of leaf emergence. However, the number of leaves at the same DVI was scarcely influenced by T_w (Fig. 2b), and the relationship between the two parameters was well expressed by the following logistic function of DVI:

[5]

where LN_max is the maximum leaf number on the main culm, and a and b are regression parameters that determine the relationship between LN and DVI (LN_max = 12.2, a = 2.11 and b = 3.46).

View larger version (28K): [in this window] [in a new window]   Fig. 2. (a, b) Number of leaves on the main culm (LN) of rice grown under different water temperatures, and (c, d) relative tiller number (RTN, the ratio of the number of tillers to the initial number at transplanting) from 1997 to 1999. DAT, days after transplanting; DVI, developmental index; Tw, water temperature; HUt, heat units for tiller number (HUt = sum [Tw – 15]). *** P < 0.001; ** P < 0.01.

[6]

where t_s and t_i are regression parameters (t_s = 4.45, t_i = –18.3).

The increase in leaf area index (LAI) was strongly influenced by LN and the tiller number per unit area (TN) during the vegetative growth period, but only by LN during the reproductive growth period. To quantify the relationship between LN, TN, and LAI, we defined the total leaf number index (TLNI) as follows:

[7]

[8]

where TN_PI is the tiller number at panicle initiation.

With increasing TLNI, LAI increased exponentially during the vegetative growth period and linearly during the reproductive growth period (Fig. 3 ). The following equations expressed the change in LAI well under different T_w:

[9]

[10]

where L_a, L_b, and L_c are regression parameters (L_a = 0.0000269, L_b = 1.25, L_c = 0.00185), and LAI_PI is LAI at panicle initiation. The increase in LAI during the reproductive growth period was assumed to terminate when the flag leaf had fully developed (DVI 1.6) (Shimono et al., 2001).

View larger version (15K): [in this window] [in a new window]   Fig. 3. Relationship between leaf area index (LAI) and total leaf number index (TLNI) of rice grown under different water temperatures during vegetative growth, and the relationship between LAI increase (LAI) and increase in the total leaf number index (TLNI) from panicle initiation for rice grown under different water temperature conditions during reproductive growth from 1997 to 1999. *** P < 0.001.

[11]

where LDW is leaf dry weight (g m^–2), and SLA is the specific leaf area (cm² g^–1) using the fixed values estimated at full heading stage (DVI = 2.1). The LDW was calculated from the dry matter partitioning described below; plants of lower fertility had higher LDW compared with plants of higher fertility after heading stage due to sink limitation.

Radiation Use Efficiency and Dry Matter Production
As shown in Fig. 4 , RUE increased linearly with increasing DVI until panicle initiation (DVI = 1), after which RUE reached a plateau between DVI values of 1.3 and 2.3 until the mid-grain-filling stage. After the mid-grain-filling stage, RUE decreased linearly with increasing DVI. The change in RUE was expressed well using two logistic functions of DVI:

[12]

in which RUE_max (g MJ^–1) is the maximum RUE, and R_w, R_x, R_y, and R_z are regression parameters. The parameters in the first equation were estimated first, and then those in the second equation were estimated using the preestimated RUE_max. The estimated values were RUE_max = 3.24, R_w = –5.72, R_x = 0.702, R_y = 0.000425, and R_z = 0.119.

View larger version (18K): [in this window] [in a new window]   Fig. 4. Radiation use efficiency (RUE) as a function of the developmental index (DVI) of rice under different water temperature conditions from 1996 to 1999.

[13]

where is determined from LAI as follows:

[14]

where PAR is total daily photosynthetically active radiation, which was assumed to be half of the incident global solar radiation (MJ m^–2 d^–1), and k is a constant (0.4) for ‘Kirara 397’ and is not affected by T_w (Shimono et al., 2002). By integrating TDW, TDW can be calculated.

Spikelet Fertility and Dry Matter Partitioning
Partitioning dry matter into storage organs is strongly affected by spikelet fertility, which is largely determined by both T_w and T_a during the reproductive growth period (Matsushima et al., 1964; Shimono et al., 2005). In this part of our analysis, therefore, the effect of temperature on spikelet fertility was quantified and the relationship between spikelet fertility and dry matter partitioning was then evaluated.

Spikelet fertility is affected by short-term low temperatures, but also by the duration of the exposure to coolness (Hayase et al., 1969). To quantify the magnitude of the crop exposure to cool temperatures, the concept of cooling degree-days (CDD, °C d) is useful (Uchijima, 1976); this represents the cumulative temperature lower than a defined threshold. Because panicle primordia differentiate at the base of the shoot and change their vertical position as a result of internode elongation, their surrounding thermal conditions change from T_w to T_a when the panicles emerge above the water surface, indicating that both T_w and T_a determine spikelet fertility (Matsushima et al., 1964; Satake et al., 1988; Shimono et al., 2002). In the present model, the effects of both T_w and T_a on spikelet fertility (FRT) was evaluated based on the concept described in our previous study (Shimono et al., 2005): the temperature of the panicle (T_i) is estimated based on the relationship between water depth and the vertical position of the panicle, which is determined by culm length (CL, length from shoot base to neck of panicle) and is expressed as a function of DVI (Eq. [15]). When the panicle is below the water surface, T_i = T_w. When the panicle is above the water, T_i = T_a. Because this function is based on DVI, it allows us to estimate the position of the panicle in relation to the water surface, and thereby defines the thermal conditions experienced by the developing panicles at any given stage. The CDD of the panicles is then calculated using Eq. [16]. The overall relationship is expressed well by a logistic function (Eq. [17]):

[15]

[16]

[17]

where CD is the magnitude by which the daily temperature is below 22.5°C. The CD is accumulated throughout the reproductive growth period (1.0 DVI < 2.0) to give CDD.

Spikelet fertility is closely correlated with the harvest index at maturity (HI_mt), which equals the weight fraction of grain yield to total biomass: HI_mt = h_a x FRT (FRT + h_b), where h_a = 0.00346 and h_b = 47.5 of regression parameters (r = 0.982, P < 0.001). The HI_mt was linearly correlated with the weight fraction of the panicle to total biomass (excluding roots) at maturity (RPW_max), where RPW_max = 0.0102 HI_mt + 0.120 (r = 0.992, P < 0.01).

As shown in Fig. 5 , the ratio of panicle weight to total biomass (RPW) during the grain-filling period started to increase just before heading stage, and the initial rate was similar for all data despite greatly different RPW_max values. Therefore, the change in RPW could be expressed using the Blackman equation with a linear increase phase plus a parameter phase. The regression line for the linear increase phase was determined using data sets with RPW_max > 0.5, as follows:

[18]

where y_s and y_b are regression parameters (y_s = 0.578, y_b = 1.79).

View larger version (25K): [in this window] [in a new window]   Fig. 5. Ratio of panicle dry weight to total weight (RPW) as a function of the developmental index (DVI) of rice during the grain-filling period from 1996 to 1999.

[19]

[20]

To determine the partitioning of dry matter into leaf and leaf sheath plus culm, the change in the weight ratio of leaves (LDW) to total vegetative organs (leaf, LDW, and leaf sheath plus culm, SDW) (LDW/VDW) was plotted against DVI (Fig. 6 ). The LDW/VDW decreased linearly with increasing DVI and the regression coefficients for the pre- and postheading growth periods were not significantly different. Therefore, one regression line was used for the whole growth period to describe the change in LDW/VDW as a function of DVI:

[21]

where d_s and d_i are regression parameters (d_s = –0.161, d_i = 0.600). Using Eq. [19–21], the dry weight of each organ can be calculated.

View larger version (26K): [in this window] [in a new window]   Fig. 6. Changes in ratio of leaf dry weight to total vegetative organ dry weight (leaf and leaf sheath plus culm dry weight) (LDW/VDW) as a function of the developmental index (DVI) of rice under different water temperature conditions from 1996 to 1999.

[22]

All the calculations are terminated when DVI becomes three. In addition, the present model sets the minimum temperature for grain filling at 13°C (Hanyu and Ishiguro, 1972), and calculation stops when T_a after heading stage becomes lower than 13°C.

Model Validation
The estimates produced using the model were in good agreement with measured LAI throughout the growth cycle (root mean squared deviation (RMSD) = 0.29 – 0.74, r = 0.911 – 0.989, P < 0.01, Fig. 7 ). The accuracy of the estimation was particularly high during the early growth stages, when LAI increased exponentially. After heading stage, LAI in most of the treatments decreased gradually with increasing developmental stage, but LAI in the Low-Reproductive treatment increased (Fig. 7d). This increase was attributed to limited dry matter partitioning to the panicles as a result of low spikelet fertility. Although the model underestimated the leaf area increase after heading stage in Low-Reproductive treatment, a range of patterns resulting from differences in spikelet fertility was generally well simulated.

View larger version (13K): [in this window] [in a new window]   Fig. 7. Time courses of measured and estimated leaf area index (LAI) for rice grown under different water temperature conditions, with LAI data obtained from field experiments conducted at Sapporo, Japan, from 1996 to 1999. Symbols represent observed values, and lines represent estimated values. DAT, days after transplanting; RMSD, root-mean squared deviation; r, correlation coefficient between measured and estimated values. *** P < 0.001; ** P < 0.01.

View larger version (14K): [in this window] [in a new window]   Fig. 8. Time courses of measured and estimated radiation use efficiency (RUE) for rice grown under different water temperature conditions, with RUE values obtained from field experiments conducted at Sapporo, Japan, from 1996 to 1999. Symbols represent observed values, and lines represent estimated values. RMSD, root-mean squared deviation; r, correlation coefficient between measured and estimated values. ** P < 0.01; * P < 0.05; ns, not significant.

View larger version (19K): [in this window] [in a new window]   Fig. 9. Time courses of measured and estimated total dry weight (TDW), leaf dry weight (LDW), leaf sheath plus culm dry weight (SDW), and panicle dry weight (PDW) for rice grown under different water temperature conditions, with dry weights obtained from field experiments conducted at Sapporo, Japan, from 1996 to 1999. Symbols represent observed values, and lines represent estimated values. RMSD, root-mean squared deviation for TDW; r, correlation coefficient between measured and estimated values of TDW. *** P < 0.001; ** P < 0.01.

View larger version (19K): [in this window] [in a new window]   Fig. 10. Relationship between measured and estimated spikelet fertility and grain yield of rice under different water temperature conditions obtained from field experiment at Sapporo, Japan, in 1996–1999. Lines represent y = x, and the 10% intervals on either side of that line.** P < 0.01, * P < 0.05.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION DISCUSSION CONCLUSION REFERENCES

Leaf Area Dynamics
An accurate estimation of leaf area development in the early growth stage is the key to an accurate estimate of dry matter production, because a small error in a leaf area estimate before canopy closure will result in a significant error in canopy radiation interception and thereby dry mater production (Monteith, 1977). Several methods have been used for modeling leaf expansion. Conversion from leaf weight to leaf area using SLA is widely used for this purpose (Iwaki, 1975), and has an advantage in its simplicity. However, SLA, particularly when leaves are developing, is largely variable with climatic conditions such as radiation conditions (Kumura, 1975). In this study, low T_w affected SLA before heading stage (up to 24%) and there was a large yearly variation in the relation between SLA and T_w, indicating the difficulty to use SLA for leaf area estimation. Relative leaf growth rate (RLGR) is an option to express leaf expansion, which can estimate leaf area growth independently of leaf weight (Horie, 1987). However, a small error in RLGR will result in a substantial error in LAI estimation. In addition, this method does not take into consideration the processes that affect leaf area growth. To simulate the processes of leaf area growth, the method using leaf number and leaf size is widely used in other crops (for wheat, Amir and Sinclair, 1991; for maize, Muchow et al., 1990; for peanut, Hammer et al., 1995; for sunflower, Villalobos et al., 1996), which generally have much less tiller number than rice. Because of high tillering ability of rice, there has been no attempt to use this approach for rice leaf area modeling.

In the present model, the process of leaf area development is expressed as a function of the TLNI defined as a product of leaf number on the main culm and tiller number per land area (Fig. 3). Leaf number and tiller number showed different growth patterns with development: Leaf number increased immediately after transplanting (Fig. 2a), while tillering occurred about 18 to 25 DAT (Fig. 2c). Base temperatures were also different between leaf appearance and tillering, as reviewed by Nishiyama (1985). The TLNI concept, therefore, could easily incorporate different growth patterns and temperature responses of leaf appearance and tillering, and the model could well simulate early growth of leaf area (Fig. 7). Leaf number on the main culm and tiller number can be easily measured so that the model can be tested at various levels.

The present model simulated well the time-courses of LAI under different T_ws and years (Fig. 7). To evaluate the effects of error in LAI estimation and on yield estimation, a simulation test using measured LAI values (estimated by linear interpolations between each measured LAI through the whole crop cycle) was conducted. Compared with the present RMSD for yield estimated using the estimated LAI (Fig. 7), RMSD estimated using the measured LAI was lower only by 1 g m^–2. This confirms that the present LAI estimation is highly accurate, and further improvements in LAI estimation have small effects on the improvement in yield estimation.

Radiation Use Efficiency
The RUE changes with the developmental stage. For instance, Campbell et al. (2001) measured the half-hourly averages of CO₂ exchange and the amount of radiation interception of field-grown rice, and showed that RUE based on the canopy CO₂ exchange rate substantially decreased after anthesis, as a leaf N concentration decreased. Hasegawa and Horie (1996) analyzed the effect of leaf N and crop age using a model based on a leaf N-photosynthesis relationship and found that RUE was initially low but increased toward the mid-reproductive stage and decreased afterward. The present study also found a similar change in RUE with DVI (Fig. 4 and 8). With increasing radiation intensity, the leaf photosynthetic rate shows an asymptotic response. In a small canopy, most leaves receive high solar radiation and their photosynthetic rates are light-saturated. Low RUE in the early growth observed in the current study likely resulted from light-saturation of photosynthesis. Low RUE in the late growth stage in this study, on the other hand, was likely due to a decline of leaf N caused by leaf senescence.

The present model took into account the change in RUE by means of age-dependent functions (Eq. [12], Fig. 4). Using a constant value for RUE can result in an intrinsic error for dry matter production. In fact, when grain yield was calculated using a constant RUE (2.27 g MJ^–1, an average RUE obtained from the relation between accumulated radiation interception and dry matter accumulation for the whole growth period), RMSD was 167 g m^–2, which was substantially larger than RMSD simulated using age-dependent RUE of 94 g m^–2. Therefore, the use of the age-dependent RUE values made a substantial contribution to the accurate estimates of dry matter accumulation in the present model.

To evaluate the effects of errors in RUE estimation on yield estimation, a simulation test using the measured RUE was also conducted. Compared with the present RMSD for yield estimated using the estimated RUE (Fig. 8), RMSD estimated using the measured RUE was lower only by 1 g m^–2. This confirms also that the present estimation of RUE is accurate, and that further improvements in RUE estimation have small effects on the improvement in yield estimation.

Spikelet Fertility
There are a number of models that predict spikelet fertility based on T_a during the reproductive growth period (Uchijima, 1976; Yajima et al., 1989). However, T_w in addition to T_a is an influential factor for spikelet fertility (Shimono et al., 2002) because developing panicles are submerged until the mid-reproductive growth stage. Under cool climates, T_w is generally higher than T_a, and the deep-flooding water management is a common practice to reduce the floral sterility-type cool weather damages (Sakai, 1949; Satake et al., 1988). The present model, which takes into account the effects of both T_w and T_a on spikelet fertility, will likely improve accuracy of spikelet fertility estimation of the previous models based only on T_a.

Variations in spikelet fertility due to T_w and years were generally well explained by the present model, but the model largely underestimated spikelet fertility in the Middle-Reproductive treatment in 1999 (Fig. 10). Possible reasons for this underestimation are as follows. The present model does not take into account the different sensitivity to cool weather damages depending on growth stages. Hayase et al. (1969) exposed pot-grown rice plants to low T_a treatment (12°C for 4 d) at different stages of the reproductive growth, and showed that low T_a around the critical stage (11 d before heading stage, DBH) reduced spikelet fertility by more than 50%. The reduction in spikelet fertility became smaller when the treatment was imposed away from the critical stage, and no reduction was observed in the treatments before 16 DBH or posterior to 8 DBH. When T_a from the critical stage to heading stage was high in 1999 (25°C on average), the reduction in spikelet fertility by the Middle-Reproductive treatment in this year might not have been as large as that estimated by the current model. In addition, a considerable variation exists in developmental stage and culm length within a hill. Kobayashi (1979) monitored the stages of individual spikelets through the reproductive growth period in the field, and showed that the difference in time of critical stage varied in a range of a week within a hill. The within-hill variation in developmental stage and the vertical position of the panicle was neglected by the present model, which might also have resulted in a gap between measured and estimated spikelet fertility. Further studies are necessary to determine these effects on spikelet fertility.

Yield estimation is significantly affected by estimation of spikelet fertility. The simulation using the measured spikelet fertility (calculation with inputting measured spikelet fertility) substantially reduced RMSD for yield estimation by 45 g m^–2, which was much larger than the effects of LAI and RUE of 1 g m^–2. To improve accuracy of yield estimation, improvement of estimation of spikelet fertility is essential.

	CONCLUSION

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION DISCUSSION CONCLUSION REFERENCES

 
Our model appears to have successfully covered the major growth processes that are affected by T_w, and was able to quantify the response of growth and yield to changes in T_w. Because the model is simple and based on robust relationships between various parameters of rice, it should be possible to use the model to analyze temporal and regional variations in growth and yield under cool climates. However, it's important to note that it may be necessary to parameterize the model for different regions such as soil fertility, fertilization method, and possibly for other rice cultivars (following the procedures described in this paper), to determine whether any modifications of the model will be necessary to account for unique environmental or plant characteristics.

	REFERENCES

TOP ABSTRACT INTRODUCTION MODEL DESCRIPTION DISCUSSION CONCLUSION REFERENCES

 

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