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Published online 19 October 2005
Published in Agron J 97:1524-1536 (2005)
DOI: 10.2134/agronj2005.0043
© 2005 American Society of Agronomy
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Modeling

Modeling Spikelet Sterility Induced by Low Temperature in Rice

Hiroyuki Shimonoa,*, Toshihiro Hasegawab, Masahisa Moriyamac, Shigeto Fujimurad and Takayuki Nagatad

a Dep. of Biology and Environment Sciences, National Agric. Res. Center for Tohoku Region, Shimokuriyagawa, Iwate, 020-0198, Japan and the Japan Society for the Promotion of Science, Tokyo, 102-8577, Japan
b Dep. of Global Resources, National Inst. for Agro-Environmental Sciences, Tsukuba, Ibaraki, 305-8604, Japan
c Dep. of Biology and Environment Sciences, National Agric. Res. Center for Tohoku Region, Shimokuriyagawa, Iwate, 020-0198, Japan
d Graduate School of Agriculture, Hokkaido University, Sapporo, 060-8589, Japan

* Corresponding author (shimn{at}affrc.go.jp)

Received for publication February 3, 2005.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Accurate prediction of spikelet sterility in rice (Oryza sativa L.) is a prerequisite for accurately predicting grain yield in cool climates, since severe yield losses frequently occur when spikelet sterility is induced by cool temperatures during reproductive growth. Both cool air temperature (Ta) and cool water temperature (Tw) are detrimental factors that can cause spikelet sterility, but a large discrepancy between Ta and Tw is often observed in paddy fields. The depth of water can also affect spikelet sterility. We proposed a model that accounted for the effects of Ta, Tw, and water depth on spikelet sterility, and was based on panicle temperature (Tp), then tested the model using 23 independent sets of field data from northern Japan. We also quantified the role of daily amplitude (the difference between maximum and minimum temperatures) and differences in plant sensitivity to temperature in determining spikelet sterility. A cool-irrigation experiment revealed that spikelet sterility depended more strongly on Tp than on Tw or Ta. We also developed six models using "cooling degree-day" concept. The model based on Tp had higher accuracy than models based solely on Tw or Ta. In addition, average temperature was a better predictor than minimum temperature. Accounting for the difference in temperature sensitivity also improved the model's accuracy. A model that considers these factors would thus improve prediction accuracy for spikelet sterility due to cool weather.

Abbreviations: CDD, cooling degree-day • CL, culm length • DAP, days after transplanting • DVI, developmental index • DVR, developmental rate • RMSD, root-mean-square deviation • STR, spikelet sterility • Ta, air temperature • Tw, water temperature • Tp, panicle temperature


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
SPIKELET STERILITY induced by low temperature, particularly when those temperatures occur during reproductive growth, is a major constrain on rice production in cool climates. Hokkaido, Japan's northernmost island, is located between 41.3 and 45.5° N lat and is thus one of the coldest rice-producing areas in the world. On Hokkaido, severe yield losses are caused by low temperatures roughly once every 4 yr. One recent period of cold damage occurred in 1993, when the average rice yield on Hokkaido decreased by 60% compared with the normal yield; this amounted to a net loss of 0.37 million Mg of rice, which was equivalent to 15% of the total loss in Japan that year. In 2003, a year with a cool summer, a 27% yield reduction due to low temperatures was reported on Hokkaido. In addition to losses in the northern part of Japan, yield losses caused by low temperatures have been reported in Australia (Godwin et al., 1994), the USA (Board et al., 1980), and Korea, Bangladesh, India, Nepal, and other countries (Kaneda and Beachell, 1974). Improved cold tolerance has been a key goal of rice breeding programs, and management practices such as changing the planting schedule, water management, and fertilization have been widely introduced to farmers in an effort to prevent yield losses (reviewed by Wada, 1992). However, there have been few attempts to evaluate the impact of these improvements on yield and its stability (Yajima, 1994). For that purpose, a process-based growth model would be a powerful tool that could quantitatively and separately analyze the causal effects of weather and management factors, and that could also be used to predict spikelet sterility and yield losses as a result of cold weather.

Spikelet sterility of rice grown under flooding is determined by the temperatures of both the irrigation water (Tw) and the air (Ta), but the plant organ that is most sensitive to low temperature and that determines spikelet sterility is the panicle itself (Sakai, 1949; Satake et al., 1988). After panicles have differentiated at the base of the shoot, the vertical position of the panicles changes as a result of internode elongation; as a result, their ambient thermal condition changes from that of the water (Tw) to that of the air (Ta) when they emerge above the water level. In the field of cool climates, Tw is generally higher than Ta because of solar heating. Tanaka (1962) monitored this difference in paddy fields at Aomori (40°49' N lat) in northern Japan, and showed that the maximum and minimum Tw can be higher than Ta by as much as 10 and 5°C, respectively. 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 can warm the panicles for longer than in shallower waters. To simulate the responses of spikelet sterility to low temperature in the field, three factors (Tw, Ta, and water depth) must be incorporated into the model.

Several methods are available for predicting spikelet sterility in rice. A regression model using Ta averaged over the whole period of reproductive growth (Uchijima, 1976b) or averaged over the booting stage (Abe et al., 1964; Dingkuhn et al., 1995) provides an easy and powerful criterion to predict spikelet sterility and yield losses. Average Tw over the whole period of reproductive growth has also been used (Tanaka, 1962). These attempts were able to roughly predict spikelet sterility and yield losses between locations and years, but had several limitations. First, these attempts used either Tw or Ta independently and did not consider panicle temperature even though the panicles are the organ most sensitive to changes in ambient temperature and panicle temperature changes in response to internode elongation and changing water depth. Second, the sensitivity of spikelet sterility to low temperatures varies among developmental stages during reproductive growth. The sensitivity is extremely high at the young-microspore stage, which is a stage of active cell division, and decreases as the plant develops beyond this stage (Hayase et al., 1969). This dynamic aspect of changing sensitivity cannot be simulated by aforementioned models. Finally, and most importantly, averaging temperatures over a period prevent the detection of the effects of low temperatures during a cold period that lasts only a few days. Such periods can cause the observed detrimental effects on spikelet sterility, even when temperatures during the remainder of the period of reproductive growth are normal or high (Hayase et al., 1969).

To dynamically quantify the magnitude of the crop exposure to low temperatures, the concept of a cooling degree-day (CDD, °C d) would be useful; this parameter has been defined as the cumulative temperature lower than a specified threshold (Uchijima, 1976a). Using a CDD based solely on Ta, Yajima et al. (1989) estimated spikelet sterility at 22 different locations in Tohoku (Miyagi Prefecture, Japan) in 1988, a year with an unusually cool summer. The simulated spikelet sterility was correlated overall with the measured spikelet sterility (R2 = 0.67, n = 22). However, Toriyama and Inoue (1984) pointed out that CDD based solely on Ta could not explain regional differences in spikelet sterility at different locations in Tohoku. Their simulation using a heat-balance model suggested that the observed differences in spikelet sterility could be explained by using the estimated surface temperature of the plant, and that spikelet sterility was lower during periods of higher solar radiation as a result of warming of the plant. Wind speed can also affect spikelet sterility through its effects on Tw and, thus, its effects on the temperature of the developing panicles (Tomari et al., 1980).

A CDD model based solely on Tw was developed by Godwin et al. (1994) to simulate variations in yield in Australia, even though Tw was just a function of Ta and water depth in this model (i.e., Tw = Ta + 0.025 water depth [mm]). Their model allows us to roughly evaluate the combined effects of Ta and water depth on spikelet sterility at a given location. However, the relationship between Tw and Ta has been reported to change by years at a single location (Sameshima, 2004), and Tw has been shown to differ between locations by up to 1°C, even when Ta is the same (Satake et al., 1988).

To simulate spikelet sterility over wider areas, across years, and among different management practices, a CDD model based on the temperature experienced by developing panicles (Tp) should provide the best results. Such an approach would provide a new framework for predicting spikelet sterility. An obstacle to using Tp arises from the difficulty in quantifying the vertical position of the panicles. Under low temperatures, the elongation of the culm is retarded, whereas elongation is promoted under high temperatures. This dynamic aspect of the culm elongation has prevented the use of the models based on Tp. In a previous study, we quantified the length of the main culm (from the base to the neck of the panicle) as a function of a developmental index (DVI; Horie and Nakagawa, 1990) that was well expressed in terms of Tw (Shimono et al., 2001). Using this function, we can estimate the vertical position of the panicles and can estimate Tp as a function of water depth on the basis of whether or not the panicles are underwater or above the surface.

The temperature used as the daily inputs for the model can be expressed as either average or minimum temperatures. Some researchers have used average temperature (Yajima et al., 1989; Godwin et al., 1994), whereas others have used minimum temperatures (Abe et al., 1964; Dingkuhn et al., 1995). From the results of the pot-experiment, Uchijima (1976a) plotted CDDs (calculated based on hourly temperatures or daily average temperatures) against spikelet sterility, and showed that the CDD on a daily basis explained variations in spikelet sterility better than CDD on an hourly basis. He discussed that this was because CDD on a daily basis accounted for effect of higher temperature over the threshold temperature on spikelet sterility. The phenomenon that high temperature affects spikelet sterility even at the same minimum temperature was observed in several other pot experiments (Shimazaki et al., 1964; Shibata et al., 1970). However, no researchers have evaluated the effect of daily amplitude on modeling spikelet sterility. In addition, the difference in panicle sensitivity to low temperatures during stages of reproductive growth is important in modeling spikelet sterility, but its impact on model accuracy has not been evaluated.

Our objectives were thus as follows: (i) to evaluate the dependence of spikelet sterility on Tw, Ta, and Tp, and to clarify which of these variables was most suitable for predicting spikelet sterility over wider areas and across years; (ii) to explain variations in spikelet sterility by examining whether average temperature or minimum temperatures provides the greater improvement in prediction accuracy; and (iii) to evaluate the role of differences in panicle sensitivity to low temperatures for modeling spikelet sterility.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Model Structure
Basic Structure
The models used here are based on the CDD, which can quantify the magnitude of the crop's exposure to cool temperatures by accounting for both the duration and the magnitude of the cold. The CDD was calculated as follows, using a daily time step:

[1]
where CD is any daily temperature below Tbase, which is the lower threshold temperature for increasing spikelet sterility; T is the daily temperature (average or minimum) for Tw, Ta, or Tp; and W(DVI) is a function of developmental index (DVI) that simulates the difference in sensitivity to low temperatures (described later in the section "Difference in Sensitivity to Low Temperature in CDD Calculations").

The relationship between spikelet sterility (STR, number of sterile spikelets ÷ total number of spikelets) and CDD is expressed by the following logistic function:

[2]
where Smax, Sa, and Sb are regression constants. From Eq. [2], spikelet sterility can be predicted using the CDD value calculated on the basis of the daily inputs of Ta, Tw, and Tp.

Temperatures Used for Model Input
Spikelet sterility is influenced by both Tw and Ta during reproductive growth, and the contribution of Tw or Ta to spikelet sterility changes with water depth (Sakai, 1949; Satake et al., 1988). We proposed the use of Tp, which is determined by the interaction of Tw, Ta, and water depth. As a result, Tp is dynamically estimated from the relationship between water depth and the vertical position of the panicle with respect to the surface of the water. When the panicle is below the water surface, Tp is assumed to equal Tw. When the panicle is above the water surface, Tp is assumed to equal Ta, although the measured Ta above the rice canopy will differ from the actual panicle temperature (Toriyama and Inoue, 1984).

The vertical position of the panicle is largely dependent on culm elongation. In our previous study, Shimono et al. (2001) showed that the changes in culm length (CL) from the base of the shoot to the neck of the panicle could well be expressed as a function of developmental index (DVI), a continuous variable determined by a daily integration of developmental rate (DVR).


[3]

[4]

[5]
where a = 568, b = 2.84 for cultivar ‘Kirara 397’ (Shimono et al., 2001); DVI equals 1 at panicle initiation and 2 at heading; and Ca, Cb, and Cc are regression constants. In our previous study Ca = 0.00062, Cb = –8.0, and Cc = 9.7 (R2 = 0.96, P < 0.001) for cultivar ‘Kirara 397’ (Fig. 1a) (Shimono et al., 2001). Note that, in deriving DVR, we used Tw only (Eq. [3]) throughout the reproductive period, even where the panicles are above the water surface. This was because our previous study (Shimono et al., 2001) showed that Tw also influenced the duration from booting to heading, probably by affecting culm elongation that promotes panicle emergence from the sheath. We tested three variables (Tw, Ta, and Tp) and two different daily values of each variable (average or minimum) for the model inputs.



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  		Fig. 1. (a) Culm length expressed as a function of developmental stage (DVI). (b) Difference in sensitivity of spikelet sterility, W(DVI), to low temperature during reproductive growth as a function of DVI. The parameters for the equation in (a) are for the Kirara 397 cultivar and were reported by Shimono et al. (2001). The function of "weighted" in (b) is based on the results of Yajima et al. (1989).

 
Difference in Sensitivity to Low Temperature in Cooling Degree Day Calculations
A slight difference in the growth stages that are exposed to low temperatures during reproductive growth will affect spikelet sterility, as was confirmed in the precise-pot experiment by Hayase et al. (1969). To evaluate this effect, we described this sensitivity (W(DVI), Eq. [1]) by using two functions (Fig. 1b). The first is an even function of W(DVI) in which sensitivity is assumed to be constant, with a weight equal to 1, from panicle initiation to the heading stage. The second function represents a weighted function of W(DVI) that accounts for changes in the sensitivity of the panicle (thus, of spikelet sterility induced by low temperature). The values in this second function were parameterized on the basis of the data of Yajima et al. (1989). In the latter study, the sensitivity was parameterized for a period from panicle initiation to the flowering stage, with the most sensitive stage (booting stage, DVI = 1.57) given a weight 11 times the values of the least-sensitive stage and the second-most-sensitive stage (flowering stage, DVI = 2.25) given a weight 4 times the values of the least-sensitive stage. However, the sensitivity at flowering stage has been less well-confirmed than the sensitivity at the booting stages in the field, although the sensitivity at flowering has been confirmed in pot experiments (Satake and Koike, 1983). Because the models in our study need to be simplified to facilitate interpretation of the simulated results, they exclude the sensitivity at the flowering stage.

Models Tested
We developed models based on three different variables (Tw, Ta, and Tp), two different daily bases (average or minimum temperatures), and whether or not the models accounted for sensitivity differences. On the basis of these parameters, we developed and tested the six models in Table 1 using various combinations of these three factors.


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  		Table 1. Model tested.{dagger}

 

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  		Table 3. Date of transplanting and heading, duration of flooding water, daily average and minimum air temperature (Ta), water temperature (Tw), and estimated panicle temperature (Tp) (avg. ± SD) and spikelet sterility (STR) of rice (cv. Kirara 397) in Sapporo, Pippu, Iwamizawa, and Ohno of Hokkaido, and Morioka, Kuji, and Yamagata village of Tohoku, Japan (1996–1999, 2003).{dagger}

 
Database
Field Experiment with Cool Water Temperature Treatments
We conducted 4 yr of field experiments (1996–1999) in which we imposed Tw treatments during different growth stages at the experimental farm of the Faculty of Agriculture, Hokkaido University, Sapporo, Japan (43°04' N lat; 141°20' E long; Fig. 2) . In all, we used 20 data sets obtained from these experiments for development (Table 2) and testing (Table 3) of our models. Five data sets randomly selected from each Tw treatment (Table 3) were used for independent testing, and the remaining 15 data sets (Table 2) were used for the model development.



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  		Fig. 2. Map of Japan showing the locations of the data collection site used to develop and validate our models.

 

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  		Table 2. Date of transplanting and heading, duration of reproductive growth (from panicle initiation to heading), depth of flooding water, daily average air temperature (Ta), water temperature (Tw), and estimated panicle temperature (Tp) (avg. ± SD) and spikelet sterility (STR) of rice (cv. Kirara 397) in Sapporo, Hokkaido (1996–1999).{dagger}

 
Details of the cultural practices and treatment procedures were given in the previous papers (Shimono et al., 2002, 2004). Briefly, we sowed germinated seeds of the rice cultivar Kirara 397, a dominant variety that is planted in 58% of the total paddy fields on Hokkaido (1999), in late April. Three seeds were sown in each cell of a plug tray and the seedlings were raised under a polytunnel. The seedlings were transplanted into paddy fields (a typic gray lowland soil, classified as Eutric Fluvisol) in late May. Planting density was 23.3 hills m–2 (with 13 cm of inter-hill space and 33 cm between rows) in all years except 1997 (when we used 18.9 hills m–2, 16 cm of inter-hill space and 33 cm between rows). All treatment areas received equal amounts of a basal fertilizer application (9.6 g m–2 N, 4.2 g m–2 P, and 6.0 g m–2 K), which was incorporated into the tilled soil layer before flooding.

Water-temperature treatments were applied for the period of vegetative growth (from 16 to 21 d after transplanting [DAP] until panicle initiation), for the period of reproductive growth (from panicle initiation to full heading) and during the early grain-filling period (from 0 to 20 d after full heading). Cool Tw treatments were established by drawing water from sources that had been warmed to different temperatures as a result of their variable distances from a common source of cool water (about 15°C). Cool water was supplied to plots between 0600 and 1800 h at a rate of about 300 L min–1. The treatments were designated in Table 2. The Tw treatments were not replicated because the random assignment of more than one plot to any Tw treatment would have been prohibitively difficult in the field. Each treatment plot covered between 64 and 72 m2, and was surrounded by plastic boards 30 or 45 cm in height. The location of the plots was changed each year. The water level was maintained at about 5 cm above the soil surface until about 20 d after full heading, except for in 1996 (when the water level was 20 cm above the soil surface).

The Tw was measured at the center of each plot by copper-constantan thermocouples (0.6 mm in diam.) placed 5 cm below the water surfaces, with temperature recorded at 10-min intervals using a data logger (IDL-3200, North High-Tech, Sapporo, Japan). The Ta at 1.5 m above the ground was also recorded at a single location to cover the experimental site. Daily average Tw and Ta were expressed as the mean of the daily maximum and minimum temperatures.

Spikelet sterility (number of sterile spikelets ÷ total number of spikelets) was measured for the panicles on the three tallest culms (1996) and on all culms (1997, 1998, and 1999) of 4 (1998), 5 (1996, 1997), and 12 hills (1999) in each treatment. The date of the panicle-initiation stage when the young panicle on the main stem reached 1.0 mm in length (three stem from different hills per treatment), and the date of heading stage when 50% of the tillers had heads (20 hills per treatment) were determined by measurements once every 2 d.

Field Observation at Different Locations and in Different Years
To test the models, we obtained a total of 23 data sets from experiments that had been conducted at 9 locations in 12 paddies in northern Japan from 1996 to 1999, and in 2003 (Fig. 2, Table 3): Sapporo, for Hokkaido University, grown under cool Tw treatments, 5 data sets of which were not used for the model development described above (1996–1999); Pippu (45°52' N lat; 142°29' E long), for Hokkaido Prefectural Kamikawa Agricultural Experiment Station (1998 and 1999); Iwamizawa (43°13' N lat; 141°47' E long), for Hokkaido Prefectural Central Agricultural Experiment Station (1996, 1997, 1998, and 1999); Ohno (41°53' N lat; 140°39' E long), for Hokkaido Prefectural Dohnan Agricultural Experiment Station (1997, 1998, 1999, and 2003) in the Hokkaido region; Morioka (39°45' N lat; 141°8' E long), for National Agricultural Research Center for Tohoku Region (2003); and Sunago (40°10' N lat; 141°43' E long) and Kishisato (40°9' N lat; 141°44' E long) in Kuji (2003) and Okabori (40°13' N lat; 141°32' E long) and Kamioguni (40°5' N lat; 141°38' E long) in Yamagata village (2003), for farmers' fields in Tohoku.

Cultivar ‘Kirara 397’ was grown under similar management practices (those common to the region) at these locations, and the heading date and level of spikelet sterility were recorded. Transplanting occurred in late May, ranging from 19 May to 4 June (Table 3). Since Tw in Ohno was measured only at 0900 h (Tw9am), we estimated the daily average and minimum Tw on the basis of a relationship between Tw9am and the daily average Tw at Sapporo, developed using 4 yr of data (avg. Tw = 1.11 x Tw9am, R2 = 0.51, n = 87, P < 0.001), and a relationship between Tw9am and daily minimum Tw (minimum Tw = 0.94 x Tw9am, R2 = 0.75, n = 87, P < 0.001). At Ohno, Tw data were not available before 15 July, so these temperatures were estimated from the average Ta on the basis of the relationship between average Tw and average Ta (avg. Tw = 0.839 x avg. Ta + 6.65, R2 = 0.69, n = 116, P < 0.0001). Except for Sapporo, panicle-initiation stage was not recorded, so that DVI during the period of reproductive growth was estimated from the recorded date of heading and DVR calculated from observed Tw before heading.

Statistic Analysis
For our testing of the model using independent data, we expressed goodness of fit as the root-mean-square deviation (RMSD), which was obtained as follows:

where MSRi and ESTi are the measured and estimated values, respectively, and n is the number of data sets. The RMSD represents the average distance between the measured and estimated values, and is often used as a measure of the accuracy a model (Kobayashi and Salam, 2000). This means that the estimates can vary within ±RMSD from the measured values, on average.

Bias was used to define the overall model performance, and was defined as follows:

A coefficient of determination (R2) between the measured and estimated values was also calculated.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Model Development
Weather
Cool-irrigation treatment significantly decreased Tw during the period of reproductive growth (Table 2). Average Tw ranged from 17 to 25°C, and minimum Tw ranged from 14 to 21°C, and both values differed by –7 to +1°C from the temperatures in the high Tw treatments. Note that treatments during the period of vegetative growth severely limited canopy size (Shimono et al., 2002) and then increased Tw after the treatment of reproductive growth associated with increased radiation penetration on the water surface. Yearly variations in Tw followed trends in Ta, such that Tw in 1996 and 1998 was relatively low. Average Ta ranged from 20 to 23°C and minimum Ta ranged from 17 to 19°C. During the periods of vegetative growth and grain filling, cool irrigation treatments significantly decreased average and minimum Tw by 4 to 6°C (data not shown; see the results in Shimono et al., 2002).

The period of reproductive growth (from panicle initiation to the heading stage) ranged from 24 to 41 d, and was longer under low Tw conditions during reproductive growth than under high Tw conditions.

Dependency of Spikelet Sterility on Cool Water Temperature and Air Temperature
Spikelet sterility was increased by cool irrigation treatments during reproductive growth, but not by cool irrigation treatments before and after the period of reproductive growth (Table 2). The cool irrigation treatments at different growth stages produced large variations in spikelet sterility, ranging from 3 to 100%, in response to changes in Tw, Ta, and water depth.

An average Tw of less than about 22.5°C during a period of reproductive growth substantially increased spikelet sterility, and explained most of the variation in spikelet sterility (Fig. 3a) . However, there was yearly variation in spikelet sterility at an average Tw of less than 22.5°C. Spikelet sterility in 1996 and 1998 under the same average Tw was higher than that in 1997 and 1999. The higher spikelet sterility observed in 1996 was partially due to the water level, which was 10 cm deeper than in the other years and thus resulted in longer exposure to low Tw than was the case under shallower water.



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  		Fig. 3. Relationships between spikelet sterility (% of total spikelets) and (a, c) water temperature, Tw, and (b, d) air temperature, Ta, during the period of reproductive growth by rice grown under different water temperatures and depths at Sapporo, Japan. Range bars indicate standard error in spikelet sterility based on the variation among hills in each treatment (n = 5 [1996, 1997], n = 4 [1998], n = 12 [1999]).

 
Average Ta was less closely related to spikelet sterility as a whole (Fig. 3b), but spikelet sterility at an average Tw of less than about 22.5°C (values of spikelet sterility above 30%, circled values in the figure) was negatively correlated with Ta (STR = –20.5 Ta + 511, R2 = 0.70, n = 8 out of 15, P < 0.05). The lower Ta in 1996 and 1998 than that in other years increased spikelet sterility at lower Tw. The Ta itself cannot explain the variation in spikelet sterility well, but Ta is clearly an additional factor that affected spikelet sterility.

Similar trends were observed for minimum Tw and Ta (Fig. 3c, d). At Tw of less than 19.5°C, spikelet sterility increased, although the variation at the same temperature was larger than that observed for average Tw and Ta.

Relationships between Cooling Degree Day and Spikelet Sterility
The six CDD models in Table 1 were plotted against spikelet sterility (Fig. 4) . We determined the threshold temperature for increasing spikelet sterility (Tbase) as the temperature at which spikelet sterility was 10%. According to the fitted logistic curves, Tbase was estimated as 22.5°C for average temperature (Fig. 3a) and 19.5°C for minimum temperature (Fig. 3c).



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  		Fig. 4. Relationships between spikelet sterility and cooling degree-day calculated using models in Table 1. Range bars indicate standard error in spikelet sterility based on the variation among hills in each treatment (n = 5 [1996, 1997], n = 4 [1998], n = 12 [1999]). Even = no variation in sensitivity to temperature; Weighted = sensitivity to temperature varies as described in Fig. 1b.

 
The variations in spikelet sterility resulting from different Tw, Ta, and water depth were mostly well explained by CDD based on Tw or Tp (R2 > 0.89), not by CDD based on Ta (R2 > 0.52) (Fig. 4). We used curve-fitting to determine each parameter (Smax, Sa, and Sb) in the six models (data shown in the equations presented in the figures).

Model Validation Using Independent Data Sets
We tested our models using 23 independent data sets listed in Table 3. Because of the differences in Ta, Tw, and water depth, spikelet sterility varied from 5 to 100%. The highest spikelet sterility was observed in 2003, a year with a cool summer when Tw and Ta were lower than in other years. Average Ta ranged from 17 to 23°C, whereas average Tw ranged from 18 to 26°C, and was higher than average Ta.

Performance of Cool Water Temperature, Air Temperature, and Panicle Temperature
Among the three models based on Tw (Model I), Ta (Model II), and Tp (Model III), the model based on Tp performed best (Fig. 5a, 5b, 5c ; Table 1). The model based on Tw underestimated spikelet sterility (bias = –17.6, Fig. 5a) and the model based on Ta overestimated spikelet sterility (bias = +25.1, Fig. 5b). The Tp provided the best estimate of spikelet sterility, with a bias of only –5.5 (Fig. 5c).



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  		Fig. 5. Comparison of estimated vs. measured spikelet sterility obtained in northern Japan (1996–1999, 2003).

 
Daily Temperature
The overall performance of models based on average Tp (Model III) and minimum Tp (Model IV) were similar in terms of RMSD, bias, and R2 (Fig. 5c, 5d; Table 1), but the model based on minimum Tp greatly overestimated spikelet sterility at Pippu in 1998 by +37%. Model VI, which accounted for differences in sensitivity, increased this error to +59% for the same time and location. In addition, the residual between the measured and estimated values in models using minimum Tp (Models IV, VI) was significantly and positively correlated with the difference between the minimum and maximum daily temperatures (the "daily amplitude"; Table 4), whereas no significant relationship was observed for models using average Tp (Models III and V). This indicated that models based on minimum Tp overestimated spikelet sterility when the daily amplitude was high, and underestimated them when the daily amplitude was low. We can also conclude that average Tp was better than minimum Tp for predicting spikelet sterility.


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  		Table 4. Relationship between the residual (between measured and estimated spikelet sterility) and the daily amplitude of panicle temperature (the difference between daily maximum and minimum panicle temperature).{dagger}

 
Difference in Sensitivity to Low Temperature
In 2003, a year with a cool summer, the RMSD of model that accounted for differences in sensitivity to low temperature (Model V) was 4% lower, and the R2 was 0.11 higher than in the model that did not account for this sensitivity (Model III), whereas there was only a small difference in predictive accuracy between these two models in warm years (Fig. 5c, 5e; Table 1). Model III, which did not account for sensitivity, underestimated spikelet sterility at Kishisato (Data set no. 19) by 33% and Kamioguni (Data set no. 22 and 23) by 17 to 20%. We conclude that using average Tp and accounting for sensitivity differences (Model V) is preferable to accurately predicting spikelet sterility over wider areas and between years.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 REFERENCES
 
Although a number of previous models that predicted spikelet sterility of rice were simulated on the basis of either Ta (Abe et al., 1964; Uchijima, 1976a, 1976b; Yajima et al., 1989; Dingkuhn et al., 1995) or Tw (Tanaka, 1962; Godwin et al., 1994), the present study revealed that variations in spikelet sterility across years, locations, and water management practices in northern Japan were well explained by the models based on Tp rather than those based solely on Tw or Ta (Fig. 5a, 5b, 5c). Spikelet sterility is a result of the combined effects of Ta, Tw, and water depth. Using only Tw underestimated spikelet sterility (Fig. 5a) because of overestimation of the effects of warmer Tw when panicles emerged above water. In contrast, using only Ta overestimated spikelet sterility (Fig. 5b) because of underestimation of the effects of Tw when the panicles were below water. The model we have proposed on the basis of Tp thus provides a new framework for analyzing the combined effects of Tw, Ta, and water depth on spikelet sterility in the field.

The present study demonstrated that average temperature was more effective than minimum temperature for modeling spikelet sterility (Fig. 5 and Table 4). Shimazaki et al. (1964) exposed pot-grown rice to low Ta (13°C) for different duration during the day (6–24 h), and found that the daily maximum temperature affected spikelet sterility even with the same daily minimum temperature, supporting our simulation results. Our CDD based on average temperature can account for both minimum temperature and daily amplitude in a simple manner. However, under climatic conditions with an unusually large daily amplitude, as is the case in Australia, a high maximum temperature might mask the effects of declining minimum temperature. In such cases, there is an alternative way to calculate CDD on the basis of daily average temperature (referred to by McMaster and Wilhelm, 1997; in their case "growing degree-days"). Although our model calculated CDD by comparing average temperature with Tbase, the comparison with Tbase can instead be made before calculating the average temperature by comparing Tmax (maximum temperature) and Tmin (minimum temperature). In this approach, if Tmax > Tbase then Tmax = Tbase, and if Tmin > Tbase then Tmin = Tbase. This method produces a "calibrated" average that excludes extremes when Tmax is above Tbase. Using our data set, the model based on this calibrated average Tp did not greatly improve prediction accuracy (RMSD = 12, R2 = 0.92, Bias = –1) compared with Model V (Table 1), although the calibrated Tp approach may improve accuracy under a climate such as that of Australia.

Our model that incorporated the difference in sensitivity (Model V) increased prediction accuracy (Fig. 5c, 5e). The model that did not account for sensitivity differences (Model III) underestimated spikelet sterility, particularly in a year with a cool summer (2003). Figure 6 shows the seasonal changes in Ta and Tw plotted against DVI at Kishisato and Kamioguni in 2003. The Tw and Ta were high early and late in the reproductive period (DVI < 1.1 and DVI > 1.8), but dropped during the middle of the reproductive period, which represents the most sensitive stage (Hayase et al., 1969; Satake, 1976). Model III could not simulate the effect of this cooling period, whereas Model V was able to simulate this effect because it incorporates the change in sensitivity around this stage (Fig. 1b).



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  		Fig. 6. Seasonal change in the temperatures of water (Tw) and air (Ta) as a function of the developmental index (DVI) at Kishisato and Kamioguni in 2003 during the period of reproductive growth. The horizontal line at a temperature of 22.5°C represents the temperature below which spikelet sterility begins to become significant (ref. Fig. 3a).

 
It must be noted that several factors have not been accounted for by the present models, possibly leading to intrinsic prediction errors when the model is applied to a wider range of environments. First, the level of fertilizer application and soil fertility are both influential for spikelet sterility (Amano and Moriwaki, 1984; Watanabe and Takeichi, 1991). All the experiments that provided data for development of the present model were conducted under a standard fertilization regime and using standard management practices at a single experimental paddy in Sapporo, on Hokkaido. Soil N fertility, as measured by N content, varies greatly between regions on Hokkaido. For example, approximately 20% of the paddy fields on Hokkaido have a peat soil with high N levels, but 7% have gray upland soil with low N levels (Tanaka, 1994). In addition, the soil moisture level before flooding, which is influenced by management practices and climatic conditions (Toriyama, 1994), and the application of manure (Miyazaki et al., 1981), can both strongly affect N mineralization.

Second, we used a single function of culm length to determine the vertical position of the panicles even though this calculation was based on data from rice grown under different Tw conditions. Culm length is influenced by environmental factors such as soil fertility, N fertilization, and light conditions (Kamiji et al., 1993; Sasaki et al., 2001) and differs among cultivars (Kobayashi and Satake, 1979).

Third, actual Tp was not always identical to Ta measured above the rice canopy. Toriyama and Inoue (1984) simulated that the surface temperature around the developing panicle when the panicle was located above water level, and found that Tp was higher than Ta above the canopy by around 1°C, although the magnitude of the difference depended on level of incident radiation. Watanabe and Takeichi (1991) monitored temperature inside the leaf sheath during reproductive growth of rice under different N fertilization levels, and showed that this temperature was lower at higher N fertilization levels, caused by low penetration of radiation inside the canopy. The size of the canopy also affected panicle temperature.

Fourth, we used a single value of Tw, but Tw is not vertically uniform because warm water rises to the surface and cool water sinks to the bottom; this may affect the Tp estimation, particularly where deep water irrigation is practiced. Toriyama and Inoue (1984), however, showed that Tw at two depths of 5 and 20 cm from the water surface was not different by more than 0.5°C, whereas the Ta and Tw difference was as much as 5°C. This suggests that use of a single Tw value is not a significant source of error in model prediction.

Fifth, a considerable variation exists in developmental stage and culm length within a hill. Kobayashi (1979) monitored individual spikelets throughout the periods of reproductive growth period in the field, and showed that the time of the critical stage that panicle is most sensitive to low temperature varied by as much as 1 wk within a hill. Variation in both the within-hill developmental stage and the vertical position of the panicle was neglected by the present model.

Finally, the sensitivity at the flowering stage was excluded in the present model. Without incorporating a measure of sensitivity at this stage, the present model nonetheless provided a good prediction over the range of conditions covered by the present model, including a cool summer in 2003 (Fig. 5e). If low temperatures occurred only during the flowering stage, the present model would probably underestimate spikelet sterility.

The limited availability of Tw data compared with Ta data is one of the major problems in the application of the current model based on Tp. The Tw is influenced by various climatic factors, the extent of the canopy cover, and the temperature of the water source, and is more site-specific than Ta. Several Tw–estimation models have been developed that estimate Tw using Penman's method (Inoue, 1985; Takami et al., 1989). Because these models include most of the factors that affect Tw, they can be used to estimate Tw in other areas and years, and could be combined with the present model to improve the prediction of spikelet sterility.

Another problem in application of the current model involves the estimation of growth stage. In testing the present model, we used the measured dates of the panicle-initiation stage and the heading stage, and thus excluded errors caused by estimation of the growth stage. For the practical use of the current model, it would be necessary to estimate the growth stage rather than actually measuring it. In a previous study, we developed a model that estimates growth stage based on Tw and that can simulate the effects of Tw on growth stage with an RMSD of 2.37 d (Shimono et al., 2001). We conducted a sensitivity analysis under scenarios that over- and underestimated heading date by 3 d from the measured date in 2003 (Data sets 15 to 23, using Model V). The 3-d overestimation of heading date increased RMSD from 11 to 26, and the 3-d underestimation increased RMSD to 15. For the practical use of the present model, the accuracy of predicting the growth stage must be improved to permit accurate prediction of spikelet sterility. The results must also be carefully analyzed to determine what proportions of the error are caused by the model of spikelet sterility and the model of growth stage.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
REFERENCES
 
We conclude from 4 yr of field data that spikelet sterility was determined by the combined effects of Ta, Tw, and water depth on Tp, and therefore these ambient environmental factors are adequately reflected by a model based on Tp. Our proposed model based on Tp, therefore, increased the accuracy of predicting spikelet sterility. The model thus offers a new approach to predicting spikelet sterility over wider areas and across years, and lets us account for the various climatic and management factors that affect spikelet sterility. In addition, it is well known that the fact of Tw being higher than Ta plays an important role in spikelet sterility (Sakai, 1949; Satake et al., 1988). However, evaluation of this relationship is not well quantified. The present model may thus be used to guide water management by farmers, to quantitatively analyze the causes of yield losses, and to predict yields before final harvest.


   ACKNOWLEDGMENTS
 
We thank Y. Numao and H. Tanno of the Hokkaido Prefectural Kamikawa Agricultural Experimental Station, and K. Tanaka of the Hokkaido Prefectural Central Agricultural Experimental Station for allowing us to use data of water temperature and spikelet sterility at Pippu, Iwamizawa and Ohno in Hokkaido. We also thank M. Yajima of National Agricultural Research Center for Tohoku Region for his demonstration of his program on differences in sensitivity of spikelet sterility to low temperature, M. Okada for his valuable comments for model analysis, and E. Kanda for giving the map of Japan. Thanks are due to N. Moki and S. Ichikawa of Hokkaido University for help with field experiments. The collaboration of H. Asaishi, A. Itoh, C. Kashiuchi, T. Nishimura, and M. Yamakawa of Hokkaido University are gratefully acknowledged. We wish to express sincere gratitude to Professor K. Iwama of Hokkaido University for his guidance and the critical reading of the manuscript. This study is a part of the doctor thesis of Hokkaido University. A grant-in-aid for scientific research (B) from the Japan Society for the Promotion of Science (Project no. 11460006) supported this study in part.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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H. Shimono, T. Hasegawa, and K. Iwama
Modeling the Effects of Water Temperature on Rice Growth and Yield under a Cool Climate: I. Model Development
Agron. J., September 10, 2007; 99(5): 1327 - 1337.
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