Responses of Irrigated Winter Wheat Yield in North China to Increased Temperature and Elevated CO2Concentration

TAN Kaiyan(谭凯炎),FANG Shibo(房世波),ZHOU Guangsheng(周广胜), REN Sanxue(任三学),and GUO Jianping(郭建平)

Chinese Academy of Meteorological Sciences,Beijing 100081

Responses of Irrigated Winter Wheat Yield in North China to Increased Temperature and Elevated CO2Concentration

TAN Kaiyan(谭凯炎),FANG Shibo(房世波),ZHOU Guangsheng∗(周广胜), REN Sanxue(任三学),and GUO Jianping(郭建平)

Chinese Academy of Meteorological Sciences,Beijing 100081

North China is one of the main regions of irrigated winter wheat production in China.Climate warming is apparent in this region,especially during the growing season of winter wheat.To understand how the yield of irrigated winter wheat in North China might be affected by climate warming and CO2concentration enrichment in future,a set of manipulative field experiments was conducted in a site in the North China Plain under increased temperature and elevated CO2concentration by using open top chambers and infrared radiator heaters.The results indicated that an average temperature increase of 1.7℃in the growing season with CO2concentration of 560µmolmol−1did not reduce the yield of irrigated winter wheat.The thousandkernel weight of winter wheat did not change significantly despite improvement in the filling rate,because the increased temperature shortened the duration of grain filling.The number of effective panicles and the grain number per ear of winter wheat did not show significant changes.There was a large increase in the shoot biomass because of the increase in stem number and plant height.Consequently,under the prescribed scenario of asymmetric temperature increases and elevated CO2concentration,the yield of irrigated winter wheat in North China is not likely to change significantly,but the harvest index of winter wheat is likely to be greatly reduced.

CO2enrichment,climate warming,winter wheat yield,open top chamber,infrared heating, combined impacts

1.Introduction

The impact of climate change on grain production and food security has become an important research topic.The increases in the atmospheric CO2concentration(hereafter referred to as[CO2])and the surface temperature are two key features of modern global change,which are expected to influence crop growth,development,and yield.Therefore,many manipulative experiments and crop simulation modeling studies have been carried out during recent decades to understand the responses of crop growth and yield to elevated[CO2]in the atmosphere and to climate warming.Previous experiments showed that increased [CO2]stimulated photosynthesis,inhibited respiration,and reduced water use in C3plants such as wheat(Kimball et al.,1995;Bai and Zhou,2004; Leakey et al.,2009).Meanwhile,elevation of[CO2] substantially increased their phytomass accumulation and yield(Wang et al.,1997;Amthor 2001;Yang et al.,2007),despite of the overestimated effects(Long et al.,2006).Conversely a temperature increase during the growing season of annualcrops facilitated their ontogenetic development,shortened growth stage,reduced chilling effects,and affected seed formation and yield(Xiao et al.,2010;Grant et al.,2011;Song and Zhao,2012;Tan et al.,2012;Tian et al.,2012;Fang et al.,2015),but the effects of temperature increaseon crop yield usually depend on the background climate conditions,geographical location,and magnitude of temperature rise(Grant et al.,2011;Tan et al.,2012).

So far few studies have been conducted to investigate the combined effects of elevated[CO2]and climate warming on crop growth and yield.Some manipulative experiments have examined the responses of crop growth and yield to the combination of elevated[CO2]and increased temperature(Batts et al., 1997;Wang,2001;Heinemann et al.,2006;Kim et al.,2007;Cheng et al.,2009;Matsunami et al.,2009; Yoon et al.,2009;de Oliveira et al.,2012;Roy et al., 2012),but most ofthem were conducted in glasshouselike facilities(Batts et al.,1997;Matsunami et al., 2009)and the day/night air temperatures were maintained at fixed values(Heinemann et al.,2006;Kim et al.,2007;Cheng et al.,2009;Yoon et al.,2009). In glasshouses or polyethylene-covered tunnels,temperatures increase more during the day than at night, which is inconsistent with the temperature increase trends from global warming.According to statistical analyses,global warming is characterized by an asymmetrical increase in daily maximum and minimum temperatures and a narrowing of the diurnal temperature range(Easterling et al.,1997;IPCC,2001).The results of these previous studies have contributed to exploration of influencing mechanisms and the interaction of elevated[CO2]and increased temperature, but cannot be relied on to reflect the effects of future scenarios of[CO2]and temperature on crop growth and yield.

Crop simulation models are often employed to predict the responses of crop growth and yield to increased temperature,elevated[CO2],precipitation variation,and their combined effects(Luo et al.,2005; Xiong et al.,2006;Krishnan et al.,2007;Ko et al., 2010;Lee et al.,2011;Tao and Zhang,2013),but predictions from different models are rarely in concordance(Asseng et al.,2013),and need to be validated by field experiments related to future climate scenarios.The influence of climate change on crops varies with the CO2emission scenarios,crop types,and regions(Supit et al.,2012).The results of field experiments under simulated climate change scenarios in the prescribed regions are the most direct basis for accurate understanding and evaluation of the influence of climate change on crops.Therefore,it is imperative to run field experiments to investigate the influences of prescribed future climate scenarios on crop growth and yield and to provide data for model verification under prescribed future climate scenarios.

North China is one of the main production areas of irrigated high-yield winter wheat in China.Climate warming is apparent in this region,especially during the growing season of winter wheat(CCNARCC, 2007).In past decades,the winter wheat phenology in North China exhibited obvious changes under current climate warming(Tao et al.,2012,2014),and increased temperature during growing season also improved winter wheat yield(Chen et al.,2014;Tao et al.,2014;Xiao and Tao,2014;Xiong et al.,2014). However,the trend of winter wheat yield in this region under future climate change remains uncertain, despite a lot of predictions of winter wheat yield in this area that have been published in terms of crop models(Li et al.,2010;Song et al.,2012;Tao and Zhang,2013;Yang et al.,2014).

In this study,manipulative field experiments ofirrigated winter wheat in North China were conducted during the entire growing season of winter wheat by using the combined technologies of open top chamber(OTC)and infrared radiator heaters.Environmental settings mimicked the increases in[CO2]and temperature predicted for the middle of the century for this region(Xu et al.,2005;CCNARCC,2007; IPCC,2007)and incorporated asymmetric increases in day and night temperatures(IPCC,2001;Ren et al.,2005).The aim of this research is to examine the responses ofgrowth and yield ofirrigated winter wheat in North China to a prescribed future climate scenario, as well as to be used for model verification.

2.Materials and methods

2.1 Experimental design

The experiments were conducted by using a group of OTCs at the Gucheng Ecometeorological Observa-tion Experiment Station,Chinese Academy of Meteorological Sciences(Dingxing County,Hebei Province, 39°08?N,115°40?E)from October 2010 to June 2012. The experiment station is located in the northern North China Plain and experiences a mean annual temperature of 11.7℃and mean annual precipitation of 551.5 mm.The soil is a typical cinnamon soil,with organic matter content of 10.3 g kg−1and total nitrogen content of 0.80 g kg−1.The air chambers were octagonal plastic-steel glass structures.Each chamber had a height of 2.5 m,an indoor area of 10 m2,and was ventilated by a 2000 m3h−1centrifugal fan at uniform speed through a PVC pipe system.

In the 2010-2011 season(from October 2010 to June 2011),three treatments were applied,namely the control(ambient[CO2]and air temperature,CK), the increased temperature treatment(ambient[CO2] and increased temperature,TI),and the combined treatment(elevated[CO2]and increased temperature, ECTI),and each treatment was replicated in two chambers.In terms of the possible scenario of CO2concentration and temperature in the middle of this century,as well as the asymmetric feature in day and night temperatures increase in study region,[CO2]of 560µmolmol−1and air temperature increase of 1℃in the daytime and 2-2.5℃at night were manipulated as the elevated[CO2]and increased temperature respectively in TI and ECTI.In the 2011-2012 season(from October 2011 to June 2012),the experiment focused on the combined influence of increased temperature and elevated[CO2]with two treatments,namely the control and the combined treatment,and each treatment was replicated three times.The[CO2]and temperature increases in the combined treatment were the same as in the 2010-2011 season.The increased temperature treatment commenced after the planting of winter wheat and the combined treatment(increased temperature and elevated[CO2])was applied after the reviving of winter wheat until the wheat ripened.

The CO2fumigation source in the chambers for the combined treatment was highly purified cylinder gas.The fumigation treatment was sustained from 26 February to 9 June 2011 and from 5 March to 10 June 2012.An infrared gas analyzer(QGS-08C; BAIF-Maihak,Beijing,China)was employed to monitor the[CO2]in the chambers and a rotor flow meter was used to adjust the gas transmission capacity in real time.The glass panel on the north face of the control air chamber was removed and a 25-cm opening was left at the bottom of the glass in both the east and west sides so as to eliminate the temperature increase effect caused by the air chamber itself. In the combined treatment air chambers,the passive warming effect was partially offset by the cooling effect of the ventilation system so that the temperature difference with the controlair chamber in the daytime was compliant with the experimental design requirements.At night time(2100-0700 BT),four infrared radiator heaters(600 W)installed on the top edges of each chamber increased the temperature in the chamber.The infrared heaters were positioned so as not to shade the crops.A temperature sensor and a humidity sensor with a naturally ventilated radiation shield were mounted at 50 cm above the ground in the center of each chamber and a data logger recorded the temperature and humidity readings at 10-min intervals.

Fig.1.Seasonal variations in average temperature during daytime and nighttime of 2010-2011 in the control and temperature increase treatments.TID:temperature increase treatment during daytime,CKD:control treatment during daytime,TIN:temperature increase treatment during nighttime,and CKN:control treatment during nighttime.

CO2enrichment and day-night asymmetric temperature increases during the experimentaltreatments were satisfactorily controlled(Fig.1 and Table 1). During the two experimentalseasons,the average temperature in the combined treatment air chamber was 1.7℃higher than that in the control air chamber, which was close to the projected temperature increase range in the experimental area by the middle of thecentury(Xu et al.,2005;CCNARCC,2007),and the extents of day and night temperature increase were compliant with the characteristics of asymmetric increased temperatures(Ren et al.,2005).Despite modifications to the control chambers to eliminate passive warming effects during the daytime,a daily temperature difference of 0.5±0.4℃existed between the control chambers and the ambient temperature in the two experimental seasons.The relative air humidity in chambers with increased temperature was slightly lower than in the control chambers,with average differences between them during overwintering,from reviving to booting and from booting to milky maturity of-5.3%,-2.0%,and-8.9%,respectively.

Direct sowing was adopted for the winter wheat in the chambers.Two hundred and seventy grams of seed of Jimai-22,a variety of semi-winter wheat, was sown in each chamber on 10 October in both 2010 and 2011.Unified management measures were applied in each chamber after sowing.Water supply was adequately maintained.Irrigation(100 mm in control plots and 120 mm in combined treatment plots)was applied at five time points during the growth of winter wheat(after planting,before overwintering,after reviving,during booting,and during grain filling),as per local practice.Precipitation during the two growing seasons(2010-2011 and 2011-2012)was 67.6 and 99.4 mm,respectively.The combined amount of irrigation and precipitation was enough to ensure that wheat plants did not suffer water stress,given the average water surface evaporation of nearly 750 mm during the winter wheat growing season in the experimental region.Base fertilizer(60-g m−2diammonium phosphate,N16:P2O545)was applied during sowing and 25-g m−2carbamide,and diammonium phosphate was applied after reviving.

2.2 Observations and methods

The observations were executed during the developmentalstages ofwinter wheat according to the Specifications for Agrometeorological Observation(State Meteorological Administration,1993).Ten plants from each chamber were sampled to measure plant height,stem,leaves,aboveground biomass,leaf area, and wheat ears.A leafarea meter(LI-3000A)was used to measure the leafarea.Dry matters were determined by weighing samples after drying under the constant temperature of 80℃in the oven for 48 h.Areas of 2 m2were sampled for grains from each chamber at ripening.After the grains were air dried,the following data were measured:total ear number,number of effective panicles,number of non-productive ears,grain yield,total dry matter weight,and thousand-kernel weight.Forty wheat ears were randomly selected to determine the number of kernels per ear.The harvest index was calculated as the ratio of the grain weight to the aboveground biomass in the 2-m2sample area.

Table 1.Observed[CO2]and temperature differences under different treatments

3.Results

3.1 Growth and biomass of irrigated winter wheat

The combined treatment had a marked influence on the growth of winter wheat compared with the control treatment(Figs.2 and 3,and Table 2).The growth rate under the combined treatment was higher than that under the control treatment,and the difference in dry biomass per plant between the control and the combined treatments increased continuously. The combined treatment reduced overwintering mortality,promoted tillering,and elevated plant height. Additionally,the combined treatment increased green leaf area per plant and reduced specific leaf area.At maturity,the dry matter weight per plant under the combined treatment was 17.4%higher than that under the control treatment(2012).At the same time, the total dry biomass of winter wheat per unit areaunder the combined treatment was 21%greater than that under the control treatment,indicating that the combined treatment dramatically promoted the accumulation of shoot biomass.

3.2 Grain filling

The combined treatment greatly affected the rate and duration of grain filling under the yield formation stage of winter wheat(Fig.4).The rapid filling stage lasted for about 20 days(5-25 May)under the combined treatment and the average thousand-kernel filling rate reached 1.88 g day−1during this period. Grain filling had ceased in the combined treatment by the beginning of June,which was about 10 days earlier in the controltreatment.Compared with the combined treatment,the filling rate in the control treatment was slower,the average filling rate for 20 days(15 May-4 June)with the highest filling intensity was 1.72 g day−1,and the duration of grain filling was longer. According to the observation of developmental stages, flowering began on April29 in the combined treatment and on May 6 in the control,thus the filling duration in the combined treatment was 3-5 days shorter than that in the control.As a result of the effects of increased temperature and elevated[CO2]on rate andduration of grain filling,the thousand-kernel weight of winter wheat was not significantly affected by the combined treatment.

Fig.2.Effects of elevated[CO2]and temperature on aboveground dry biomass of winter wheat plants,expressed as dry matter per plant(g)in 2012.

Fig.3.As in Fig.2,but for 2011.As there were two replicates for each treatment,analysis of variance was not done.

Table 2.Effects of the combined treatment on population,tiller number,green leaf area,specific leaf area,plant height,and total dry matter

Fig.4.Effects of the combined treatments on the progress and rate of winter wheat grain filling in 2012.

3.3 Developmental stages of winter wheat

Increased temperature accelerated the development of winter wheat before winter,and caused the tillering stage to occur 3 days earlier than in the control treatment(Table 3).The effect of increased temperature on the reviving stage was more notable.The developmentalstages ofwinter wheat after winter were brought forward as a whole and the ripeness stage occurred 6-7 days earlier than in the control treatment. The main change in phenology of winter wheat under the increased temperature treatment was that the duration of the winter dormancy stage was obviously shortened.The duration from reviving to ripeness was not significantly influenced.The average temperatures in the two treatments during the growing periods were given in Table 4,which showed that the average temperature in the increased temperature treatment during the post-reviving stages did not increase as expected.In comparison with the effects of increased temperature,elevated[CO2]in the combined treatment had almost no effect on the development period. As a result,the combined effects of elevated[CO2] and increased temperature on the development period of winter wheat can be mainly attributed to the influence of increased temperature.

3.4 Grain yield and its components

The combined treatment of elevated[CO2]and asymmetrically increased day/night temperature during the whole growing season had no significant effect on winter wheat yield and its components compared with the control treatment(Table 5).The grain weight per unit area increased slightly(+3.7%)compared with the control treatment,but the difference was not statistically significant(p=0.26).The results from the experiment in 2011 suggested that the effects of warming on grain yield were negative(Table 6),but that the fertilization effect of CO2enrichment in combined treatment compensated for the negative effect of increased temperature on winter wheat yield.Comparison of winter wheat yields in the control between the two years showed that the interannual fluctuation in yield was greater than the changes caused by the combined treatment owing to different weather conditions during the growing seasons.

The combined treatment increased the number of effective panicles compared with the control treatment by 8.7%(2010-2011)and 6.6%(2011-2012).The thousand-kernel weight increased slightly under the combined treatment compared with the control treatment.The effects of the combined treatment on both the number of effective panicles and the thousandkernelweight were not significant when compared with the control treatment.Furthermore,the combinedtreatment had little influence on grain numbers per ear.

Table 3.Effects of increased temperature and elevated[CO2]on winter wheat developmental stages(2010-2011, day/month)

Table 4.Average temperature(℃)in control treatment and combined treatment chambers during different developmental stages

The combined treatment reduced the harvest index(Table 7)of winter wheat.The combination of elevated[CO2]and increased temperature stimulated tillering of winter wheat,reduced overwintering mortality,and increased the total number of stems and ears per unit area and the percentage of nonproductive wheat ears.Although the grain yield of winter wheat in the combined treatment changed little compared with the control,the total shoot biomass of winter wheat increased significantly.

Table 5.Effects of the combined treatment on yield and yield components of winter wheat in 2012

Table 6.Comparison of the effects of increased temperature and the combined treatment on grain yield and yield components of winter wheat in 2011*

Table 7.Impact of the combined treatment on the harvest index of winter wheat

4.Discussion

Evidence suggests that elevated[CO2]decreases the stomatal conductance and transpiration rate of crop leaves,which leads to increases in leaf temperature,accelerates individual development,and shortens the growth period(Kimball et al.,1995;Wang et al.,1997;Streck,2005).Nonetheless,some studies also indicated that elevated[CO2]exerted little influence on winter wheat developmental stages(Batts et al.,1997;Yang et al.,2007).This study found that the effect of elevated[CO2]on developmental stages of winter wheat was negligible compared with the effect of increased temperature in the combined treatment,which might mean that the magnitude of increase in leaf temperature due to elevated[CO2]is much less than the extent of air temperature increase in the combined chambers.This result was in agreement with the conclusion of an experiment on an annualweed(Lee,2011).Conversely,increased temperatures generally facilitate the ontogenetic development rate in annual plants(including most grain crops)and markedly shorten their key growth stages(Morison and Lawlor,1999).This experiment suggested that the most important effect of increased temperature throughout the growing season on the phenology of winter wheat was the significant advance in the reviving stage,but the duration of post-reviving growth was not shortened except for the grain filling period. The winter wheat sown in autumn in North China underwent winter dormancy during the growing season.Increased temperature significantly shortened the duration of overwintering,shifting forward the subse-quent growing periods,but the average temperature of the post-reviving stages did not increase as expected (Table 4).This result confirms the conclusion of a warming experiment with a temperature rise of 2℃conducted by using winter wheat in North China(Tan et al.,2012),and is also in agreement with the findings of a similar experiment conducted by using an annual weed(Lee,2011).

Previous experiments indicate that elevated [CO2]hastened photosynthesis and reduced transpiration of winter wheat(Kimball et al.,1995;Bai and Zhou,2004;Leakey et al.,2009),leading to increasing phytomass accumulation,yield,and water-use efficiency.The effects ofwarming were more complicated. Increased temperature might exert impacts on CO2fixation,respiration,evapotranspiration,phenology, and seed set of winter wheat,but the effects depend on the background temperature conditions(Morison and Lawlor,1999;Grant et al.,2011).Data from Baoding Meteorological Station(40 km away from this experimental field)showed that in the winter wheat growing seasons of 2010-2011 and 2011-2012,the atmospheric temperature anomaly before reviving was negative,but the average temperature in the postreviving stages approached or was slightly higher than the climate average value.Therefore,in this experiment,increased temperature before reviving(Table 4)accelerated phytomass accumulation and tillering, and reduced overwintering mortality,as reported in Tan et al.(2012).From reviving to booting the average temperature in combined chambers was a little lower than in the control owing to the early commencement ofgrowth stages,thus in this period the increased temperature treatment exerted little effect on growth and phenology of winter wheat.This finding is quite different from the results of a controlled experiment with higher temperature in spring only(Fang et al.,2010),where the increased temperature treatment, commenced after the reviving stage,accelerated plant development and shortened growth stages,dramatically reducing grain numbers per ear and thousandkernel weight.From flowering to ripeness,the average temperature in the combined treatment chambers was a little higher than in the control,which caused more frequent appearance of extreme high temperatures at midday in the later grain filling stage and shortened the duration of grain filling,partially offsetting the positive effects of elevated[CO2]on thousand-kernel weight(¨Ozdo˘gan,2011).

Under the combined treatment of elevated[CO2] and increased temperature,shoot biomass significantly increased but grain yields changed little,and as a result the harvest index significantly decreased compared with the control.In the late-growth stages,the high density of stems caused by both elevated[CO2] and increased temperature intensified internal competition in the population,which led to a reduction in the percentage of ear bearing tillers and an increase in the number of non-productive ears,especially under limited nutrient application(Cui et al.,2011).

During the experiment,heating caused some reduction in relative air humidity and thereby increased evapotranspiration in the combined treatment chambers.The increase in evapotranspiration did not induce drought stress in wheat plants because ample water was supplied by the supplemental irrigation to compensate for the increase in evapotranspiration caused by infrared heating(Kimball,2005)and elevated[CO2]partly compensated for the water shortage (Amthor,2001).The experiment with asymmetrically increased day and night temperatures mitigated the impacts of the temperature increase,especially during the filling stage.Related experiments(Fang et al., 2012)and models(Cynthia and Tubiello,1996)also reported that the negative effects of an asymmetrical increase in day/night temperatures on winter wheat yield were less than that ofequally increased day/night temperatures.

Although elevated[CO2]tended to improve winter wheat yield(Amthor,2001),the effect of increased temperature on wheat yield depends on the specific region and the climate condition of the experiment (Grant et al.,2011).In a field experiment on the effects of infrared heating on winter wheat in eastern China,increased temperature inhanced the average grain yield by 16.3%(Tian et al.,2012),whereas,in a similar experiment on winter wheat in North China, the yield of winter wheat decreased in a warmer grow-ing season,but increased in a colder growing season (Tan et al.,2012).Consequently,in different regions and under different climate conditions,the results for the combined treatment of elevated[CO2]and increased temperature would be expected to vary.The experimental results obtained in these two years reflected the effects of the combined treatment under a normalor warmer climate background during the main growing season of winter wheat.Although there is a lack of experimental data on the combined treatment effect obtained in a cold climate,based on the results ofa warming experiment conducted under cold climate conditions at the same site(Tan et al.,2012),it can be predicted that the grain yield of winter wheat is likely to increase in colder years under the combined impacts of elevation of[CO2]to 560µmolmol−1and a temperature increase of 1.7℃.Hence,excluding the effects of other factors and extreme weather conditions, a moderate temperature increase and[CO2]enrichment will not lead to a significant decline in irrigated winter wheat yield in the study region.This finding is consistent with those modeling trends of irrigated winter wheat yield in the same area under prescribed future climate scenario(Liu et al.,2010;L¨u et al., 2013;Tao and Zhang,2013).

This study examined the potential effects of increased temperature and elevated[CO2]on the growth and yield of irrigated winter wheat in North China under a predicted scenario of future climate change. However,there are many uncertainties in future climate change scenarios;the responses of crop yield to climate change depend on the magnitude of climate change and crop yield may drop sharply when the temperature increases beyond a certain threshold value.Apart from temperature and[CO2],other global change factors such as precipitation,radiation and O3also affect winter wheat yield(Amthor,2001; Zhu et al.,2011;Zheng et al.,2013).Crop varieties and cultivation practices may alter in the future. The adoption of more efficient management measures may mitigate some of the adverse effects of climate change.For instance,reduction of the sowing density in warmer years can help to avoid overpopulation and improve canopy structure.At the same time,the combined effects of temperature increase and[CO2] enrichment on winter wheat vary under different growing season conditions.To gain a comprehensive understanding of the effects of climate change on the growth and yield of winter wheat,more studies with elevated [CO2]and temperature are urgently required.

5.Conclusions

Under the combined treatment of asymmetric temperature increases and elevated[CO2],the number of wheat stems and ears increased,the shoot biomass increased significantly,and the number of effective panicles slightly increased,when compared with the control treatment.The positive and negative effects of the combined treatment on thousand-kernel weight appeared to be more or less balanced out. The combined treatment exerted little influence on the grain number per ear.In the experimental area, assuming that other factors remained unchanged,if [CO2]increased to 560µmol mol−1by the middle of the century and the average temperature increased (with asymmetric day/night temperature increases) by about 1.7℃during the growing season,the yield of winter wheat would not be lower than the present level,but the harvest index of winter wheat would be greatly reduced.

Acknowledgments.The authors would like to thank the staff of the Gucheng Ecology and Agrometeorology Experiment Station,Chinese Academy of Meteorological Sciences,for their assistance with the experiments.

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Supported by the National Natural Science Foundation of China(41075085 and 41375118)and National(Key)Basic Research and Development(973)Program of China(2010CB951303).

∗gszhou@cams.cma.gov.cn.

©The Chinese Meteorological Society and Springer-Verlag Berlin Heidelberg 2015

January 13,2015;in final form March 23,2015)