Development of a Winter Abnormal Cold Climate Index and Its Influencing Factors


 The prediction of extreme weather and climate events is a difficulty in the field of climate prediction. In practice, seasonal and monthly mean temperature has been used as the climate prediction index. However, the mean temperature forecast on seasonal and annual time scales cannot truly reflect the real climate situation as the mean temperature on a certain time scale smoothes abnormal cold and warm climate events. For instance, an abnormal cold climate event may occur even if the winter mean temperature is forecasted to be normal in a certain year. An abnormal warm climate event may also occur at the same time. Both affect the accuracy of climate prediction. Based on extreme weather events, this paper constructs a winter abnormal cold climate index, named WACCI, to represent the characteristics of extremely low temperature events. The index is composed of three factors, including cold duration, extremely cold temperature anomaly, and temperature cumulative anomaly. Taking Heilongjiang Province in China as the study area, relationships between WACCI and winter mean temperature, atmospheric circulation, and sea surface temperature (SST) are analyzed and compared. The analysis shows that the polar and mid-high latitude circulations have a significant impact on WACCI. The meridional circulation is dominant in the mid-high latitudes of Eurasia when the polar vortex area in the Northern Hemisphere is large, the intensity of the polar vortex is weak, and the polar vortex splits southward. Additionally, the intensity of the East Asian trough is strong and arctic oscillation (AO) is in an abnormal negative phase, which tends to result in a large WACCI. According to those atmospheric circulation factors, the regional and even global abnormal cold climate can be predicted in practice instead of using the prediction of winter mean temperature. The abnormal cold climate index proposed in this paper provides a new way for the extreme climate event occurrence trend, mechanism research, and short-term climate prediction (i.e., monthly or seasonal).


35
Under the background of global warming, there are various types of short-term and regional abnormal 36 changes in the global climate system. In recent years, regional low temperature extreme events (RELTEs) 37 occur frequently in the Northern Hemisphere with large impact range and long duration.  Brown, 1992). At present, the prediction of long-term temperature change on seasonal and annual scales is 43 mainly based on the seasonal and annual mean temperature which, however, can only reflect the average 44 situation in a certain period. If there are strong low and high temperature extreme events in this period, the 45 mean temperature would smooth out the extreme temperature signal. Therefore, the mean temperature cannot 46 truly reflect the occurrence of extreme climate events. There are many past studies on the detection, diagnosis, 47 and analysis of extreme climate events in China and abroad (Alexander et Wang and Ding, 2006). Nevertheless, the prediction of extreme 49 climate events is still weak, especially for the seasonal and annual low temperature extreme events with long 50 time scales. Meanwhile, the atmospheric circulation situation of cold and warm extreme events are different in 51 the atmospheric circulation system. If the mean temperature is taken as the prediction index of extreme climate 52 events, two possibly opposite atmospheric circulation index signals would be mixed and make it difficult to 53 reveal the mechanism of atmospheric circulation affecting extreme climate events. Hence, if an abnormal 54 extreme climate index could be constructed to separate low temperature extreme events from high temperature 55 extreme events, it should realize the forecast and prediction of extreme climate events and promote the 56 progress of climate operations. Furthermore, it should be able to objectively reflect the distribution and change 57 of extreme climate events and reveal the occurrence mechanism of extreme climate events. 58 An extreme climate event refers to the occurrence of an abnormal climate variable value which is higher 59 ( the daily maximum temperature is higher than 35°C, it is defined as a high temperature extreme event. If the 66 daily minimum temperature is lower than 0°C, it is defined as a low temperature extreme event. The percentile 67 method is defined relative to the percentile critical values of the local climate state, that is, the small 68 probability events counted from the perspective of probability distribution (Bonsal et al., 2001). To be specific, 69 this method is to arrange the mean temperature of a certain period in an ascending order and take the 90th and 70 10th percentiles as the threshold values of extreme temperature events. If the temperature is greater than the 71 90th percentile value, it is considered that there is a high temperature extreme event in that year. If it is less 72 than the 10th percentile value, it is considered that there is a low temperature extreme event in that year. Last 73 but not least, the standard deviation method uses the standard deviation of ±n times of the mean value of 74 regional temperature to determine the threshold value. The value of n depends on the distribution of specific 75 values (Qian et al., 2007). The three methods have a common feature where they all can diagnose the 76 frequency of extreme temperature events but cannot express the degree of extreme temperature events. 77 Therefore, in addition to frequency, the abnormal extreme climate index should include the degree of abnormal 78 extreme climate events. 79 The paper constructs a comprehensive extreme climate event based on the frequency and degree of 80 extreme weather events. The extreme cold climate events are separated from the extreme warm climate events. 81 The seasonal scale is defined to represent the WACCI of winter low temperature extreme events. Besides, the 82 paper analyzes the long-term change trend of low temperature extreme event index, reveals the impact 83 mechanism of atmospheric circulation factors and external forcing of SST on the index, provides a new idea to 84 realize monthly and seasonal short-term climate prediction, and promotes the climate prediction operations. 85 Also, the paper provides a new method to study the distribution and change trend of extreme climate events 86 under the background of climate change and to reveal its mechanism. Moreover, the paper illustrates the 87 advantage of WACCI, taking Heilongjiang Province in China as an example. northerly territory of the country (Fig. 1

Construction of WACCI 150
In the paper, the cold duration days ( , d), extremely cold temperature anomaly (tm, °C), and temperature 151 cumulative anomaly (ta, °C) were selected to construct the WACCI.

152
(1) Determination method of cold duration days ( ) in a certain year: was based on historical long 153 sequences of daily temperature data. First, the standard deviation method was used to select the winter 154 abnormal cold climate events in Heilongjiang Province. Next, the accumulated days of winter abnormal cold 155 climate events were calculated. The specific method was to calculate the daily mean temperature and standard 156 deviation of the historically recorded daily mean temperature sequences (from 1961 to 2018 in the paper). The 157 mean value was subtracted from daily temperature values in order to obtain the anomaly sequence (Δt) and 158 calculate the sequence standard deviation (σ). In the sequence, an abnormal cold climate event was defined if 159 the negative anomaly was more than 1 time of standard deviation (Δt > σ) in the daily mean temperature 160 anomaly sequence for 5 consecutive days. If there were multiple winter abnormal cold climate events in a 161 certain year, the accumulated days of all abnormal cold climate events were calculated. If there was no 162 abnormal cold climate event, the one with the longest duration of negative daily temperature anomaly was 163 selected as the general cold climate event and the duration days were calculated. Lastly, the duration was 0 if 164 the winter mean daily temperature anomaly was positive.

165
(2) Determination method of extremely cold temperature anomaly tm in a certain year: In winter abnormal 166 cold climate events in a certain year, the temperature anomaly on the day with the lowest daily temperature 167 was selected as the extremely cold temperature anomaly. If there was no winter abnormal cold climate event, 168 the temperature anomaly was calculated on the day when the temperature was the lowest in the same period of 169 history and was defined as an extremely cold temperature anomaly. Lastly, the term was 0 if the winter mean 170 daily temperature anomaly of a certain year was positive.

171
(3) Determination method of temperature cumulative anomaly ta in a certain year: The temperature 172 cumulative anomaly of all the days in a winter abnormal cold climate event was calculated. If there was no 173 winter abnormal cold climate event, the days of a general cold climate event were selected to calculate the 174 temperature cumulative anomaly. The term was 0 if the winter daily temperature anomaly was positive. 175 St, Stm, and Sta were obtained after standardizing , tm, and ta. The WACCI was constructed as follows: 176 (3) 177 It can be seen from Equation (3)   North Pacific and Ural Mountains had a negative correlation between 40°N and 60°N. The majority of the 230 regional correlation coefficients passed the significance test (P < 0.05). The analysis explained that the 231 intensity of the polar vortex center was weak when the positive altitude anomaly occurred at 500 hPa in the 232

Relationship between WACCI and atmospheric circulation field
Arctic. The polar vortex center was easy to split southward, which led to the anomaly distribution pattern of 233 "positive in the North and negative in the South" in the height field. At this time, frequent cold air activities 234 easily resulted in strong cooling in Heilongjiang Province. 235 Fig. 4(b) shows the distribution of correlation coefficients between winter mean temperature and 500 hPa 236 height field in the same period. The correlation between the distribution characteristics and WACCI was 237 consistent in the mid-high latitudes. However, the correlation coefficients in subtropical low latitudes were 238 quite different than those in Fig. 4(a), i.e., the correlation between the winter mean temperature and most 239 regions north of the equator passed the significance test (P < 0.05). This result indicated that the low latitude 240 system also had an impact on the temperature, in addition to the mid-high latitude circulation system. However, 241 the low latitude system had small impact on WACCI. Therefore, compared with winter mean temperature, 242 factors affecting the WACCI were fewer and WACCI prediction is less difficult. Siberian high, though East Asia is far away from the north pole. In terms of dynamic mechanism, when the AO 252 phase was positive, the polar vortex was strengthened and the westerly belt in the middle latitudes was 253 strengthened and northerly. The cold air was confined in the polar region, which was easy to cause a warm 254 winter in East Asia. When the AO phase was negative, the corresponding polar vortex weakened and the 255 westerly belt in the middle latitudes weakened and moved southward. The Arctic cold air easily erupted 256 southward, affecting North America, Europe, and Asia. 257 It can be seen from Fig. 5 that WACCI and AO had a significant negative correlation. The correlation 258 coefficient was −0.61 (P < 0.01). AO was significantly in the negative phase and WACCI was in a strong stage 259 from the 1960s to the middle and late 1980s. From the middle and late 1980s to the end of 1990s, AO was 260 mainly in the positive phase while WACCI correspondingly appeared in a weak stage. After the 21st century, 261 AO fluctuated significantly. There was a reverse relationship between WACCI and AO in 15 a of the total 19 a 262 from 2000 to 2018. It can be seen that the variation of the mid-high latitude circulation system was an essential 263 factor affecting WACCI in Heilongjiang Province. When AO was in the negative (positive) phase, the 264 distribution pattern of geopotential height field in the mid-high latitudes of the Northern Hemisphere was the 265 opposite. That is, the polar region was positive (negative) and negative (positive) height anomaly occurred 266 from the south of the polar region to the subtropical zone. This distribution pattern was beneficial (unfavorable) 267 to the transportation of cold air to Heilongjiang Province, which led to the occurrence (no occurrence) of 268 abnormal cold climate events. 269 The relationship between WACCI, winter mean daily temperature, and AO was further compared. The 270 AO was divided into strong and weak degrees. AOs greater than 1 (less than −1) were marked as abnormal 271 positive (negative) phase and the rest were normal positive (negative) phase. From 1961 to 2018, there were 8 272 a with the abnormal positive phase of AO. In the 8 a, WACCI was less than −2 for 6 a while the winter mean 273 temperature anomaly was more than 2°C for only 3 a. There were 14 a with the abnormal negative phase of 274 AO. In the 14 a, WACCI was greater than 2 for 6 a while the winter mean temperature anomaly was less than 275 −2°C for 8 a. It can be seen that when AO appeared in the abnormal positive phase, its indicative significance 276 for WACCI was stronger than that for winter temperature. In the special six years (1989, 1982, 2005, 2011, 1999, and 1972) that had large differences between WACCI and temperature anomaly, both AO and WACCI 278 showed a significant reverse relationship in 2011, 1999, and 1972. Specifically, AO was positive while 279 WACCI was negative, which further indicated that the positive phase of AO had a strong indicative 280 significance for the negative WACCI.  respectively. In addition, the correlation coefficients between winter mean temperature and four indices were 290 −0.48, −0.34, 0.57, and 0.48, respectively. It can be seen that the correlation between WACCI and the polar 291 vortex area index and the polar vortex center intensity index was better than that of temperature. The 292 correlation between temperature and Eurasian zonal circulation index was stronger than that of WACCI. 293

Relationship comparison between WACCI and the atmospheric circulation indexs
Moreover, correlations between the East Asian trough intensity index and WACCI and temperature were 294 similar. From the perspective of physical mechanism, when the polar vortex area in the Northern Hemisphere 295 was large, the polar vortex center intensity was weak, the meridional circulation was dominant in the mid-high 296 latitudes of Eurasia, and the intensity of East Asian trough was strong. As a result, it was conducive to a large 297 WACCI. Specifically, when the polar region was controlled by positive height anomaly, the polar vortex 298 intensity was weak and the polar vortex split southward. At this time, the meridional circulation appeared in 299 the mid-high latitudes of Eurasia and the East Asian trough was significantly established. Heilongjiang 300 Province was located behind the ridge front trough and controlled by the northwest airflow, which were 301 conducive to the transportation of cold air to Heilongjiang Province. Consequently, it caused strong abnormal 302 cold climate events and made WACCI large. Hence, the corresponding relationship between WACCI and 303 atmospheric circulation index was better than that of mean temperature. 304 The responses of WACCI and winter temperature to the above circulation indices (the polar vortex area 305 index in the Northern Hemisphere, the polar vortex center intensity index in the Northern Hemisphere, the 306 zonal circulation index in Eurasia, and the East Asian trough intensity index) were analyzed by using specific 307 examples. As shown in Table 1, except for the East Asian trough intensity index, the corresponding 308 relationships between WACCI and the other three factors in abnormal years were better than that of winter 309 temperature. Through the analysis of special years (1989, 1982, 2005, 2011, 1999, and 1972), it was found that 310 the polar vortex area index in the Northern Hemisphere corresponded to WACCI for 5 a in those 6 a. 311 Furthermore, the corresponding relationship was better than that of winter temperature. 312

Relationship comparison between WACCI and SST field 315
The correlation coefficients of WACCI, winter mean temperature, and moving mean SST field every 316 three months in the previous year (starting from December last year, December to February, January to April, 317 and so on) were calculated. The correlation coefficient of WACCI, winter temperature, and mean SST field in 318 summer (June to August) was the highest. Fig. 6 shows regions where the correlation coefficients were 319 significant for WACCI, winter temperature, and summer mean SST field. It can be seen that WACCI was 320 negatively correlated with summer mean SST field. Winter mean temperature was positively correlated with 321 summer mean SST field.Meanwhile, the spatial distribution of the correlation coefficients was also different. 322 As shown in Fig. 6(a), regions of good correlation with WACCI (P < 0.01) were located in the South Pacific, 323 the West Pacific warm pool to the offshore China, and sea waters of Northwest Australia. Fig. 6(b) shows that 324 regions of good correlation between winter temperature and summer SST were also located in the South 325 Pacific, Northwest Pacific, and offshore China. In addition, there were high correlation regions in waters of 326 North Australia and East Indian Ocean. The greatest difference occurred in the Indian Ocean, comparing the 327 two figures. Compared with the two charts, the biggest difference of correlation coefficient is in the Indian 328 Ocean area. The correlation coefficient between the Indian Ocean SST and WACCI in the Indian Ocean area is 329 greater than that with winter average temperature. 330 In Fig. 6(a), 330 grids with negative correlation between summer mean SST and WACCI and passing 331 99% significance test were selected. Besides, the key SST index (KSI) with significant impact on WACCI was 332 calculated. The correlation coefficient between KSI and WACCI was −0.49 (P < 0.01). In Fig. 5(b), 330 grids 333 with negative correlation between summer mean SST and winter mean temperature passed the 99% 334 significance test. The correlation coefficient between KSI and winter mean temperature was −0.49 (P < 0.01). 335 Therefore it can be seen that the relationship between wacci and mean sea surface temperature in summer is 336 greater. 337 Based on the analysis of the special years (1989, 1982, 2005, 2011, 1999, and 1972), the corresponding 338 relationship between KSI and WACCI was consistent in 5 a out of 6 a. There was only 1 a when KSI was 339 consistent with the winter temperature anomaly. It revealed that the impact of KSI on WACCI was better than 340 that of winter temperature. For most years, the abnormally low summer key SST was significantly 341 corresponding to the high WACCI in Heilongjiang Province. 342  SST on the weather and climate process. WACCI is more predictive than mean temperature and the prediction 363 mechanism description is more convincing than that of mean temperature. Moreover, the accuracy of 364 prediction results may be relatively high. This is a new idea to promote the improvement of short-term climate 365 prediction ability. 366 3) Based on the WACCI proposed in the paper, the abnormal warm climate index can be constructed to 367 represent the intensity of abnormal warm climate events. Thus, the mixed cold and warm states can be 368 separated to further reveal the characteristics of temperature variation in the local area. Meanwhile, the 369 WACCI proposed in the paper can improve the prediction accuracy of extreme climate events. This research 370 idea can not only be applied to climate prediction, but also has positive significance for the analysis of extreme 371 weather and climate events. Separating the extreme events from the mean value can clearly demonstrate the 372 real spatiotemporal evolution trend of the extreme weather and climate process. 373 4) The study suggests that the two extremes can be separated in the process of monthly, seasonal, or any 374 time scale mean temperature. The monthly, seasonal, or any time scale index describing the extreme of the 375 predicted object can each be constructed. Then, the mean state or total amount is predicted based on the 376 forecast of those two indices. This research concept can be extended to other abnormal climate factor events 377 and used in the analysis and prediction of other abnormal extreme events such as abnormal precipitation events 378 and abnormal wind events. 379 7 CONCLUSIONS 380 1) WACCI is constructed, which consists of three factors including the winter cold duration days, the 381 extremely cold temperature anomaly, and the temperature cumulative anomaly. 382 2) The decreasing rate of WACCI was 0.56/10 a from 1961 to 2018, which was higher than the winter 383 warming rate (0.258/10 a) in the province. It indicates that the accelerated reduction of severe abnormal cold 384 climate events has made a principal contribution to the winter warming in the province. 385 3) Only the mid-high latitudes are correlated to WACCI in the correlation diagram of 500 hPa height field, 386 which are less than those regions correlated to temperature. The prediction effect of WACCI is better than that 387 of temperature. When AO appears in the abnormal positive phase, WACCI corresponds to more abnormal 388 years than that of temperature. At the same time, the correlation between WACCI and AO is better than that of 389 winter mean temperature. In the special years when the difference between WACCI and winter temperature is 390 large, the relationship between the polar vortex area index in the Northern Hemisphere and WACCI is better