The values in the boxes are the numbers of stations. The three subregions: east monsoon region region 1 , northwest arid region region 2 , and the Qinghai—Tibetan Plateau region 3. CHN: mainland China. Region 1: east monsoon region; region 2: northwest arid region; region 3: Qinghai—Tibetan Plateau.
A schematic diagram of distribution of observational points in the day for the maximum and minimum temperature T max , T min , 4-time fixed intervals T 4 , and time fixed intervals T Relationship of annual mean T d with meteorological variables: a relative humidity, b wind speed, and c precipitation days; and geographical variable d altitude, in mainland China. Effect of data homogenization on temperature bias of the max—min average T d as estimated based on the same observational station network in mainland China.
Shown in the figure is the difference of country-averaged annual mean biases of the max—min average temperature between homogenized and nonhomogenized data. The systematic bias of the estimated average temperature using daily T max and T min records relative to the standard average temperature of four time-equidistant observations and its effect on the estimated trend of long-term temperature change have not been well understood.
This paper attempts to evaluate the systematic bias across mainland China using the daily data of national observational stations. The results revealed that the positive bias of annual mean temperature was large, reaching 0. Furthermore, the bias showed a significant upward trend in the past 50 years, with a rising rate of 0.
These results indicate that the customarily applied method to calculate daily and monthly mean temperature using T max and T min significantly overestimates the climatological mean and the long-term trend of surface air temperature in mainland China. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy www. Temperature is an indicator of thermal state that characterizes a warm or cold climatic condition and is one of the basic climatic variables.
Accurately estimating daily mean temperature, however, is affected by the observations and the statistical methods used for calculating average temperature. To understand the possible effect of current observational practices and statistical methods on daily and monthly mean temperature estimates, therefore, has important significance for both climatological and climate change research Brooks ; Edwards ; Tang and Ding Currently, the T max and T min are more frequently shared in the international exchange data, and usually the daily mean temperature can be obtained by averaging the maximum and minimum temperatures i.
Furthermore, several datasets of global land historical temperature primarily use the max—min average method to calculate the daily and monthly mean temperatures Lawrimore et al. According to the Specifications for Surface Meteorological Observation of the China Meteorological Administration CMA , however, it is stipulated that the daily mean temperature of the national meteorological stations be calculated based on the average of 4 temperatures recorded at , , , and Beijing time. This 4-time-observation average is the most frequently used average temperature in the national meteorological service and the scientific research works conducted in China Tang and Ren ; Ren ; Li and Yan ; Cao et al.
In the studies conducted by Brooks , Miller , and Edwards , it is shown that the annual and seasonal mean temperatures obtained using the max—min average method are generally higher than the mean temperatures estimated based on records at regular intervals like the 4-time-observation method.
Additionally, Tang and Ren and Tang and Ding compared the monthly and annual mean temperature obtained from the max—min average method versus the temperature obtained from averaging four regular observations for eastern China and concluded that the difference in the temperature anomaly series and the rate of temperature increase was not significant.
Moreover, Tang and Ren and Tang and Ding found that, when a large enough number of stations are used, the two methods were interchangeable. However, the research in China only used the observation data from a limited number of stations and focused on the influence of the estimation of temperature trends in the previous works; the systematic analysis of the error as calculated by using the max—min average method is lacking.
Some works have been focused on data homogenization and uncertainties e. Considering the inhomogeneities and uncertainties, however, the previous studies found, by using the monthly and annual mean temperature as an indicator, that global and regional climates had been in a significant warming trend IPCC ; Carrasco ; Osborn and Jones ; Kothawale et al. This warming is characterized by an asymmetry between the maximum and minimum temperatures Karl et al.
The following problems remained, however: 1 what is the difference between the temperatures obtained from the max—min average method and from the average of 4-time-observation per day at equal intervals? Finally, 3 how much does the bias affect the estimation for the trend of long-term temperature change? Currently, our understanding of these issues is insufficient both in China and around the world.
This study focuses on the three questions by taking China as an example. Using the observation data of daily and hourly temperature of the national reference climate and basic meteorological station network, the temperature bias in different regions and seasons, and its effect on the estimate of long-term change of temperature, was analyzed. The analysis results will provide new insights into the systematic errors of surface air temperature and its change as calculated from the max—min average method for studies of climatological and climate change.
To ensure the accuracy of the observation records at stations and to avoid the analysis bias caused by the short-term absence of measurements at individual stations, only data from stations with complete records and consecutive observations were retained.
Thus this study applied data of stations with complete records ranging from to The data were quality controlled but not homogenized for possible inhomogeneities induced by relocation and instrumentation. To examine the effect of homogenization on temperature bias and its trends, the homogenized data from monthly mean temperature based on 4-time observations Li et al.
The distribution of the annual and monthly mean temperature biases were analyzed using both the raw and the homogenized data. To understand the long-term trend of temperature change, the correlation coefficient i. This minimizes the effect of variance of meteorological variables and the unit on the numerical values of linear regression coefficients, and thus makes it easily comparable across geographical locations and suitable for studying the spatial characteristics of long-term trends of large-scale temperature change.
There were more stations distributed in the east than in the west. If regional average is calculated by simple arithmetic mean of all the sites with equal weights, then the data from the eastern region will outweigh that from the western region. To avoid this imbalance, the method by Jones and Hulme was utilized.
According to this method, the average regional climatic time series are calculated by using an area-weighted average procedure. The whole study region was divided into longitude—latitude boxes of 2. A total effective boxes with more than one station in each throughout mainland China was produced Fig. When calculating the national or regional average series, the arithmetic mean of the temperature recorded by the stations in each box was calculated first to obtain box averages; the cosine of the center latitude of each box was used as the weight coefficient and the regional average time series was then calculated by using the area-weighted average method.
Citation: Journal of Applied Meteorology and Climatology 58, 10; The study region is divided into three subregions referring to G. Ren et al. For the temperature analysis and the convenience of calculation, the boundaries of the three subregions were further simplified on basis of the previous studies Ding et al. To address whether T 4 could be used as a criterion or reference temperature for evaluating the temperature bias, we compared the h observation data T 24 of 3 stations located in northern China from east to west : Jixi, Beijing, and Urumqi stations.
The deviation of T 4 relative to T 24 Table 1 was calculated. T 24 is the daily mean temperature of h observations hourly means. The months January, April, July, and October were used as representatives for winter, spring, summer, and autumn, respectively.
Comparison of average difference between T 4 and T 24 at three meteorological stations of northern China Jixi, Beijing, Urumqi in The mean temperature values for T 4 and T 24 were calculated for ; there were certain differences in these values. The T 4 of Jixi station was lower than T 24 in summer, but higher than T 24 in other seasons.
The T 4 of Urumqi station was higher than T 24 in winter and lower than T 24 in other seasons. However, the biases of T 4 relative to T 24 were small overall, and the average annual mean absolute difference was well below 0. Therefore, the bias of the T mn can be evaluated using T 4 as a benchmark.
The reason for the applicability of the T 4 as standard to assess the uncertainty of T mn will further discussed below. The analysis period was from to The seasonal division was made using the definition of meteorological season. The seasonal mean temperature was calculated as the average of the 3 monthly mean temperatures in the season.
The annual mean temperature was calculated as the average across the 12 months. Decadal means were also calculated, where the first 10 years for decadal means ranged from to , and the fifth decade ranged from to The analysis results for annual and seasonal mean T d for the country and different regions are shown in Table 2. The T d values were positive in every season of every region of mainland China.
The national average annual mean T d was 0. The average T d was the highest in region 3 0. In all seasons, the average T d values in region 3 were the highest, with the maximum value in autumn 1. In spring and summer, the T d values of region 2 were the lowest 0. The annual and seasonal mean T d values of region 1 were close to the national averages.
The values of autumn and winter were relatively high, while the spring and summer were lower. T d values were positive in most parts of the country, indicating a universally higher average of the T mn than that of T 4 Fig. The areas with a high T d value were located in the eastern part of the Qinghai—Tibetan Plateau region 3 and the Sichuan basin and the Yunnan—Guizhou Plateaus, where T d was greater than 1.
The highest values were found at Malcolm of Sichuan 1. The T d values of regions 2 and 1 were relatively low less than 0. Only two stations in the whole study region showed a small negative T d i. All national average seasonal mean T d values were positive for each season, with the lowest value in the spring 0. The autumn mean T d value was the highest 0. The areas with high seasonal mean values were found in the eastern part of the Qinghai—Tibetan Plateau region 3 , where the autumn and winter mean T d was higher than those of other seasons 2.
Figure 4 shows the within-year variations in daily mean T d averaged for 30 years of — in mainland China and the three subregions. The daily mean T d series, starting from 1 January, experienced a decrease—increase—decrease variation within a year Fig. In late January, the T d value in region 3 was noticeably lower, while the T d values in region 1 and 2 did not notably decrease.
The T d values of region 1 and 2 rapidly decreased in mid-February and this decrease continued through mid- and late May. The T d value of region 3 stopped decreasing in late February to early March, when it began to slightly increase. This increase continued through late September when there was another noticeable decline. The T d values of region 1 and 2 rose at the beginning of June, peaked in early November, and then decreased. The T d of region 2 declined relatively quickly from April to May, showing a large fluctuation in the bias of T mn.
The T d of region 3 also showed a large fluctuation in February and December. It is also notable from Fig. The largest difference appeared between region 2 and region 3 from late April to early June, reaching 0. In addition, a larger variability of daily mean T d was obvious in region 2 during period of mid- to late April. From to , both annual mean T mn and T 4 in mainland China showed a significant upward trend, as shown in Fig. The temperature increase rate of annual mean T mn is 0.
It is also clear from Fig. Since the beginning of the twenty-first century, this increase has become more notable and the annual mean T d was higher than the average from to After , however, the T d underwent a slight decrease, but it rose again in with a historical maximum value 0.
The annual mean T d values of all 3 subregions were positive and exhibited significant upward trends from to Fig. The most apparent increase appeared in the twenty-first century, when all T d values were above the year average. The highest rising rate was in region 2 [0.
In contrast, the rising rate of T d in region 1 was lower [0. Figure 7 shows that, for each season, the T d value of region 3 was the highest, and the seasonal mean values were 0. In the summer, the T d value of region 3 was 0. All of the seasonal mean T d values in the three subregions and in the country as a whole showed upward trends during —, with the most obvious increases generally occurring after In the autumn, the T d value of region 3 was 0.
The possible causes for the accelerated increase in more recent years needs to be further examined, but it may have been related to the more widespread urbanization, which will result in a greater increase in T min in the north and in T max in the south Ren and Zhou , or the alleviated air pollution Wang and Yang ; Lowsen and Conway , which leads to a more rapid increase in T max.
The linear trend and significance test results of seasonal mean T d in different subregions and in mainland China on a whole are shown in Table 3. There was a significant increasing trend in annual and seasonal mean T d for the 3 regions and for mainland China as a whole, except for winter for region 1, region 2, and the whole region Table 3.
The maximum linear increasing trend was found for summer in region 1 and region 2, whereas in region 3, it appeared in spring. Linear trends and significance test results of annual and seasonal mean biases T d in mainland China and the three subregions — Therefore, there is certain bias of the daily and monthly mean temperature as calculated from the daily T max and T min records.
In this study, the magnitude and detailed spatial—temporal pattern of the bias, and in particular the trend of its long-term change, were analyzed with the mainland China as an example. The analysis revealed that the daily mean temperature value obtained from the max—min average method was warmer than the standard 4-time observation average. The national average annual mean T d reached 0.
The average T d of autumn and winter were even higher. The analysis results also showed that the annual and seasonal mean T d values exhibited a significant upward trend from to , with the rate of increase in mainland China average annual mean T d reaching 0. The trends of increase in three subregion average annual and seasonal mean T d was also significant, with the exception for winter.
Overall, the T mn average values were higher than the T 4 or T The two observational points are separated by only 8 h, with the records of and Beijing time in the T 4 absent Fig. They are therefore more affected by the daytime surface heat condition and especially the impact of the hottest afternoon period, but they escape in a larger extent from the effects of ground thermal conditions of nighttime when the surface air is colder than the daytime.
In the eastern part of northeast China and western China, the daily T max and T min occur slightly earlier or later than those in Beijing.
In western China, the T max and T min occur 3 h later at most than those in Beijing. The interval between the occurrence of the T max and T min does not increase. The impact of time difference between east and west of the country on T 4 and T 24 would be minor, because the four times of observations are made with an equal interval 6 and 1 h in a day. I understand to get two's complement of an integer, we first flip the bits and add one to it but I'm having hard time figuring out Tmax and Tmin?
In a 8-bit machine using two's compliment for signed integers how would I find the maximum and minimum integer values it can hold? The minimum value of a signed integer with n bits is found by making the most significant bit 1 and all the others 0. The maximum value of a signed integer with n bits is found by making the most significant bit 0 and all the others 1. Read about why this works at Wikipedia. Due to an overflow that would lead to a negative zero, the binary representation for the smallest signed integer using twos complement representation is usually a one bit for the sign, followed by all zero bits.
If you divide the values in an unsigned type into two groups, one group for negative and another positive, then you'll end up with two zeros a negative zero and a positive zero. This seems wasteful, so many have decided to give that a value. What value should it have? Well, it:. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams?
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