2.1 Data sources

Several data sources are used in the study. The observed sub-daily SAT records and the associated metadata of Qingdao (1899–1913; Table 1) have been archived by DWD. Note that these SAT records from 1905 to 1914 have a high temporal resolution of 24 records for each day. The homogenized monthly SAT of Qingdao station (WMO station number is 54857) from 1961 to 2013 is selected from CMA, which has developed the first national homogenized temperature dataset (Li and Yan, 2009) and its updated version (Xu et al., 2013). Moreover, three gridded SAT datasets with high spatial resolution starting from the late 19th century have been used in the construction: (1) the monthly mean SAT from the global precipitation and temperature of Willmott and Matsuura, which is developed in the Department of Geography, University of Delaware (referred to as SAT W&M v4.01; Willmott and Matsuura, 2012); (2) the monthly mean SAT data of the Climatic Research Unit (Harris et al., 2013; referred as CRU TS3.230); and (3) the monthly mean SAT data of the 20th Century Reanalysis version 2c (referred to as 20CR v2c; Compo, et al., 2011). More details about the three datasets are shown in Table 2.

Table 1Coordinates, heights and daily observation times of Qingdao and Schatsykou in the earlier time.

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Table 2Three gridded SAT datasets that are used in this study.

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2.2 Testing for significance of correlations and trends

When we test the significance of correlation between two time series and the significance of the presence of trends in a time series, an important question needs to be considered, that is, how large sample correlations and sample trends could be, even if the stochastic processes, which generate the series, are not correlated at all and exhibit no trends. Firstly, we have to make an assumption, namely the processes X and Y share no correlation, or segments of length L of the process have no trend. Standard procedures are available in the literature, namely p value for correlations and Mann–Kendall for trends (e.g., Kulkarni and von Storch, 1995; von Storch and Zwiers, 1999) that there are “no correlations” between the underlying processes and trends can hardly appear in limited segments of an infinite stationary time series.

In the case of correlations, the assumption is that the underlying processes are stationary (free of systematic trends) and serially independent, i.e., X_t and X_t+1 for any t are independent. In the case of trends, the assumption is the independence of $X_t^{\prime }$. However, in geophysical cases, these assumptions are not satisfied – the result is that the null hypotheses are often falsely rejected (i.e., in cases where there are no correlations or no trends; cf. Kulkarni and von Storch, 1995) than stipulated by the significance level (normally 5 %).

A practical remedy for avoiding such errors is to deal with normalized series (mean = 0, standard deviation = 1) $X_t^{\prime }$ (and $Y_t^{\prime }$) as follows:

• 1.

  “detrend” the time series before testing for correlations between two time series X_t and Y_t. Firstly, determining the linear fit $f_t^X$ and $f_t^Y$, and then do the hypothesis testing with $X_t^{\prime }=X_t-f_t^X$ and $Y_t^{\prime }=Y_t-f_t^Y$,

• 2.

  “prewhiten” the time series, by first determining the sample autocorrelation $\mathit{\alpha }=\mathrm{1}/L{\sum }_t{X}_t{X}_{t+\mathrm{1}}$ of the time series X_t of length L, and forming a series $X_t^{\prime }=X_t-\mathit{\alpha }{X}_t$, and then testing for the null hypothesis of no trend.

The standard routines are applied to both cases. If the null hypothesis is rejected at the stipulated significance level of 5 %, then the sample trend $f_t^X$, or the sample correlation $\mathrm{1}/L{\sum }_t{X}_t{X}_{t+\mathrm{1}}$, is “significant”.

In this paper, four seasonal mean SAT time series are defined by calculating the average of each three-month period: December(−1 yr)–January–February (Winter), March–April–May (Spring), June–July–August (Summer) and September–October–November (Autumn). Then, the linear trend of each season is also shown in this study; also the significance of each trend has been tested.

3.1 Processing of the earlier data from 1899 to 1913

3.1.1 Quality control and construction of missing data

The earlier SAT data from 1899 to 1913 have been digitized manually and passed through a quality check. The quality checking routine of DWD starts with a formal check, followed by climatological, temporal, repetition and consistency checks (Leiding et al., 2016). From April to December 1901, the original observations of Qingdao are not available. These missing values are filled in using the SAT time series of a neighboring station. We find that the value and variability in SAT monthly time series from July 1900 to December 1901 in Schatsykou exhibits a good agreement with these in Qingdao (Fig. 2). Consequently, the SAT data in Schatsykou is merged into the SAT data of Qingdao to fill the missing data.

Figure 2Comparison of the monthly mean SAT in Qingdao (solid line) with that in Schatsykou (dashed line) during July 1900 to December 1901.

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Here, we have to point out that these quality checks above account for errors in coding and archiving, but are not efficient in dealing with inhomogeneities (Karl et al., 1993). In fact, changes in station height and changes in daily observational times (Table 1) can affect the SAT during 1899–1913. It is important in observational studies that the data used should be homogeneous (Trewin, 2010; J. F. Wang et al., 2014; Li et al., 2016). And in this study, homogenization of the data is the key factor. Thus, the homogenization of the SAT time series from 1899 to 1913 needs to be done in the next step.

3.1.2 Homogenization of SAT time series from 1899 to 1913

Inhomogeneities in land-based observations of air temperature may dampen or introduce noise to estimates of long-term air temperature trends. SAT data from 1961 to 2014 have been homogenized by CMA (Xu, et al., 2013). Here, we pay more attention to the detecting and adjusting of the SAT homogeneity from 1899 to 1913, which is newly digitized without homogenization.

Details of non-climatic factors were recorded in the metadata back to January 1899 (Table 1). Among these factors, the changes in observation height and daily observation times are the main causes of inhomogeneities. In the earlier time from January 1899 to April 1905, SAT was observed at 36^∘04^′ N, 120^∘17^′ E, which was a harbor near the coast of Qingdao (Fig. 2). From May 1905 to March 1914, SAT was observed at 36^∘04^′ N, 120^∘19^′ E, which was a small hill. The meteorology station was located at the top of this hill, without the effect of buildings and forest. Thus, the observation heights have been changed three times since 1899: 24 m (1 January 1899–30 April 1905), 50 m (1 May 1905–31 August 1905) and 78.6 m (1 September 1905–31 March 1914). The observing schedule was also changed in July 1899 from local time 08:00, 14:00, 20:00, to 07:00, 14:00, 21:00 (the same as Beijing time); and the observing schedule was changed again in April 1905 from local time 07:00, 14:00, 21:00 to hourly (24 times a day). In different periods the daily mean was calculated by the following different formulas:

$$\begin{array}{}\text{(1)}& {\displaystyle }& {\displaystyle }{T}_{\mathrm{daily}}\left(\text{I}\right)=\left(T_{\mathrm{07}}+T_{\mathrm{14}}+\mathrm{2}\cdot T_{\mathrm{21}}\right)/\mathrm{4},\text{(2)}& {\displaystyle }& {\displaystyle }{T}_{\mathrm{daily}}\left(\text{II}\right)=\left(T_{\mathrm{08}}+T_{\mathrm{14}}+\mathrm{2}\cdot T_{\mathrm{20}}\right)/\mathrm{4},\text{(3)}& {\displaystyle }& {\displaystyle }{T}_{\mathrm{daily}}\left(\text{III}\right)=\left(T_{\mathrm{01}}+T_{\mathrm{02}}+\mathrm{\dots }+T_{\mathrm{24}}\right)/\mathrm{24}.\end{array}$$

In order to adjust the inhomogeneities caused by observation height change and observation times change, the best way is to find neighboring reference series and then modify the candidate series based on several mathematical methods. But actually it is hard and even impossible to find a reference series in such early times. In this case, air temperature in Qingdao was transformed into temperature at sea level using an average environmental lapse rate (6.0 ^∘C km⁻¹). Furthermore, to avoid the inconsistency of calculating a daily mean SAT from different observational times, the deviation caused by change of observational times is assessed firstly. We use T_daily(I), T_daily(II), T_daily(III) to calculate the daily mean SAT using the observation data from 1908 to 1913, which were recorded 24 times a day. Then, monthly means in the whole period (1908–1913) are obtained by the average of the days in each month.

Figure 3Distribution of difference between the daily mean temperature T_daily(III) and T_daily(I) (gray bars) and difference between T_daily(III) and T_daily(II) (black bars) in the 72 months from January 1908 to December 1913 in Qingdao. The SAT differences in the green frame are considered as physically insignificant.

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Figure 4Annual mean SAT series (^∘C) of the raw and homogenized recorded at Qingdao from 1899 to 1913. Black line is the original observation series; red line is the homogenized series.

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Generally, the SAT calculated by T_daily(III) can represent the “real” daily mean SAT best. Thus, we calculate the frequency distributions of deviation between the monthly mean SAT of T_daily(III) and T_daily(II), as well as T_daily(I) from January 1908 to December 1913 to assess the bias caused by different calculation formulas. Results are shown in Fig. 3. The majority of differences between T_daily(III) and T_daily(II) are from −0.1 to 0.2 ^∘C. These discrepancies are small and can be ignored as physically insignificant. So the SAT from July 1899 to August 1905 do not need to be adjusted for the bias caused by T_daily(II). However, the mean deviation between T_daily(III) and T_daily(I) is −0.27 ^∘C and 35 % of the differences are larger than −0.3 ^∘C. It suggests that the SAT calculated by T_daily(I) has significant time-varying biases with that calculated by T_daily(III), about 0.27 ^∘C. Consequently, the SAT during January 1899 to June 1899 has applied to an adjustment of −0.27 ^∘C. Figure 4 exhibits the annual mean SAT series before and after adjustment.

Figure 5Annual mean SAT time series in Qingdao from 1899 to 2013 (black solid line: SAT OBS; dashed line and cross: 20CR v2c; dashed line and circles: SAT W&M v4.01; dashed line and diamond: CRUTS 3.230).

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3.2 Construction of SAT series in the past 115 years (1899–2014)

A previous study pointed out that the observation SAT from 1914 to 1960 was discontinuous with many missing data (Cao et al., 2013). For Qingdao station before 1960, the missing times of records were in July 1914 to March 1915, September 1937 to January 1938, and January 1951 to December 1960. However, all data from 1916 to 1950 has not been homogenized. In light of this, we attempt to use some grid-box datasets to fill with the gap from 1914 to 1959. Here, each of the three gridded SAT datasets have been evaluated for consistency with homogenized observations. Then the best one was used to estimate the SAT from 1914 to 1959. We calculated the correlation coefficient between the three SAT series with homogenized observations from DWD and CMA in Qingdao station (hereinafter referred to as SAT OBS) in two periods (1899–1913 and 1960–2014) after detrending described in Sect. 2.2. Results show that all of the correlation coefficients are statistically significant on the 95 % confidence interval (Table 3). The highest correlation coefficients (r = 0.98 and r = 0.95) are found between SAT OBS and SAT W&M v4.01. However, the correlation with the estimate of the CRUTS 3.230 shows rather low values, which are considerably smaller than those obtained with W&M v4.1 or 20CR v2c.

Table 3Correlation coefficients between the three SAT time series and the observational SAT time series in Qingdao. All of these time series have been detrended. The largest correlation coefficients are in bold.

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Then, we compare the three annual mean SAT time series with the SAT OBS in Fig. 5. It can be seen that except for the 20CR v2c, the annual mean SAT series of W&M v4.01 and CRUTS 3.230 both have the similar climate variability with that of the SAT OBS. Interestingly, the difference between 20CR v2c and CRUTS 3.230 shows marked non-stationarities. In the first years, both series are similar, but exhibit relatively smaller interannual variability. Since about 1920 until 1950, the temperatures of 20CR v2c are mostly smaller than the CRUTS 3.320. But since about 1960 until 2005, the yearly means of 20CR v2c are strongly larger than CRUTS 3.320. The abrupt change in 20CR v2c around 1960 is not replicated in the W&M v4.01 series, and we suggest that this jump is an artifact in the analysis of 20CR v2c. Other non-stationarities have been found in the 20CR analyses (e.g., Krueger et al., 2014) and we suggest to rely more on the other two descriptions of past temperature variations. However, there is a relatively large systematic difference between the SAT OBS and the CRUTS 3.230 data and the difference even exceeds 3.5 ^∘C (see also Cao et al., 2013). These discrepancies may derive from different quality control routines for data and the inconsistency of statistical methods used (Li et al., 2016). Based on these findings, we use SAT W&M v4.01 for filling the gap in the observational series between 1914 and 1959 to obtain continuous SAT series in Qingdao.

Using a linear regression method, each monthly mean SAT OBS in each period can be estimated from SAT W&M v4.01. Take SAT OBS in January for example, SAT OBS = (SAT W&M v4.01 + 0.62)∕0.95 during 1899–1913 and SAT OBS = (SAT W&M v4.01 + 1.15∕0.94) during 1960–2014. Then, we give the estimated linear relationship during 1914 to 1959 in January, SAT OBS = (SAT W&M v4.01 + 0.85)∕0.95 to get the monthly mean SAT OBS in the period of 1914–1959 in January. Consequently, monthly SAT OBS in each month from 1914 to 1959 was obtained. The SAT series in Qingdao from 1899 to 2014 is shown in Fig. 6.

Figure 6Construction of annual mean SAT (^∘C) in Qingdao for the period 1899–2014 (red solid line) and the 10-year running mean (long dashed line). The short dashed line represents the long-term linear trend. The thin black solid line shows the climate annual mean SAT relative to 1961–1990.

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3.3 The temporal variations in the SAT trend of the constructed series

The newly constructed annual mean SAT in Qingdao from 1899 to 2014 (Fig. 6) exhibits a warming rate in Qingdao over the last 116 years of 0.11 ± 0.03 ^∘C decade⁻¹, slightly larger than the global mean warming rate over 1901–2012 (about 0.09 ^∘C decade⁻¹; IPCC AR5, 2013). It indicates that the warming trend is significant (significant at 95 % confidence intervals tested by the Mann–Kendall test, p value < 0.05). From the time series, we also find that the coldest years occurred in 1917 and 1969, with 11.03 and 11.05 ^∘C. The warmest years occurred in 2007 and 1999, with annual means of 13.80 and 13.78 ^∘C. Recently, Cao et al. (2013) calculated the average warming trend over the last hundred years based on SAT from 16 stations in China, with the rate of 0.15 ^∘C decade⁻¹, which is consistent with our result in Qingdao.

Since 2000, the SAT undergoes a decreasing trend, with a rate of −0.4 ^∘C decade⁻¹, even if the other SAT series (Fig. 5) exhibit positive SAT anomalies for the continuous 15 years (2000–2014). This slowdown or warming “hiatus” in this period is also found on regional and global scales. The Intergovernmental Panel on Climate Change Fifth Assessment Report (IPCC AR5) pointed out that during recent years (1998–2013), the global warming rate has slowed down. This period has been discussed in a number of papers (Kosaka and Xie, 2013; Smith, 2013) and has been known as a “hiatus” (Fyfe et al., 2013) or “global slowdown” (Guemas et al., 2013). Recent studies indicate that the recent “warming hiatus” is also found in Chinese SAT changes (J. F. Wang et al., 2014; Li et al., 2015). Proposed mechanisms for the recent warming hiatus at the global scale are still under debate, including changes in deep-ocean heat uptake, anthropogenic aerosols, solar variations, volcanoes and sea surface temperature (Meehl et al., 2011; Kaufmann et al., 2011; Kosaka and Xie, 2013). At regional and local scales, other factors may also play a significant role, which makes attribution challenging.

It is also interesting to note that during 1899–1910 there is another decreasing trend, with the rate of −1.1 ^∘C decade⁻¹, which is likely an expression of natural variability, as we have no noteworthy global or regional forcing during that time. This cooling rate is quite high, but the period extends only across 12 years, followed by a rapid warming for several decades until about 1940 (Fig. 6).

Figure 7Averaged annual mean SAT anomalies for each decade (^∘C) in Qingdao during 1899–2014 relative to the 1961–1990 reference period (black line in Fig. 6; gray bar means negative values and black bar means positive values).

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Figure 8Constructed seasonal mean SAT series (^∘C) in Qingdao for the period 1899–2014 (solid line) and the 10-year running mean (dashed line). (a) Spring, (b) summer, (c) autumn and (d) winter.

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Table 4Definitions of temperature indices used in this study.

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Figure 9Differences in TX, TN and DTR between the period 1907–1913 and the period of 2007–2013 (^∘C).

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The constructed 10-year annual mean SAT from 1899 to 2014 are shown in Fig. 7. Five main periods are associated with larger than normal SAT. The three maximum warm periods occurred during 1989–1998, 1999–2008 and 2009–2014. The average anomaly SAT of 1999–2008 is the largest which is higher than normal of about 0.96 ^∘C. On the other hand, cold periods occurred in the following decades: 1899–1908, 1909–1918 and 1949–1958.

The seasonal mean SAT time series are also shown in Fig. 8. The linear change trends and 95 % uncertainty ranges are also calculated, with the warming rate of about 0.12 ± 0.04 ^∘C decade⁻¹ in spring, 0.06 ± 0.04 ^∘C decade⁻¹ in summer, 0.08 ± 0.04 ^∘C decade⁻¹ in autumn and 0.10 ± 0.07 ^∘C decade⁻¹ in winter. These values suggest that the most significant warming occurred in spring, followed by winter. The interdecadal variations in the seasonal mean temperature in spring and winter appeared as a series of waves with a timescale of about 50–60 years. However, the trends in summer and autumn are much lower. The seasonal difference of the warming rate was also exhibited in other research on SAT in other stations of China, or SAT in the whole of China (Fong et al., 2009).