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 History of Meteorology 2 (2005) 87 
 

 

 

 

 

 

 

 

 

 

 

Simulated and Reconstructed Temperature  in China since 1550 AD 
  

Jian Liu
1
, Hans von Storch

2
, Eduardo Zorita

2
, 

Xing Chen
3,1

, and Sumin Wang
1
 

  

1. Nanjing Institute of Geography and Limnology, Chinese 

Academy of Sciences, Nanjing 210008, P.R.China   

2. Institute for Coastal Research, GKSS Research Center, 21502 

Geesthacht, Germany  

3. Department of Atmospheric Sciences, Nanjing University, 

Nanjing 210093, P.R.China   

 

 

Abstract  

 

In this paper, reconstructed decadal mean temperature anomaly series of 8 regions of 

China are compared to those generated in two multi-century simulations with a climate model, 

which was forced with time variable volcanic aerosols, solar output and atmospheric greenhouse 

gas concentrations. The two model simulations are rather similar but do exhibit some 

differences. Both the reconstructed and simulated developments of the temperature exhibit a 

“hockey-stick” pattern, with a marked increase of temperatures since the beginning of the 

twentieth century. The variations of time scales of a few decades are, however, mostly dissimilar 

in the historical and proxy-based account and also in the model data.  

An attempt is made to assess whether the warming during the twentieth century is within 

the range of “normal’’ variations related to solar and internal dynamical influences. It is found 

that the reconstructed data are well above the pre-industrial noise level of temperature 

fluctuations during most of the twentieth century. Within the adopted framework, only the 

increased greenhouse gas concentrations can account for these significantly elevated 

temperatures.  

Key words: China, climate, temperature, climate model, climate change, detection  

 

Introduction  

 

Research of climate change since the Little Ice Age (LIA, 1550-1850AD) has received 

extensive attention in China. Widespread and severe famine and serious social turmoil have 

occurred in China during the LIA (Xu, 1998). Also, the warm conditions after the LIA had great 

impact on human life and the national economy (Yang, et al. 2002). Because of this broad 



 Simulated and Reconstructed Temperature in China 88 
 

 

interest, the climate of China during the last 2000 years has been reconstructed by Chinese 

scientists, in particular temperature and precipitation since LIA with a variety of proxy data, such 

as historical documents, tree rings, ice cores, lake warves, archaeological materials, etc.
 

(Wang et 

al., 1998; Wang and Gong, 2000; Liu and Cai, 2002; Liu and Ma, 1999, Liu and Shao, 2002, 

Zheng and Zheng, 1993; Yao et al. 1996).  

Recently, two long-term climatic simulation experiments have been done by a consortium 

of scientists from the Institute for Coastal Research, the GKSS Research Centre and other 

institutions. The first run, named “Christoph Columbus” (CC) was run over 535 years beginning 

in 1450, and is described in some detail by Zorita et al. (2003). The second run, named “Erik den 

Røde” (EdR), was begun in 900 and ran over 1100 years. Both simulations were done with the 

same ECHO-G climate model with, however, different code versions adapted to different 

computer systems. Reconstructed time series of the radiative effect of the presence of volcanic 

aerosols, greenhouse gases in the atmosphere as well as variable solar output were used as 

forcing (see below). The modeling results reveal global and regional patterns of natural and 

anthropogenic climate change, which have some similarities with the observational record (Zinke 

et al., 2004, De Zolt et al., 2003). The purpose of the present study is to compare these simulated 

data with observational evidence for the territory of China, and to interpret the recent changes of 

Chinese temperatures in the context of the forced climate model.  

In Section 2 we briefly introduce the reconstructed temperature data used in this 

comparison, and in Section 3 the simulations are sketched. In Section 4 the simulated and 

reconstructed historical temperature anomalies are compared. In Section 5, the warming in the 

last century is identified as being beyond the range of variations related to natural and internal 

causes, and in Section 6 the paper is concluded with a brief discussion.  

 

Reconstructed temperature from China  

 

Continental monsoon dynamics with complicated seasonal patterns are the major 

characteristics of China’s present climate. The northerly monsoon prevails in winter, the 

southerly in summer, and the four seasons are very distinct. The season with most of rainfall is 

summer. From September to April each year, the cold and dry winter monsoon blows from the 

Siberia and Mongolia plateau to the mainland of China and weakens gradually from northwest to 

southeast, causing the cold and dry climatic state with a very large difference in temperature. The 

length of the wet summer monsoon control is shorter, from April to September. The warm and 

wet summer monsoon blows from the western Pacific and Indian Oceans, causing a state with 

high temperature and much rain, with little difference in temperature from north to south.   

China can be divided into 10 districts (Wang at al., 1998a), which are relatively 

homogeneous in terms of temperature, precipitation and growing season. These are northeast 

China, north China, east China, the middle of China, south China, southeast China, southwest 

China, northwest China, the Xinjiang region and the Tibet region. With proxy data from 

historical documents, tree rings and ice cores available, reconstructions of the temperature series 

have been made for all these regions, except regions of northeast China and Xinjiang region 

(Figure 1). The reconstructions of 10-year mean temperature anomalies are based on proxies, 

such as temperature index, tree ring width and density, 
18

O of ice cores, via statistical 

techniques which rely on establishing empirical relationships between modern observations and 

environments (Wang et al., 1998a). The proxy data and time series length of the reconstructed 

temperature anomalies can be found in Table 1. They are anomalies relative to 1880-1979.  



 History of Meteorology 2 (2005) 89 
 

 

 

The reconstructions have been compared with the empirical evidence available from the 

past century. Unfortunately, this evidence is very uncertain. One analysis of decadal mean 

temperatures has been prepared by Wang et al. (1998b), who used three kinds of data: 1951-1996 

CMA's monthly temperature series from 165 stations for whole China, 1911-1950 CMA's 

temperature grade diagram series for 139 stations of China, and 1880-1910 documentary, ice 

core and tree-ring data. On the other hand, Jones et al. (1999) made an attempt to reconstruct 

Chinese temperatures from 1856 to 1998 AD. This reconstruction is also rather uncertain, in 

particular for before 1949 (Jones, pers. comm.). Both reconstructions deviate markedly from 

each other also in recent decades, as is demonstrated in Figure 2.   

The fit of the historical data and the "observed" data is facilitated by using data from the 

Wang et al. analysis (1998b). Unfortunately, we have no access to the original analyses by Wang 

et al. (1998b) except for region 3. Also, robust measures of skill for this reconstruction are not 

available either, and it seems plausible that the very good fit shown in Figure 2 is the result of 

overfitting. Unfortunately we have no means to assess which of the two reconstructions (Wang 

and Jones) is more skilful, nor to do our own analysis with the raw data. Therefore we have to 

rely on the published results, even if we have some doubts about the methodology.  

We therefore adopt the pragmatic, and admittedly to some degree questionable 

standpoint, that Wang's reconstruction is essentially valid on time scales of several decades, e.g., 

5-decade running means. The root mean square difference between the 5-decade running means 

given by the historical reconstruction (based upon historical evidence and geoscientific proxies, 

fitted to the unavailable Wang et al. (1998b) data set) and Jones et al. (1999) varies between 

0.13ºK and 0.36ºK in the eight regions, and averaged 0.24ºK for all regions. We consider this 

number a crude but educated estimate of the inherent uncertainty of the historical temperature 

variations in China on the time scale of 50 years.   

The time-averaged time series are shown in Figure 3. They all share a marked warming 

since about 1900 by 0.5ºK and more. In 7 out of the 8 regions, the last decades are associated 

with a cooling, and only in region 4 is the warming continuing. Before 1900 the temperatures 

vary very differently in the 8 regions. In particular region 7 and 8, for which the estimates are not 

based upon on historical data but on geoscientific proxy data (Table 1), which exhibit rather 

strong negative temperature swings, with additional temperature differences in the warmer 

regions by 0.5ºK. It is not entirely plausible that the temperature variations are so unconnected 

even on time scales of 50 and more years. In fact, the variations simulated in the climate model 

are much more uniform, but it is unclear if this is a realistic property or not.  

  
Table 1. Proxy data and reconstructed series length of 8 regions. (Wang et al., 1998a) 

  

No.  Region  Proxy data  Length  

1  North China  Historical materials  1380-1990  

2  East China  Historical materials  1380-1990  

3  South China  Historical materials  1500-1990  

4  Southeast China  Historical materials  1500-1990  

5  Central China  Historical materials  1470-1990  

6  Southwest China  Historical materials  1500-1990  

7  Northwest China  Ice cores  1000-1990  

8  Tibet  Tree rings  1000-1990  



 Simulated and Reconstructed Temperature in China 90 
 

 

  
 

Fig. 1. Regions of China with reconstructed temperature series 

 

 

   
Fig. 2. Conflicting assessment of decadal mean temperature fluctuations in region 3 of China – according to the 

Wang et al. (1998b) analysis of mainly instrumental data (CMA data), Jones et al. (1999), the historical 

reconstruction by Wang et al. (1998a), and the CC simulation with ECHO-G. The decades are labeled by 

the first year of a decade, e.g., 1920 stands for the years 1920-1929.  

  



 History of Meteorology 2 (2005) 91 
 

 

 

   
 

Fig. 3. Time series of reconstructed, temporarily smoothed mean temperatures for the 8 regions shown in Figure 1. 

A running mean filter, averaging 5 consecutive decadal means is applied so that effectively 50-year means 

are shown.  

 

ECHO-G simulations, 1550-2000  

 

Two multi-century integrations have been performed with the state-of-the-art climate 

model ECHO-G, which is a combination from the ocean model HOPE-G in T42 resolution and 

the atmospheric model ECHAM4 in T30 resolution, both developed at the MPI in Hamburg 



 Simulated and Reconstructed Temperature in China 92 
 

 

(Legutke and Voss, 1999). Two runs, named “Christoph Columbus” (CC) and “Erik den Røde” 

(EdR) were executed, one over 535 years and another over 1100 years. The runs were exposed to 

time-variable external forcing related to solar and volcanic activity and changing atmospheric 
concentrations of greenhouse gases. The CO

2
 and methane atmospheric concentrations were 

derived from air trapped in Antarctic ice cores (Blunier et al., 1995; Etheridge et al., 1996). The 

variations of solar output and the influence of volcanic aerosols on the radiative forcing were 

derived from the number of sunspots after 1600 AD and concentrations of cosmogenic isotopes 

in the atmosphere before 1600 AD (Crowley, 2000). The forcing due to volcanic aerosols was 

estimated from concentrations of sulphuric compounds in different ice cores, located mainly over 

Greenland. These forcing factors were then translated to effective variations of the solar constant 

in the General Circulation Model (GCM) taking into account the corresponding geometric 

factors and the mean earth albedo. Changing the loading of industrial aerosols has not been 

incorporated in the simulation.   

In the following we consider only the time simulated in both runs, namely 1550 to today. 

For this time Figure 4 shows the history of the effective solar activity, greenhouse gas and 

volcanic-aerosol concentrations used to force the model. The global mean near-surface 

temperature is also shown.  

The CC model integration was started in the year 1465 AD with the forcing conditions of 

1990, and slowly driven in a 30-year transition period to the corresponding solar, volcanic-

aerosol and greenhouse gas concentrations estimated for 1500 AD. The model attained an 

equilibrated state in about the model year 1550. The EdR simulation was started in the year 900, 

and the model attained its new equilibrium within the first 100 years of the integration.  

The CC simulation is described in some detail by Zorita et al. (2003). Its consistency with 

observational evidence during the Late Maunder Minimum is described by Zinke et al. (2004), 

and the relationship between forcing on the one side, and the NAO and European temperature on 

the other side by de Zolt et al. (2003). Aspects of the EdR run are presented in González-Ruoco 

et al. (2004). The material presented in the following is demonstrating that the temperatures in 

China simulated in the two runs are rather similar, even though the period up to about 1700 EdR 

in some regions seems to be systematically cooler than CC.  

The simulated data are available on a grid with about 300 km mesh size. The data are 

spatially averaged to obtain spatial mean values for the eight larger boxes shown in Figure 1.   

  



 History of Meteorology 2 (2005) 93 
 

 

 

  
 

Fig. 4. Time series of simulated global mean temperature (black) in the CC simulation, of atmospheric methane and 

carbon dioxide concentration and effective solar constant (red), mimicking the presence of volcanic 

aerosols and a variable solar output used in both CC and EdR.  

 

Comparisons between modelling results and reconstructions  

 

All data are anomalies relative to the 10-decades (1880-1889, 1890-1899, … 1970-1979) 

mean. The decades are labeled by the first year, i.e., 1980 represents the years 1980-89.  

We first examine the past century, because during that time the temperature estimates are 

based mostly on direct observations. During that time we consider decadal (10 year mean) data. 

In the second step, we consider the longer perspective, when only the reconstruction by Wang et 

al. (1998a) is available.   

Previous analyses (de Zolt et al., 2003) have shown that the solar and volcanic forcing is 

not strong enough to imprint a strong signal on time scales of years to a few decades. Therefore, 

we limit our comparison to multi-decadal time scales, specifically to 5-decade running mean 

values (i.e., averages of 5 consecutive 10 year means). It is hoped that this smoothing also will 

overcome in part the inherent uncertainty of this reconstruction.  

 

Comparison with instrumental data, 1880/1920-1979  

 

Here we compare decadal mean temperatures for the eight boxes as simulated in the 

model, and as estimated from historical and geoscientific evidence (Wang et al., 1998a).   

The bias between the reconstructed and simulated box-mean temperatures varies between 

0.07ºK and -0.15ºK, which is, however, considerably less than the systematic difference between 



 Simulated and Reconstructed Temperature in China 94 
 

 

Wang’s estimate and Jones’ estimate of 0.16ºK and -0.34ºK. For the root mean square error a 

similar result is found. The rmse between Wang’s estimate and the simulated data is on average 

0.30ºK, with a maximum value of 0.34ºK, while the two estimates differ by 0.45ºK on average, 

and a maximum value of 0.58ºK. Thus the difference between model and reconstruction seems 

insignificant when compared with the inherent uncertainty of the historical reconstructions.   

Since 1920 the Jones instrumental data have relatively few gaps. Therefore, we compare 

for this time the variances as given by Wang’s reconstruction, the Jones reconstruction, and the 

model output (Table 2). The simulated temperature variations are usually similar to Jones’ data, 

with the largest difference in region 8, the Tibetan region, where the model simulates a variance 

up to four times the variance deduced from instrumental observations. In case of the Wang’s 

reconstructed data, the variance is larger than the instrumental variance in 6 out of 8 cases, which 

is surprising insofar as the reconstructed data are derived from a regression, which 

underestimates variance. The largest difference is again found for the Tibetan region, but this 

time the factor amounts to fifteen. Again, the simulated data are consistent with the observational 

evidence, if we use the discrepancy between the two reconstructions as a measure of uncertainty.  

We will later see that this consistency of the model data is mainly due to the strong 

warming trend in the past century, which is well captured by all three data sets, Wang’s 

reconstruction and the two model simulations.  

 
Table 2. Variances for the 8 regions since 1920 (10 year mean values)  

  

Region  1  2  3  4  5  6  7  8  

reconstructed  0.15  0.05 0.07 0.08 0.10 0.17  0.20  0.30 

CC simulated  0.15  0.05 0.04 0.05 0.05 0.08  0.11  0.08 

EdR simulated  0.14  0.06 0.02 0.02 0.03 0.04  0.05  0.03 

Jones’ estimation  0.20  0.07 0.04 0.06 0.06 0.05  0.08  0.02 

 

 

Comparison of reconstructed and simulated data, 1550-2000  

 

The 50-year running mean temperatures for the eight regions (Figure 1) as reconstructed 

by Wang et al. (1998a) and as simulated by the two ECHO-G runs CC and EdR are shown in 

Figure 5. The inherent uncertainty of the reconstructions, as estimated from the root mean square 

difference between Wang et al.’s (1998a) analysis of twentieth century temperature variations 

and Jones et al.’s (1999) analysis, is shown as well. Note that the rmse is the expected mean 

error, i.e., in about half the time, the error would be larger than the rmse, and in the other half 

smaller. Thus it is a much less stringent error margin than a 2  confidence band.  

In all cases, the warming trend since about 1900 is shared by both the reconstructed 

temperatures and the simulated changes. In all 8 regions, both simulations warm with a rate of 

about 0.4-1.1ºK/100a, whereas in Wang et al.’s reconstructions the warming is considerably 

weaker, -0.05 – 0.4ºK/100a, which may be due to a significant cooling caused by the emissions 

of industrial aerosols, which is not accounted for in the GCM simulations. An exception is region 

4, in SE China, where the reconstructions reveal a heating of 1.3ºK/100a, and the GCM runs 0.5 

and 0.8ºK/100a.  

In the pre-industrial time (1590-1910), the GCM simulates temperatures lower than 

Wang’s estimates. In particular in the regions 1, 2, 5 and 6, the differences are larger than the 



 History of Meteorology 2 (2005) 95 
 

 

 

rmse. Only in the regions 4 (SE China) and 8 (Tibet) do the simulated temperatures vary within 

plus/minus one rmse. In case of Tibet, the coincidence between the GCM and the proxy data is 

excellent. Also, the development in the Northwest, in region 7, is similar, even if the low-

frequency variations are different. In the GCM world, temperatures vary around a level of -0.5ºK 

and less, while the reconstructed temperatures vary around a level of -0.3ºK or decline from a 

value close in 1550 to zero to a minimum in the late nineteenth century (regions 3 and 6 in 

Central and Southern China).  

In general, the decadal variations are dissimilar in the reconstructed data and in the 

simulated data, even though the data are already heavily smoothed with a 5-decade running mean 

filter. The correlations between the reconstructed data and the CC-simulation for the entire 

period, 1590-1980, is positive (0.47 – 0.84), but these high values are essentially reflecting the 

presence of the hockey-stick pattern. If the two periods, pre-industrial 1590-1910 and industrial 

1920-1980 are considered separately, the correlations become much smaller, namely -0.32 

(region 6) to 0.72 (region 8) for the pre-industrial times, and -0.17 (region 1) to 0.32 (region 7) in 

modern times. (Because of the heavy serial correlation in the data, the determination of 

significance levels is not meaningful.)  

Interestingly, the simulated curves are among themselves rather similar, quite differently 

from the large region-to-region variations displayed in Figure 3 for Wang’s reconstruction.  

  



 Simulated and Reconstructed Temperature in China 96 
 

 

 
 

Fig. 5. Comparisons of reconstructed (red) and simulated (black: CC; blue-dashed: EdR) 5-decade running mean 

temperature anomaly series for 8 regions of China as given in Figure 1. The uncertainty (vertical hatching) 

of the reconstructed temperature variations (Wang et al., 1998) is estimated by the rmse between the 

reconstructed values by Wang et al (1998) and those obtained by Jones et al. (1999) since 1880. The 

horizontal lines with triangles indicate thresholds estimated to represent the expected range of natural 

variations, as estimated from Wang et al.’s reconstructions (downward triangles) and as estimated for the 

CC simulation (upward triangles). The 5-decade running means are labeled by the last decade, e.g., 1980 

refers to 1940-1989.  



 History of Meteorology 2 (2005) 97 
 

 

 

 

EOF analysis  

 

An EOF analysis is used to determine the joint spatial variability of the 5-decade running 

mean temperature for the entire time period 1590-1980. The EOFs are normalized so that the 

time series have a standard deviation of one, so that the magnitude of the signals is given by the 

patterns.  

Not unexpectedly is one EOF enough to explain the bulk of the variations, namely 86% 

in the case of the historical reconstruction, and 99% for the two GCM data sets (Table 3). In case 

of the historical data, two more EOFs carry a noteworthy amount of variance, namely 5% each. 

As already mentioned, the synchronicity in the reconstructed data is weaker than in the GCM 

data (cf. Figure 5). It is unclear if this greater spatial variability (or, in other words, the larger 

degrees of freedom) is reflecting real temperature variations, or if it is due to the insufficiencies 

of the reconstruction process.  

The EOF is describing a synchronous warming, or cooling, in all eight regions. The 

loadings in the GCM EOF are higher than in the reconstructed data EOF. This is to some extent 

due to the fact that less variance is described, but it is also reflecting the fact that large swings in 

the simulated temperature, for instance in the early eighteenth century, are absent in the 

reconstructed data. Again, the similarity is best in case of Tibet (region 8).  

The time series associated with the first EOF modes of simulated and reconstructed data 

is shown in Figure 6. The correlation coefficient of these two series is 0.80. The overall 

similarity is remarkably large, in particular with respect to the century-scale changes, but with 

time scales shorter than a century, the time series differ substantially. Again the hockey-stick 

pattern clearly emerges. Note that the similarity in the range of variation is caused by the 

normalization of the EOFs.  
 

Table 3. First EOF of reconstructed and simulated temperature in the eight regions. Prior to the EOF analysis, the 

data are smoothed with a running 5-decade filter. The EOFs are normalized so that the time coefficients 

(Figure 6) have a standard deviation of 1.  

  

Region  1  2  3  4  5  6  7  8  Described  

variance (%)  

reconstructed  0.36  0.38  0.25 0.24 0.38 0.31 0.63 0.53 0.86  

Christoph 

Columbus  0.65  0.59  0.44 0.48 0.50 0.56 0.74 0.50 0.99  

Erik the Red  0.82  0.70  0.54 0.55 0.67 0.53 0.75 0.50 0.99  

 



 Simulated and Reconstructed Temperature in China 98 
 

 

   
 

Fig. 6. Time series of the first EOF coefficients of 5-decade running mean simulated and reconstructed temperature. 

Note that the EOFs are normalized to standard deviation 1, so that the patterns (in Table 4) carry different 

magnitudes of variations.  The 5-decade running mean values are labeled by the last considered decade, so 

that 1970 refers 1930-1979.  

 

Assessment of the warming during the last century 

 

The similarity of the century-scale variations in the reconstruction and in the GCM output 

is remarkable. The main feature of the similarity is the relatively stationary conditions until about 

1900, on top of which significant decade-to-decade variations are taking place. In the GCM, 

these variations are related to changing forcing conditions, as displayed in Figure 4. The 

variations in volcanic activity contribute mostly to variations that extend only over a few years. 

The solar activity contributes to variations on all time scales, but the dominant signal is exerted 

by the increasing greenhouse gas concentrations in the twentieth century.  

The question is if the reconstructed record may be interpreted similarly. This is the 

“detection and attribution” problem (Hasselmann, 1979; Hegerl et al., 1997; Zwiers, 1999). That 

is, one has first to demonstrate that the recent warming is beyond the variations one would 

expect from “natural variations”, i.e. variations prior to 1910 due to natural and internal causes. 

Next, one has to demonstrate that the recent decades warming trend is consistent with the 

simulated response to the given forcing, i.e., to the forcing spectrum given in Figure 4.  

 

Detection  

 

To accomplish this, we first determine the variability of the smoothed temperature time 

series displayed in Figure 5 during pre-industrial times, and compare these with the changes 

which have taken place in the twentieth century. In Table 4, the mean value of Wang’s 

reconstruction for 1590-1910 is listed together with the standard deviations for that time in 



 History of Meteorology 2 (2005) 99 
 

 

 

Wang’s reconstruction, as well as in the two simulations. We consider this period of 1590-1910 

as “pre-industrial time”, which is not significantly affected by anthropogenic factors.  

The level of variability during pre-industrial time is mostly consistent in the 

reconstructions and in the GCM simulations, even though there are sometimes larger differences. 

We consider a temperature above the range of “normal” variations, when it is larger than the 

mean plus two standard deviations. This “pre-industrial” noise level, as given by the mean value 

derived from the reconstructions plus 2 standard deviations, taken from either the reconstructions 

or from the CC simulations, is displayed in Figure 5 by horizontal lines marked with triangles.   

  
Table 4. Characteristics of 5-decade running mean temperature during the “pre-industrial time” (1590-1910) in the 

eight Chinese regions. Wang et al.’s reconstruction (mean and standard deviation) is shown in the top two 

rows. GCM simulations CC and EdR (standard deviations) are shown in the bottom two rows.  

 

Parameter  Data  1  2  3  4  5  6  7  8  

time mean  Wang et al.  

reconstruction  

-0.38  -0.40  -0.27  -0.24  -0.41  -0.34  -0.68  -0.53  

standard deviation  Wang et al.  

reconstruction  

0.16  0.14  0.14  0.08  0.16  0.18  0.26  0.18  

standard deviation  CC GCM  0.27  0.23  0.13  0.15  0.17  0.16  0.24  0.14  

standard deviation  EdR GCM  

  

0.22  0.26  0.21  0.20  0.26  0.18  0.21  0.13  

 
Table 5. Times during which the 5-decade running mean temperature reconstructed by Wang et al. (1998) is above 

the “pre-industrial noise level”, given by mean plus 2 standard deviation for the time 1590-1910.  

 

Region  times with significantly elevated temperatures  

1  1920-1980  

2  1930-1980  

3  1930-1970  

4  1950-1980  

5  1930-1980  

6  1940-1960  

7  1920-1980  

8  1920-1980  

 

The times when the reconstructed temperature is beyond the 1590-1910 average plus 2 

standard deviations are listed in Table 5, with the parameters given in Table 4. On average, about 

98% of all pre-industrial temperatures should be below this level. In fact, this estimate of the pre-

industrial noise level is conservative, as all temperatures were beyond this level (Figure 5). This 

is due to the skewing of the temperature distribution.  

In all 8 regions, most of the twentieth century temperatures were above the pre-industrial 

noise level, as defined by either the CC model data or Wang et al.’s reconstructions (Figure 5). If 

the standard deviations derived from Wang’s reconstruction are replaced by the larger standard 

deviations derived from the pre-industrial periods in the GCM simulations, similar noise levels 

are obtained (Figure 5) with the same overall conclusions, namely that during most of the 



 Simulated and Reconstructed Temperature in China 100 
 

 

twentieth century the reconstructed temperatures are significantly elevated compared to the pre-

industrial period 1590-1910.  

Thus, we conclude that the recent warming in China, as it is documented in Wang et al.’s 

(1998a) reconstruction, is beyond the range of natural variation, and that an explanation of the 

phenomenon requires the consideration of other factors, in particular increased levels of 

atmospheric greenhouse gas concentrations.  

 

Attribution  

 

In order to assess the likelihood that greenhouse gas forcing would be responsible for the 

recent warming; a simple statistical model for the temperature evolution is fitted to the output of 

the GCM simulation for each of the eight boxes:  

 

 
 

Here, T
t
 is the smoothed temperature deviation from the pre-industrial mean (1590-1910; 

given in Table 4); S
t
 is the time-variable solar forcing deviation from the pre-industrial mean 

1590-1910, and C
t
 the time variable deviation in greenhouse gas concentrations, n

t
 stands for the 

remainder which is consider in this context as noise. The coefficients , , and  are determined 
so that the model variations are best described:  

  
Table 6. Regional coefficients of the model. 

 

Region     

1  0.604  0.118  1.697  

2  0.643  0.087  1.562  

3  0.867  0.009  1.365  

4  0.740  0.039  1.272  

5  0.709  0.064  1.443  

6  0.962  -0.008  1.351  

7  0.714  0.040  1.306  

8  0.836  0.043  1.456  

 
A direct comparison of the three parameters is not possible since the variance of the 

temperature itself and of the two forcing factors is different. However, the memory term T
t
 is 

the most important – the very magnitude of  is due to the heavy smoothing by the 5-decade 
running mean filter. The influence of the solar forcing varies substantially between the 8 regions, 
and in one case the fit even results in a physically implausible negative value – indicating that 
the fit may suffer somewhat form estimation problems. The parameter -coefficient is similar in 
the eight boxes.  

The model is linear, so that sum of the response T
t

s

 to solar and volcanic forcing alone 

and of the response T
t

c

 to greenhouse gas forcing alone equals the response to both forcings, if 

the noise is disregarded and both are integrated with the same initial value T
1590

. Therefore, 



 History of Meteorology 2 (2005) 101 
 

 

 

equation (*) allows an estimate of the relative importance of the two forcing factors. In following 
table 7, we list the reconstructed change of temperature according to Wang et al. (1998a), the 
change estimated through (*) to solar and volcanic forcing alone, to greenhouse gas forcing 
alone, and to both of them. These are all deviations from the pre-industrial values (1590-1910)  
 

Table 7. Reconstructed change of temperature according to Wang et al. (1998a), the change estimated through (*) to 

solar and volcanic forcing alone, to greenhouse gas forcing alone, to both forcings, and the ratio of Wang to 

(*). These are all deviations from the pre-industrial values (1590-1910). 

 

Region  1  2  3  4  5  6  7  8  

Wang et al. (1998a)  0.47  0.49 0.36 0.28 0.50 0.47  0.81  0.70  

(*) with S
t
=0  0.48  0.47  0.69  0.47  0.50  0.72  0.69  0.45  

(*) with log C
t
=0  0.59  0.45  0.04  0.23  0.38  -0.18  0.31  0.23  

(*) with both forcings  1.08  0.93  0.73  0.70  0.88  0.58  1.00  0.68  

Ratio Wang/(*)  0.44  0.53  0.49  0.40  0.57  0.81  0.81  1.02  

 

When comparing the historical warming with the estimated warming (second and fifth 

rows) we find that (*) gives higher values. The ratio of the two numbers (last row) varies 

between 0.40 in the eastern part of China and 1.02 in the western part. We suggest that this 

overestimation by model (*) reflects the increasing cooling effect of regional emissions of 

industrial aerosols, which are strongest in the densely populated east and south of China, while 

the western part of China experiences less increasing emissions.  

Apart from region 1, the estimated warming due to solar and volcanic effects (fourth row) 

is smaller than the estimated anthropogenic greenhouse effect (third row). Only the 

anthropogenic greenhouse effect is strong enough to explain the observed warming, in spite of 

the fact that the latter is considerably reduced by the unaccounted-for effect of the increasing 

industrial aerosol impacts.  

We conclude that the total estimated response is consistent with the empirical evidence in 

terms of sign and, to a lesser extent, with magnitude. The major part of the twentieth century 

warming can be explained only with the help of the anthropogenic greenhouse gas effect, 

whereas the solar effect can account for only a smaller proportion. Differently from the 

development in the GCM simulations, which is a steady upward trend throughout the twentieth 

century, there is in the reconstructions a decline in the second half of the twentieth century. We 

suggest that this is reflecting the steady increase of industrial aerosol emissions (Krüger, pers. 

communication) in China.  

 

Conclusions  

 

We have analyzed Wang et al.’s (1998a) reconstruction of regional temperatures in China 

since the sixteenth century with respect to traces of the impact of changing forcing conditions. 

We found that the reconstructed temperatures are reasonably well simulated by a climate model 

subject to time-variable solar, volcanic and greenhouse gas forcing. The similarity is good on 

time scales of a century, while the model generates variability on shorter time scales without a 

counterpart in the reconstructions.  

The development of regional temperature in the recent decades of the industrial period is 

towards significantly elevated levels, where the significance is assessed by comparison against a 



 Simulated and Reconstructed Temperature in China 102 
 

 

pre-industrial “normal” and “noise level”. Thus, the presence of non-normal external factors 

must be assumed. Using the GCM simulations to assess the relative importance of the solar, 

volcanic, and greenhouse gas forcing, we find that only the greenhouse gas forcing can account 

for the recent warming.  

There are a number of potential sources for errors. The most severe is the reliability of the 

historical reconstructions of regional temperature in China. These temperatures are rather 

uncertain not only because of the usual uncertainties in data derived from, for instance, tree ring 

width, but also since the data base of instrumental data to build the empirical transfer functions is 

not good. Other caveats refer to the model simulations. For instance, the inclusion of the volcanic 

effects is relatively rough. Also, the effect of industrial aerosols of cooling the regional 

atmosphere is not represented in the model simulations. Finally, the utilized forcing factors 

suffer from uncertainties.  

 

Acknowledgements  

 

Financial support was provided by the Natural Sciences Foundation of China (40272123), 

the Chinese Academy of Sciences (KZCX3-SW-321) and by the GKSS Research Center in 

Geesthacht, Germany. Valuable help and advice were given by Fidel Gonzàlez-Ruoco and Olaf 

Krüger. Beate Gardeike helped professionally with the diagrams. 

 



 History of Meteorology 2 (2005) 103 
 

 

 

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