Statistical modeling techniques and the Vaganov-Shashkin (VS) forward model of tree ring formation were used to investigate tree growth response of Pinus tabulaeformis to climate variations in semi-arid north central China. Both statistical and process-based modeling techniques were shown to be capable of simulating and evaluating climate-tree growth relationships for the study area, but the process-based VS model produced results that were more physically interpretable. Statistical modeling results indicate that both moisture and temperature have significant effects on tree growth during the growing season, with the most important months being May–August. The VS modeled results validated the above statistical modeling results, and further clarified the effects on tree growth of the seasonal distribution of temperature and soil moisture, soil moisture status prior to the growing season, and the start and end dates of the growing season. Under current and projected climate scenarios, our modeling results suggest significant tree growth reduction in north central China, and the possibility that regional forests may reduce their capacity to sequester carbon.
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 The traditional approach for dendroclimatic reconstructions is to calibrate tree rings with climate variables using some type of linear regression technique [Cook and Kairiukstis, 1990]. However, tree growth response to climate is often nonlinear [Fritts, 1976]. A few recent studies demonstrated that the response of tree growth to climate might vary in a changing climate regime, leading to the failure of this simple linear climate-tree growth relationship. For instance, Briffa et al. , Wilmking et al.  and Driscoll et al.  reported reduced or divergent tree growth responses to temperature at some high latitudes of the Northern Hemisphere for recent decades. Barber et al. , Biondi  and Lloyd and Fastie  found evidence of enhanced tree growth response to temperature-induced drought stress for recent decades. Biondi , Solberg et al.  and Carrer and Urbinati  reported the temporal inconsistency in the responses of tree growth to individual monthly temperature or precipitation during the last one or two centuries. These findings imply that alteration of tree growth responses to climate may exist, and this sort of alteration may affect some statistical model based paleoclimate reconstructions, as well as current modeling of forest carbon sequestration [Briffa et al., 1998; Barber et al., 2000]. Therefore evaluation of climate-tree growth relationships is essential in order to validate both statistical modeling of paleoclimates and forest carbon uptake simulations.
 Methods employed to assess climate-tree growth relationships generally fall into two categories: statistical modeling techniques and process-based model simulations. From the statistical perspective climate–tree growth relationships can be assessed with correlation and response functions, and their temporal stability and consistency can be measured by means of evolutionary (backward and forward) correlation and response functions [Fritts, 1976; Briffa et al., 1998; Biondi, 2000; Carrer and Urbinati, 2006] and the Kalman filter [Cook et al., 2002; Cook, 2003]. However, such statistical analyses generally require long-term climate data to satisfy statistical stationarity, and thus are often difficult to validate for long period processes and for areas where the instrumental measurements are relatively short. An alternative method is using process-based model simulations. Although there are several process models of tree growth and ring formation [Fritts et al., 1999; Foster and LeBlanc, 1993; Misson, 2004], the VS forward model of tree ring formation [Vaganov et al., 1990, 2006; Shashkin and Vaganov, 1993] often has been used to simulate the response of tree growth to climate factors [Vaganov et al., 1999; Anchukaitis et al., 2006; Evans et al., 2006]. This model was recently validated by a hemisphere-wide evaluation, proving its capacity for accurately simulating tree growth responses to climate forcings over a range of climate regimes, with better results in arid and semi-arid areas [Evans et al., 2006]. In the current study we will use the VS forward model to investigate tree growth response of Pinus tabulaeformis to climate variations in semi-arid north central China at both intra-annual and inter-annual scales.
 Understanding tree growth responses to climate in semi-arid north central China has great implications not only for regional paleoclimate studies and for forest carbon uptake simulations, but also for future forest planning and management. Previous studies suggested that tree growth in this area was mainly limited by moisture availability [Liu et al., 2004; Li et al., 2007]. However, these results were purely based on statistical analyses. Statistical analyses alone can not reveal the physical or biological processes of tree growth. A process-based model simulation will help interpret the underlying physiological processes that modulate the details of tree growth, and thereby will help to both accurately reconstruct the history of past climate and adjust models of carbon sequestration. Furthermore, a few recent studies indicated there was an increase in temperature but a decrease in precipitation for recent decades in north central China and its surrounding areas [Wang and Zhou, 2005; Zhai et al., 2005; Ma and Fu, 2006]. How this type of climate change will impact tree growth and regional ecosystems is of great concern to human populations living in this semi-arid area. Our objectives are (1) the use of a statistical model to reveal the main climatic factors affecting regional tree growth, (2) application of the VS forward model to monitor the effect of climatic factors on tree ring formation at both intra-annul and inter-annual scales, and (3) assessment of the possible response of tree growth in relation to the projected climate changes in the study area.
2. Material and Methods
 Tree ring data were collected from Chinese pine (Pinus tabulaeformis) at three sites located in the high-altitude forest areas of the Helan Mountains, north central China (Figure 1). The Helan Mountains extend over 200 km from north to south, but only 15–60 km from east to west. The elevation for much of the mountain range is between 2000 and 3000 m above sea level (a.s.l.). Two sites (MHL02 and MHL04) are located at the west side of the Helan Mountains (39°05′N, 106°05′E; 38°31′N, 105°46′E), with an elevation of 1500–2000 m and 2400–2500 m, respectively. The third site (NHL04) is located at the east side of the Helan Mountains (38°43′N, 105°59′E), with an elevation of 2500–2600 m. The forest stands at these sites are rather open, and the trees from which core samples were extracted grew up on thin soil conditions or even directly from cracks in the rocks.
 Following the standard dendrochronological techniques [Cook and Kairiukstis, 1990], two cores per tree were extracted using increment borers, and at least 20 trees were cored for each site. All the samples were processed using standard procedures [Stokes and Smiley, 1968], and then were visually cross-dated. Each tree ring width was measured to 0.001 mm precision. Dating and measurement errors were further checked with the COFECHA computer program [Holmes, 1983]. Subsequently, each ring width chronology was developed using the ARSTAN program [Cook, 1985] by removing biological growth trends while preserving variations that were likely related to climate. All the measurement series were detrended by fitted negative exponential curves or linear regression curves of any slope. The detrended series were arithmetically averaged to produce a standard chronology for each site, producing three standard ring width chronologies.
 The climate data used in this study include local monthly temperature and precipitation records from National Meteorological Information Center, China Meteorological Administration (L. Yi, personal communication, 2006) as well as the monthly Palmer Drought Severity Index (PDSI) data developed by Dai et al.  (Figure 1). The PDSI grid point used in this study is located at (38°45′N, 106°15′E), which is the nearest one to the sampling sites. The time span of the PDSI for this grid is from 1953–2003. The instrumental temperature and precipitation data were obtained from the AZQ (38°50′N, 105°40′E, 1561.4 m a.s.l.) meteorological station (Figure 2). Available data at the AZQ span from 1953–1999.
 Several descriptive statistics were used to evaluate the quality of the three site chronologies. These commonly adopted statistics include the mean of each chronology, mean sensitivity and standard deviation, mean correlation among all series of each site, signal/noise ratio, expressed population signal, and the variance explained by the first principal component (PC1) [Fritts, 1976]. Standard correlation function analysis was employed to statistically assess the main controlling climatic factors of tree growth [see also Fritts, 1976].
 The VS forward model of tree ring formation [Vaganov et al., 1990, 2006; Shashkin and Vaganov, 1993] was used to simulate the response of tree growth to climate factors. This forward model assumes that tree ring width is exclusively determined by such environmental factors as daily temperature, precipitation, and sunlight [Vaganov et al., 2006]. It has been successfully employed to accurately simulate, evaluate and interpret the relationships between climate and tree ring formation for a variety of environmental conditions [Anchukaitis et al., 2006; Evans et al., 2006]. This model was used in this study to simulate regional patterns of climate-tree growth relationships over north central China at both intra-annual and inter-annual scales.
3. Statistical Analysis
 Statistical properties of the three chronologies are listed in Table 1. The three chronologies exhibit strong in-site covariability, as indicated by high values of mean correlation among all series of each site and the high percentage of variance explained by the PC1. Meanwhile, the high values of mean sensitivity, standard deviation and signal/noise ratio indicate tree growths at all sites are very sensitive to some external forcings, probably to climate.
Table 1. Statistics of the Three Tree Ring Width Chronologiesa
Common intervals are from 1875 to 1995, from 1860 to 1994, and from 1886 to 1994 in Mhl02, Nhl04 and Mhl04, respectively.
Mean correlation among all series
Expressed population signal
% variance in first eigenvector
 Similar to other chronologies developed from the same region by Li et al. , our three chronologies are cross-dated and have high site inter-correlations. Correlation coefficients of chronologies from MHL02 and NHL04, MHL02 and MHL04, NHL04 and MHL04 are 0.45, 0.64, and 0.62, respectively (all significant at p < 0.001). The first principal component of the three chronologies explains 71.42% of their total variance. These significant inter-correlations and high value of explained common variance indicate large-scale homogeneity of tree growths and their responses to climate in the study area. In order to facilitate model simulations we preferably used tree ring data from the site of MHL02 for the following correlation and process-based modeling analysis, since this site is closest to a local meteorological station (AZQ), and the two places have a similar elevation (Figure 1).
 The climate-tree growth relationships in north central China were first assessed by statistical correlation functions. We calculated the correlation coefficients among the MHL02 tree ring chronology and local temperature, precipitation and the PDSI for each month (Figure 3). As shown in Figure 3a, a general pattern is that tree ring chronology is correlated positively with precipitation from May to August, while negatively with temperature in the same period. Statistically significant correlation coefficients (at 0.05 level) with precipitation were found for June (r = 0.32), and July (r = 0.37), and for the prior September (r = 0.34), while significant correlation coefficients with temperature were found for August (r = −0.32) and for the prior December (r = 0.32). MHL02 also has strong positive correlation coefficients against PDSI from May to August (Figure 3b), with statistically significant correlation coefficients found in June (r = 0.50), July (r = 0.50) and August (r = 0.31).
 The above correlations suggest that the influence of climate on tree growth in north central China is mainly attributable to a combination of precipitation and temperature in the growing season, with the most important months being May–August. As shown in Figure 2b, with the exception of August, monthly mean precipitation is less than 45 mm in this semi-arid region, hardly satisfying moisture demands exerted by strong evapotranspiration during the active growing season. In August when maximum rainfall was received, the moisture stress was significantly alleviated compared to that in June–July (Figure 3a). Therefore it is not surprising that moisture availability is a critical limiting factor for tree growth in this semi-arid area.
4. Process Model Analysis
4.1. Model Parameters
 To simulate ring width formation in north central China the daily temperature and precipitation data were used from the AZQ station during 1953–1997. Since the MHL02 site is located ∼200 m higher than the AZQ station, a temperature correction of −0.9°C and a precipitation correction of 1.2 times were used for the model simulation [Shi, 2005]. For the model parameters we used the default values [Evans et al., 2006; Vaganov et al., 2006], except for the fraction of precipitation penetrating soil (i.e., 0.72 adjusted to 0.95), the lower end of range of optimal temperatures Topt1 (i.e., 18.0°C adjusted to 20.0°C), and the upper end of range of optimal temperatures Topt2 (i.e., 24°C adjusted to 22°C).
 The penetrating fraction adjustment can be justified by the fact that most trees collected from this site are isolated from each other, therefore little precipitation can be caught by the tree crown. To evaluate the effects of Topt1 and Topt2 changes, a parameter sensitivity experiment was performed. While keeping all other parameters constant, either Topt1 or Topt2 was increased and decreased up to a range of ±2°C with a step of 0.5°C, and the simulations were repeated for each new parameter set, resulting in a total of 16 simulated chronologies, which could then be compared with the actual MHL02 chronology. The correlation coefficients range from 0.63 to 0.57, all significant at the 0.01 level, which indicates that a small increase or decrease of Topt1 and Topt2 (i.e., within ±2°C range) results in slightly lower but not significantly different correlation coefficients. This result is consistent with the finding achieved by Evans et al.  in Ulan-Ude, southern Russia, that the tree ring width simulation was not very sensitive to the choice of primary temperature.
4.2. Model Behavior: Inter-Annual and Intra-Annual Simulations
 We first examined the ability of the VS model to simulate inter-annual tree ring formations. The actual and simulated annual tree ring indices for the available inter-comparison period of 1953–1997 are plotted together in Figure 4. Qualitatively, there is generally good agreement, with the exception of some misfit years such as 1954, 1955, and 1968. Correlation coefficient of the actual and simulated series during 1953–1997 is 0.63, which is statistically significant at the 0.01 level.
 Using the VS model we also simulated the daily changes of soil volumetric water content, vegetative transpiration, the relative radial growth rate, and the relative radial growth rate attributable to temperature or soil moisture. As an example we show these simulated values in Figure 5 for the select period of 1975–1982 when variations of ring width are significant, and the observed and modeled tree ring indices have best agreements (Figure 4).
 Relatively narrow rings were formed in 1975, 1981 and 1982, and relatively wide rings were formed in 1977 and 1979.
 As seen from the simulation results shown in Figure 5, moisture availability is generally the dominant limiting factor for tree ring formation, although temperature can be the limiting factor for some specific time periods at the start and/or the end of the growing season. For instance, in 1979 when above normal rainfall was received and a wide ring was formed, the model output indicates that initial soil moisture was high prior to the growing season. Modeled tree growth started in early April, and the relative growth rate increased quickly with temperature rising and reached the first peak at the end of May when temperature was not yet a limiting factor. From early June to late-August temperature remained suitable for cell formation and moisture availability became the limiting factor due to enhanced evapotranspiration. In early August when maximum rainfall was received, the relative growth rate reached another peak. From September to the end of the growing season (mid-November) the growth rate was limited by lower temperature. By contrast, in 1981 when below normal rainfall was received and a narrow ring was formed, the model indicated that initial soil moisture was relatively low prior to the growing season. The relative growth rate increased a little with rising temperature from late-March to the end of April, and after that it was controlled by water availability from May to September. In October, the last month of the growing season for that year, the relative growth rate was again limited by temperature. Therefore a wide ring was formed in 1979, mainly due to the two rapid growth periods in late May and early August, and a narrow ring was formed in 1981, mainly due to the scarcity of rainfall during the growing season. The model output indicates that the soil moisture prior to the growing season and rainfall in the active growing season are important in determining tree ring width.
4.3. Model Results Analysis: Influence of Climate Factors on Ring Width Formation
 To further investigate how climatic factors affect wide and narrow ring formation, we examined the difference in climate factors and tree growth between years when wide and narrow rings were formed (Figure 6). For this part we define a wide (narrow) tree ring as the mean number of cells plus (minus) one standard deviation. According to this definition, wide rings during the select period 1953–1997 were formed in 1954, 1964, 1970, 1979 and 1992, while narrow rings were formed in 1962, 1965, 1966, 1971, 1981, 1982, 1989 and 1997.
 With regard to mean seasonal temperature profile there is no significant difference between years when wide and narrow rings were formed (Figure 6a). This result suggests that temperature is not the dominant factor limiting tree ring formation. However, the relative growth rate due to soil moisture changed dramatically between years with wide and narrow rings. For the years with wide rings the initial soil moisture was comparatively high, with the relative growth rate due to soil moisture increasing till early June (Figure 6b). By contrast, for the years with narrow rings the initial soil moisture was comparatively low, with the relative growth rate due to soil moisture reaching its peak at the end of April. This peak was significantly lower than that in years with wide rings. From the above statistical analysis, we know that moisture availability during the end of the prior growing season helps determine the initial soil moisture level. Because of the dramatically enhanced evapotranspiration, the relative growth rates due to soil moisture decreased dramatically in June and July for both narrow and wide rings. However, the relative growth rate due to soil moisture recovered quickly in August in wide rings, while there was little recovery for years with narrow rings. There are two obviously different periods of the growth curves where changes are attributable to soil moisture. These occurred in June and late-August to September (i.e., periods I and II in Figure 6b), respectively. The differences in relative growth rates due to soil moisture largely determined the mean relative growth rate, and the same two obviously different periods also appeared in modeled mean growth rates for years with wide and narrow rings (i.e., periods I and II in Figure 6c).
 Model simulation suggests that soil moisture in late-August to September (i.e., period II in Figure 6b) has significant effects on tree growth, yet the correlation analysis shows no statistically significant relationships between the tree ring width chronology and August–September precipitation (Figure 3a). The real cause of this difference between modeled and statistically interpreted climate-tree growth relationship is unclear. One possibility is due to the autocorrelation property of soil moisture imposed by soil's capacity to hold water. That is, due to soil's water holding capacity, precipitation in July to August may remain in soil for a longer period, and thus be important for determining the September soil moisture. Correlation coefficients for the soil moisture of July and August, August and September are 0.37 and 0.52, significant at the 0.05 level, respectively. At any rate, understanding the difference between modeled and statistically interpreted climate-tree growth relationships are critical for conducting tree ring based paleoclimate reconstructions, and it requires great attention in future dendroclimatic studies.
 To clarify the relative intervals of a season limited by temperature and/or soil moisture, we calculated the percent of days with growth limitation by temperature, soil moisture and their integration during the 1953–1997 test period as shown in Figure 7. It is clear that temperature strongly affected tree growth at the beginning of the growing season (late-March to late-April), but its control was gradually replaced by soil moisture in May. Soil moisture absolutely controlled tree growth during the most active portion of the growing season (June to August), and remained the dominant limiting factor in September. Temperature gradually replaced soil moisture as the most important limiting factor from late September to early October, and remained dominant until the end of the growing season.
4.4. Model Results Analysis: Effects of Growth Start and End Dates on Cell Numbers and Tree Ring Widths
 In the VS model the start and end dates of the growing season are defined as the formation date of the first and the last cell, respectively. In our simulation the start date of the growing season falls within the range of the 91st to the 133rd day of each calendar year, with a mean of the 112th day (corresponding to 22nd April) and a standard deviation of 9 days as shown in Figure 8. The range of the end date of the growing season is from the 182nd to the 299th day, with a mean of the 272nd day (corresponding to 2nd October) and a standard deviation of 22 days. The simulated cell number for each growth ring is between 8 and 20, with a mean value of 13.4 and a standard deviation value of 2.9.
 We calculated the correlations of the start and end dates of the growing season with cell numbers, and with the observed and simulated tree ring indices during 1953–1997. Correlation coefficients for the start date series and the observed and simulated tree ring index series are 0.12 and 0.07, which are both statistically insignificant. Correlation coefficients for the end date series and the observed and simulated tree ring index series are 0.27 and 0.43, which are statistically significant at the 0.10 and 0.01 levels, respectively. Correlations of growth start and end dates with cell numbers are the same as their correlations with the simulated tree ring index series (i.e., 0.07 and 0.43, respectively). These correlations suggest that tree ring width is more closely related to the end date of the growing season, with insignificant relationship with the start date of the growing season. An earlier end of the growing season often leads to the formation of narrow rings, and wide rings are often formed in the years with an extended growing season. Among the five narrowest rings during 1953–1997 (i.e., 1957, 1965, 1966, 1981 and 1989), all but 1957 occurred during a year with an early end to the growing season (Figure 8).
5. Discussion and Conclusions
 We used both statistical modeling techniques and the process-based VS forward model to investigate tree growth responses of Pinus tabulaeformis to climate variations in semi-arid north central China. Correlation analyses revealed the seasonal control patterns of temperature and moisture on radial tree ring formation (Figure 3). The VS model accurately simulated tree ring formation at both intra-annual and inter-annual scales (Figures 4 and 5) and suggested the underlying physical mechanisms that determine tree ring formation (Figures 6, 7 and 8). Our results suggest that both the statistical and process-based modeling techniques are capable of simulating and evaluating the climate-tree growth relationships, but the process-based VS model produced more physically interpretable results for semi-arid north central China.
 Statistical modeling results suggest both moisture and temperature have significant effects on tree growth during the growing season, with the most important months being May–August (Figure 3). The VS modeled results confirm the above statistical results, and further clarify the importance of seasonal distribution of temperature and soil moisture for tree growth (Figures 6 and 7). Both the statistical and the VS modeled results indicate moisture availability has direct and positive effects on tree growth from May to August. Although the statistical results suggest that temperature has negative effects on tree growth during June–August, the VS modeled results indicate that temperature only directly affects tree growth in the short intervals of the beginning and the end of the growing season. We also notice there are significant negative inter-correlations between temperature and precipitation during June–August, as seen in Table 2, which will, at least to some extent, contribute to the negative correlations between tree rings and temperature in June–August.
Table 2. Correlations Between Temperature and Precipitation for the Period of 1953–1997 at the AZQ Stationa
Asterisk indicates values significant at the 0.05 level.
 The VS modeled results suggest that initial soil moisture prior to the growing season is important to tree ring formation (Figure 6b). The modeled results also suggest tree ring formation is sensitive to the end date of the growing season, but is insensitive to the start date of the growing season (section 4.4 and Figure 8). An earlier (later) ending to the growing season often leads to the formation of narrower (wider) rings.
 Our current modeling study has important implications for monitoring regional paleoclimates and forest carbon sequestration, and for evaluating future tree growth responses to climate. A few recent studies have reported that there is an ongoing warming and drying trend for all seasons in north central China [Wang and Zhou, 2005; Zhai et al., 2005; Ma and Fu, 2006]. This type of climate variation may drive changes in regional tree growth responses, since the modeled results suggest that a warmer and drier climate will alleviate direct effects of temperature on tree ring formation in the beginning and the end of the growing season, but will exacerbate moisture stress on tree growth during the full growing season. This warming and drying trend has been projected to continue at least for the next few decades [Tao et al., 2003]. If this is a long-term trend, then tree growth reduction is expected in north central China, and the regional forests are expected to reduce their capacity to sequester carbon.
 The first author's two affiliations contributed equally to this work. The authors thank H. Y. Lu, A. V. Shashkin, W. Wright, I. Djanseitov, V. V. Shishov, E. R. Cook, and L. M. Ma. We also thank two anonymous reviewers for their constructive comments. This research was funded by NSFC Project (Nos. 40601106, 30530050 and 90211028), China Postdoctoral Science Foundation (No. 20060390914) and Jiangsu Planned Projects for Postdoctoral Research Funds. This is LDEO contribution number 7145.