How can the parameterization of a process-based model help us understand real tree-ring growth?

This study shows great potential of the well-validated VS-Oscilloscope (a visual accurate parameterization of the VS-model) for assessment of spatial–temporal cambium phenology, which is illustrated based on the analysis of comprehensive datasets from central Siberia. Tree-growth response to changing climate varies depending on tree species, forest type, and geographical region. Process-based models can help us better understand and anticipate these outcomes. To characterize growth sensitivity to different climate parameters, we applied the VS-Oscilloscope analytical package, as a precise visual parameterization tool of the Vaganov–Shashkin model, to two contrasting habitats: one with tree-ring growth limitation by soil moisture (in the southern part of central Siberia) and the another with temperature limitation (in the middle part of central Siberia). We speculate that specific parameter values of the Vaganov–Shashkin model and their variability under local conditions and species are the key to understand different physiological processes in conifers. According to the simulation results for the temperature-limited site, wider rings of Picea obovata can result from a longer growing season. However, for the soil moisture-limited site, the final sizes of the tree rings of Pinus sylvestris were not affected by the length of the growing season but were primarily defined by the intra-seasonal variations in soil moisture, even under cold conditions. For the two sites, we obtained a 20-day difference between the two phenological dates, in which the early date could be associated with cambial initiation and the late date with the appearance of the first enlarging cell. In the case of central Siberia, the time period was half that of the southern Siberia. Such differences could be explained by both geography and species-specific responses to phenology. To test this hypothesis, additional tree-ring and climatic data for contrasted habitats would be needed.

As with most of the process-based models, the initial purpose of the VS-model was to 98 describe variability of tree-ring radial growth, particularly tree-ring formation as related to 99 climatic influence, and to determine principal factors limiting tree-ring growth. However, the 100 VS-model is a complex tool that requires a considerable number of model parameters that 101 should be re-estimated for each forest stand. This leads to problems of accurate model 102 parameterization, namely estimations of "optimal" values of the model parameters necessary  Following that purpose, we applied the VS-Oscilloscope to simulate tree-ring enlargement in 121 spruce (Picea obovata Ledeb.) and pine (Pinus sylvestris L.) trees growing in differing 122 environmental conditions. The two contrasting tree-growth habitats were: (1) the middle part 123 of Central Siberia close to the settlement of Tura within the continuous permafrost zone, 124 where temperature is a principal limiting factor of tree growth (Kirdyanov et    The site where tree-ring growth is limited by temperature (PlatPO) is located in the middle 138 part of Central Siberia (64°17' N, 100°13' E, 610 m a.s.l.) (Fig. 1). The climate is continental 139 with short and cool to mild summers and long winters. The mean annual air temperature is −9 140 °C, and the annual precipitation is 370 mm. To select the set of model parameters providing 141 the best-fit model, daily weather records from the Tura meteorological station were used.

148
The average amount of precipitation per year is 330 mm, of which approximately 81-91% 149 falls within the period from April to October. The first half of the growing season is 150 characterized by a lack of atmospheric moisture (low ratio between the amounts of 151 precipitation and evaporation). At this site, Betula pendula Roth. and Pinus sylvestris L. trees 152 dominate in the sedge-grass-forb forest on sand dunes. We used a Pinus sylvestris ring-width 153 chronology and daily weather records from the Minusinsk station. factors (e.g., age affects, abrupt changes caused by fires or defoliation caused by insects) on 162 tree radial growth, a 50%-variance cubic smoothing spline with a 2/3 cut-off time series 163 length was used as the detrending method. Autoregressive modeling was applied to remove 164 autocorrelations from the detrended time-series. Finally, the residual tree-ring chronology was 165 obtained using the bi-weight robust average procedure (Cook and Kairiukstis, 1990

VS-model 169
The Vaganov-Shashkin simulation model is a process-based forward model that describes the 170 formation of tree rings in relation to three environmental parameters: air temperature, soil 171 moisture and solar irradiation. Here we provide a very brief description of the VS-model, but 172 complete details can be found in Vaganov et al. (2006;. 173 The input data for the model are daily records of mean temperature and total precipitation.

174
Taking into consideration the amount of precipitation, intensity of transpiration depending on 175 temperature and air relative humidity, and infiltration (Thornthwaite, Mather, 1955), the  For each i-day of the year, the model provides the integral rate of tree-ring growth Gr(i) that 180 is determined as the minimum of two partial growth rates: the growth rate that is dependent 181 on the daily air temperature (GrT) and the partial growth rate that is dependent on daily soil where N is the day count in the season, and Gr is the average growth rate over the calibration 191 or verification period. The simulated ring-width indices were compared with the ring-width 192 indices of the actual chronology for MIN. 193 To quantify the agreement between the simulated and actual ring-width series, we used    In the actual chronologies and corresponding simulated growth time series for both sites, we 218 selected two groups of favorable (unfavorable) growing seasons (i.e., the years) when most of 219 the corresponding wide (narrow) tree rings were formed. We defined wide rings as those 220 whose ring-width indices exceed the mean value of the chronology by more than one standard 221 deviation, whereas narrow ring-width indices are those that are at least one standard deviation 222 below the mean value. Based on the described procedure, we selected (1) favorable growing 223 seasons for the MIN site (1936, 1938, 1970, 1982, 1993, 1995, 1997, 2003, and 2006) and 224 PlatPO site (1979, 2001, 2002, and 2005) when most of the wide rings were formed and (2) 225 unfavorable growing seasons for the MIN site (1942, 1943, 1945, 1946, 1964, 1965, 1969, 226 1974, 1983, and 1998) and PlatPO site (1950, 1951, 1961, 1974, 1977, 1987, 1988, and 1989) 227 when the narrow rings were formed. Applying the VS-Oscilloscope parameter adjustment procedure (see Table S1), we obtained  chronology: R =0.53, S=70%, p <0.0001, and n=24 years for the MIN site ( Fig. 2A) and R 239 =0.5, S=80%, p <0.0001, and n=20 years for the PlatPO site (Fig. 2B).  fixed (see Table S1). The value of Tbeg was changed from 70 °C to 150 °C in 10 °C steps, and 266 Tminwas changed from 1 °C to 10 °C in 1 °C steps.

267
When Tmin was increased from 1 °C to 5 °C, the variances of the simulated growth time series 268 did not change and equaled the variance of the actual chronology. The simulated variances 269 were higher than the observed variance as Tmin was varied between 6 and 10 °C. As Tbeg was 270 changed from 70 to 90 °C, the calculated variance was 5.2 times higher than that observed.

271
Above that, the simulated variances decreased and became equal to the actual variance at for Tbeg=110 °C and Tmin =5 o C (Fig. 3). 277 A similar sensitivity test was undertaken for other model parameters, and the most sensitive 278 (influential) parameters are presented in Table S1. We defined the parameter as influential if 279 the correlation and synchronicity coefficients varied more than 1% by changing the parameter 280 values.

Analysis of intra-seasonal kinetics of tree-ring growth 282
The VS-model provides us the ability to estimate the duration of growing seasons, describe 283 soil moisture kinetics and growth rate changes within the seasons, and determine which 284 factor, air temperature or soil moisture, limits tree-ring growth on each day of the season.

285
For the MIN site, the best-fit model parameterization shows that all growing-season timing 286 and duration values vary substantially (Table 1) greater than during the seasons when narrow rings are formed (Fig. 4). The maximum values 303 of air temperature usually occur in late June-early July (Fig. S3A). During growing seasons 304 when wide rings were being formed, the soil moisture ( Fig. S3C) as well as a partial growth 305 rate depended on soil moisture GrW (Fig. 4A), and the integral growth rates Gr (Fig. 4B) were 306 significantly higher than during the seasons when narrow rings were formed. The obtained 307 results shown in the Fig. 4 are confirmed by one-way ANOVA for the variabilities of GrW 308 and Gr in wide and narrow rings (Fig. S4A). The mean values of GrW and Gr are significantly 309 higher in the group of wide rings. This indicates the negative effects of high May-July 310 temperature on tree-ring growth during the season (Fig. S1A). Higher air temperatures 311 resulted in higher transpiration and decreased soil moisture (Fig. 5) August (Table 1). The time-lag between DOYtmin and DOYbeg can vary from 6 to 62 days.

316
The minimum temperature threshold for growth, Tmin, is reached within the period from the 317 middle of March to early June.

318
According to simulation results, a wider tree ring will result from an earlier start and a longer 319 duration of the growing season (Fig. S2B, Figs. S5C, D). Although the dates of the end of the 320 growing seasons for wide and narrow rings are almost the same (Fig. S5D), the dates of the 321 beginning of the growth seasons differ significantly (Fig. S5C). 322 The growing season for wide rings begins during the last week of May or in early June (152 323 ±7 days), and narrow rings start to grow in the middle or end of June (166±11 days) for 324 PlatPO (Table 1). The average duration of the growing season for wide rings is approximately 325 94(±15) days and that for narrow rings is 80(±10) days.

326
The narrow rings were formed in the years when the temperature values (Fig. S3B) as well as 327 corresponding partial growth rates depended on temperature GrT, and the integral growth rates formed. According to the one-way ANOVA for the variability in the growth rates in the wide 330 and narrow rings (Fig. S4B), the mean values of the GrT and Gr for wide rings are 331 significantly higher. We noted that there is a significant difference in the soil moisture 332 kinetics (Fig. S3D) and, as a result, in the partial growth rates dependent on soil moisture

346
The choice of the two tree species was due to the fact that the tree growth was required to be 347 definitely limited either by temperature or soil moisture in two sites.

348
Siberian spruce is one of the main species for Siberia. Due to its preferences to grow in moist source of moisture for the next growing season. We did not observe such an autocorrelation 387 for the temperature-limited site PlatPO (Fig. S1B). 388 It was shown that temperature can play a role as a limiting factor during late spring-early Babushkina, 2015), which can be confirmed by the formation of particularly narrow rings. 394 We especially note that the VS-model parameterization can provide important reliable 395 phenological information, e.g., the start and end of the growing seasons over several decades, 396 based on available daily climatic observations in a long-term historical context (see Table 1).

397
In practice, to obtain such information even for few years is a time consuming and complex of growing season (Fig. 4B). 412 The best similarity between the modeled and actual chronologies is obtained if we determine 413 the minimum temperature for growth as 5 (9) o C and the effective temperature sum for the 414 initiation of growth Tbeg as 110 (100) over 10 days (   Table 1). With the initiation of mother cells, it can take as many as 3-5 437 additional days to form a whole cambial zone. In the MIN case, the time cycle is even 438 longer-up to 40 days (see Table 1). Therefore, the time difference between the dates of Tmin

487
The authors declare that they have no conflict of interest.    Table 1.  where n + is the number of segments from radial growth having the same tendency and n is the 779 length of the compared period (in years) (Savva et. al., 2002).  Table S1. Estimated VS-model parameters by the VS-oscilloscope.

Parameters
Description MIN PlatPO

Tmin
Minimum temperature for tree growth ( o C) 5 9

Topt1
Lower end of range of optimal temperatures ( o C) 13 22

Topt2
Upper end of range of optimal temperatures ( o C) 22 28