Biogeosciences Process based model sheds light on climate sensitivity of Mediterranean tree-ring width

We use the process-based VS (Vaganov-Shashkin) model to investigate whether a regional Pinus halepensis tree-ring chronology from Tunisia can be simulated as a function of climate alone by employing a biological model linking day length and daily temperature and precipitation (AD 1959–2004) from a climate station to ring-width variations. We check performance of the model on independent data by a validation exercise in which the model’s parameters are tuned using data for 1982–2004 and the model is applied to generate tree-ring indices for 1959–1981. The validation exercise yields a highly significant positive correlation between the residual chronology and estimated growth curve (r = 0.76 p < 0.0001,n = 23). The model shows that the average duration of the growing season is 191 days, with considerable variation from year to year. On average, soil moisture limits tree-ring growth for 128 days and temperature for 63 days. Model results depend on chosen values of parameters, in particular a parameter specifying a balance ratio between soil moisture and precipitation. Future work in the Mediterranean region should include multi-year natural experiments to verify patterns of cambial-growth variation suggested by the VS model.


Introduction
Instrumental records such as precipitation and temperature can be extended back several centuries with proxy data in North Africa.The resulting records can provide estimates of the past frequency and severity of climatic anomalies and these in turn can be used to help anticipate the probability of such events in the future.Long time series of tree-ring growth are one of the best sources of proxy data for reconstructing past records of precipitation, streamflow, and drought on interannual to centennial time scales during the late Holocene.Tree-ring records are annually resolved, wellreplicated, and can be calibrated and validated against the instrumental record.Dendroclimatic studies have been performed in several North African countries, including Morocco (e.g.Till and Guiot, 1990;Chbouki et al., 1995;Glueck and Stockton, 2001;Esper et al., 2007;Touchan et al., 2011), Algeria (Messaoudene and Tessier, 1997;Touchan et al., 2008aTouchan et al., , 2011)), and Tunisia (Aloui and Serre-Bachet, 1987;Tessier et al., 1994;Touchan et al., 2008aTouchan et al., , b, 2011)).
Generally these dendroclimatic studies assume that annual tree-ring growth is adequately determined by a linear function of local or regional precipitation and temperature with a set of coefficients that are temporally invariant.However, various researchers have stressed that tree-ring records are the result of multivariate, often nonlinear, biological and physical processes (Fritts, 1976;Vaganov et al., 2006;Anchukaitis et al., 2006;Evans et al., 2006).There are nonclimatic influences on tree-ring records, including tree biology, size, age and localized forest dynamics (Cook and Kairiukstis, 1990).This represents a problem for both singlevariable dendroclimatic reconstructions using linear statistical calibration of the tree-ring proxy data and for prediction of the impacts of climate change on tree biology and forest ecology.Linear empirical-statistical analyses alone cannot be used to demonstrate a physical or biological mechanism for variability or change in the climate-tree growth relationship.
The process-based VS (Vaganov-Shashkin) model (Vaganov et al., 2006) can be used to resolve the critical processes linking climate variables to tree-ring formation.This model allows us to identify and account for such processes in developing better estimates of past climate.In this paper, we investigate whether a regional Pinus halepensis tree-ring chronology from Tunisia can be simulated as a function of climate alone by employing the VS model to link day length and daily temperature and precipitation from a climate station to ring-width variations (Vaganov et al., 1999(Vaganov et al., , 2006)).

Methods
We used a tree ring chronology and a modeling approach to evaluate whether the tree ring chronology could be simulated as a function of climate alone.Data used include a regional tree-ring chronology of Pinus halepensis from Tunisia (Touchan et al., 2008b) and daily precipitation and temperature (A.D. 1959-2004) for the Jendouba weather station (36.48 • N 8.8 • E, 140 m a.s.l.).The regional chronology was built from a combination of 84 series of ring-width measurements from four sites in Tunisia.The sites are at a range of elevations from 383 m to 1100 m in the region 35.58 • N-36.23 • N, 8.43 • -9.30 • E. These sites and chronologies are described in detail elsewhere (Touchan et al., 2008b).
The process-based VS model used here has two unique characteristics.First, it deals with rates of growth of cells as if their formation in the cambium is influenced entirely by the physical environment.Second, it deals explicitly with the dynamics of cell growth, division, and maturation.
The model computes the integral growth rate Gr and simulates conifer tree-ring formation from three variables: solar radiation, daily surface air temperature, and soil moisture (Vaganov et al., 2006).
The growth rate on a specific day t is modeled as where g I (t), g T (t), g W (t) are partial growth rates depending on light I , temperature T , and soil moisture W The partial rate g I (t) is a function of latitude, declination angle, and hour angles (Gates, 1980) (Fig. 1) and can be described as:   A water-balance equation is used to determine the water content in the soil from daily mean temperature and precipitation (Thornthwaite and Mather, 1955;Alisov, 1961): where W -first difference of water content in the soil, f (P ) -precipitation amount in the soil described by: W -water drainage from the soil (Vaganov et al., 2006).
k 1 -fraction of precipitation penetrating soil (not caught by crown) (see Table 1), P max -maximum daily precipitation for saturated soil (see Table 1).
In the paper we used VS model Version 5.0, developed in Fortran by A. V. Shashkin (Vaganov et al., 2006).The VS model is multi-parametric (see Table 1), and a main difficulty is determination of biologically reasonable parameters that provide a good approximation of the initial, or observed, tree-ring chronology, such that the simulated chronology is highly correlated with the observed chronology.Appropriate temperature parameters for conifer trees, such as the Aleppo pine chronology used in the model, were selected from published studies of natural (uncontrolled) systems (Deslauriers and Morin, 2005;Rossi et al., 2006Rossi et al., , 2007Rossi et al., , 2008)).Water-use efficiency in dry environments is difficult to specify because conifer trees respond differently from one environment to the other (Oberhuber and Gruber, 2010;Gruber et al., 2010).Therefore, optimal parameters were chosen manually by trial and error using the model and average daily variation of model soil moisture from 1982-2004 (Table 1, Figs. 3, 4).As this process guarantees some agreement of simulated and observed chronology, it is critical to test the performance on independent data.We did this by applying the model and climate data for 1959-1981 to simulate the chronology for that earlier period.

VS-model calibration and verification
With the estimated optimal parameters (see Table 1) we obtained highly significant positive correlation between the initial chronology and estimated growth curve (r = 0.76, p < 0.0001, n = 23 years) for the calibration period 1982-2004 (Fig. 2).When the model was applied to simulate the chronology for a period  outside the period used to tune the parameters, agreement of observed with simulated chronology was also strong: the high positive correlation (r = 0.63, p < 0.0001, n = 23 years) between curves (Fig. 2) confirms that the VS model can be used to estimate the nonlinear tree-growth response to climate changes in the past for specific local drought conditions, as well as to simulate tree growth (particularly cambial activity and cell formation) under extreme environmental changes.Fig. 2. Variations of initial tree-ring residual chronology (blue solid line) and simulated tree-growth curve (red dashed line) for calibration period  and verification period .

Analysis of internal model characteristics
The VS model allows us to analyze features of tree-ring growth response in specific environmental conditions.For example, we can estimate the partial influence of temperature and precipitation on tree-ring formation and the water content of the soil at various times throughout the growing season.Moreover, we can trace the process of cell formation in the tree ring under conditions for which we have cell measurements for model verification (Vaganov et al., 2006).The estimated soil moisture in our region is shown by the VS model to increase at the start of each year, reach a maximum in April, and then monotonically decrease till August.We note that these results are consistent with experimental observations for water content of soil in that region (Kleeberg and Koplitz-Weissgerber, 1983).
The limiting influence of climatic variables on tree growth during the growing season is a critical question.Standard multiple regression techniques using monthly climatic data cannot address that question.It is necessary to consider nonlinear influences operating down to at least the daily time step in estimating tree growth by climatic forcing (temperature, precipitation and solar irradiation) (Vaganov et al., 2006).
The VS-model output of partial tree growth rates shows that at the start of each year, growth rate g T (t) is less than g W (t), such that tree growth is limited by temperature until April (Fig. 3).From April to August soil moisture is the limiting factor to tree-ring growth: partial g W (t) is generally less than partial g T (t) (Fig. 3).
An integral growth rate Gr(t) lower than the modelspecified minimum cambial cell growth rate V cr indicates no growth.Accordingly, our results suggest that cambial activity stops in the middle of July and does not resume until next year (Fig. 4), despite partial growth rates g T (t) and g W (t) (especially, in October, November and December ) being favorable for resumption of growth again after August-September (Fig. 4).The reason growth does not resume is day-length (or solar irradiance), which continues decreasing in September.In this case, g I (t) and its nonlinear interaction with g W (t) is the common limiting growth factor beginning in late August.Detailed analysis of simulated annual growing seasons shows that in some favorable years (e.g. 1982, 1990, 1994, 2002) trees could possibly change their strategy of growth.They could change their unimodal growth pattern (with one spring-summer period of cambial activity per year) to bimodal -cambial cell division activated again in autumn by extremely favorable soil moisture.The possibility of bimodal growth patterns in Spain was shown by De Luis et al. (2011).A bimodal growth pattern in our region needs to be verified by multi-year natural experiments.
The time plot of average integral growth rate (Fig. 4), and its position relative to the minimum cambial growth rate can be analyzed to compute various growth statistics.For our example, the average duration of the growing season is 191 days, with a standard deviation of 82 days.On average, soil moisture limits tree-ring growth for 128 days and temperature for 63 days.Verifying the results from simulations would require direct measurements of cambial growth, including measurements of cell sizes over several growing seasons.Such measurements can improve the model's performance for a given species, and help in the interpretation of features such as false rings, or intra-annual density fluctuations.These features are implied by the bimodal growth curve in Fig. 4. In fact the VS model allows the user to simulate cambial activity during the entire growing season, including the estimation of the number and sizes of new cells in the current tree ring (Vaganov et al., 2006).We note that false rings were observed in some samples from one of the four tree-ring sites contributing to the regional chronology.
The VS model indicates variability in the start of the growing season.The mean start date is the 34 th day of year, with a standard deviation of 26 days.The start of the growing season is defined by the rate of cambial cell growth.If the rate of growth is more than 0.1, the growing season is assumed to have started (see Table 1, V cr ).The growing season is assumed to end when the integral growth rate Gr(t) falls below 0.1.Note that this happened in June-July of a recent year.During the 1982-2004 analysis period the principal limiting factor is soil moisture, indicated by the VS model to have limited growth in 67 % of the growing-season days.

Drought simulation and tree growth response
Tree-growth simulations will depend to some extent on the settings of all parameters.An especially important algorithm of the VS model utilizes a balance ratio between precipitation and soil moisture.Specifically, soil moisture eventually becomes stable with lower precipitation because a direct decrease of precipitation (up to 50 %) involves a decrease of tree transpiration.The sensitivity of soil moisture to precipitation in the VS model can be varied by changing the setting of the drainage coefficient , defined as an additional fraction (portion) of water evaporating from soil and not included in the tree transpiration (Vaganov, 2006).As a sensitivity experiment, we varied from 0.000 to 0.007 (with step 0.001), generated a tree-ring chronology with each setting, and observed the change in chronology statistics.Each step increase in drainage coefficient over this range www.biogeosciences.net/9/965/2012/Biogeosciences, 9, 965-972, 2012 Fig. 4. Average integral growth rate Gr(t) (red line) for calibration period  fitted by negative exponentially-weighted smoothing (Mclain 1974).Dashed line corresponds to minimum cambial cell growth rate V cr.corresponds to an increase of the water deficit by about 5 %.Such a change of drainage coefficient was strongly reflected in the estimated tree-ring growth.The primary effect was a lowered median, amplified variance and increased skewness of tree-ring chronology with increased (Table 2, and Fig. 5).The lowered median of growth reflects an increased water deficit in the soil.This result highlights the importance of parameter settings in the VS model, as a higher could result in a more sensitivity of tree growth to precipitation.

Conclusions
The process-based VS model skillfully reproduces a time series of a regional Pinus halepensis tree-ring chronology for Tunisia as a function of climate alone.The chronology simulated by the model correlates strongly with the original chronology for the calibration period used to tune the model parameters (r = 0.76, AD 1982AD -2004)).More important, the model effectively generates a tree-ring chronology for an earlier period of time outside the tuning window (r = 0.63, AD 1959AD -1981)).The results suggest that, at least for this species, The model yields important diagnostic information on the tree-growth response to climate.For example, the model shows that the average duration of the growing season is 191 days, and that on average soil moisture limits tree-ring growth for128 days and temperature for 63 days in that 191day window.The model also indicates a huge variability about the mean in such variables as duration of growing season, and leaves open the possibility of a bimodal growth season in some years.The strength of the VS model is its ability to simulate a non-linear tree-growth response to climate changes.In the Mediterranean region and elsewhere such simulations can be used to help explain observed patterns of tree-growth variation in the past and to simulate tree growth under extreme environmental changes.The VS model may also be useful in the climatic interpretation of tree-ring variations when the climate-growth signal is weaker than for the samples used in this study.Good simulation results have previously been reported for such cases (e.g.Vaganov et al., 2006;Shishov et al. 2007;Ivanovsky and Shishov, 2010).Of course, the ability of the model to handle nonlinear climate influence on growth can result in good simulations only when the climate-growth linkage is reasonably strong.
Although primarily, as in this paper, used with conifers, the VS model is also applicable to tree-ring chronologies of angiosperms (hardwood trees).Developers of the model (E.Vaganov, A. Shashkin and H. Fritts) have successfully used it on hardwoods (unpublished results) Output from the processes-based VS model includes the partial influence of temperature and precipitation (soil moisture) on tree-ring formation, the water content in the soil during the growing season, and the start and end date of the growing season.Potential applications of this type of information include assessment of likely impact of regional warming on tree-ring indices, and evaluation of the capability of particular tree species to sense climate fluctuations in various seasonal time windows.
VS-modeling and direct cell measurements enable us to estimate cell dynamics of tree-ring formation in this extremely dry Mediterranean environment, and to better understand how tree growth there is controlled by climate.Multiyear natural field studies, including cell dimension measurements, are essential to better understand the dynamics and verify model findings.

Fig. 1 .
Fig.1.Harmonic function that defines partial growth rate g I (t) depending on day length and piece-wise linear functions that define partial growth rates (g T (t) and g W (t)) depending on temperature T and soil moisture W .
h s -hour angle for the latitude θ -declination angle for the latitude I 0 -direct solar irradiation for the Earth (≈ 1360 W m −2 )

Fig. 3 .
Fig. 3. Partial growth rates depending on day length g I (t) (black circles), soil moisture g W (t) (blue line) and temperature g T (t) (red line) for 1982-2004 fitted by negative exponentially-weighted smoothing (Mclain, 1974) 2 .Blue and red dots on the graph are daily values of partial rates superimposed on each other for each year.

Fig. 5 .
Fig. 5. Simulated tree-ring growth chronologies by different values of drainage coefficients.

Table 1 .
Optimal model parameters 1 estimated calibration of VS model over period1982-2004.
1 Description of parameters is according toEvans et al. (2006)

Table 2 .
Descriptive statistics of simulated tree-ring curves obtained by different values of drainage coefficient .Last column is Pearson correlation between the initial chronology ( =0) and the estimated curve using different values of drainage coefficients.