Nanomechanical/Micromechanical Approach to the Problems of Dendrochronology and Dendroclimatology

The most widespread approach in dendrochronology (wood dating) and dendroclimatology (climate reconstruction) is based on measurement of the width of annual growth rings by analyzing optical images of wood cross sections. This approach is quite efficient and easy to implement but it has inherent drawbacks. Raw data for these techniques originate from the optical properties of the wood surface, which are not directly related to other properties of wood, mechanical properties in particular. This paper describes a new quantitative approach applicable to dendrochronology and dendroclimatology based upon measurement of the micromechanical properties of wood by employing nanoindendation and digital sclerometry. It yields not only the width of annual growth rings and early and late wood layers with an accuracy not inferior to optical methods, but also rich data on the mechanical properties of the wood with a high spatial resolution that could be brought to subcellular scale if necessary. This data can be used for the dendrochronological analysis of archeological finds and the evaluation of climatic parameters during tree growth with a time resolution of up to a month or even better, which is unlike other common methods with a time resolution of one year. Moreover, the detailed continuous profiling of local mechanical properties can form a basis for improving our understanding of the nature and mechanisms of the formation of macromechanical properties important for applications and can clarify the climate factors that have the greatest impact on such properties.


INTRODUCTION
Dendrochronology, dendroclimatology, dendrogeomorphology, dendroarchaeology, and dendroecology are disciplines that use various characteristics of the annual growth rings of trees to date wooden buildings, ancient artifacts, musical instruments, household items [1][2][3][4][5], for a retrospective analysis of climatic, geomorphological, and environmental conditions hundreds, and sometimes thousands of years ago [6][7][8].Optical methods (OMs) are the most widely used in the analysis of annual rings, usually supplemented by programs for the analysis of digitized images of a wood cross section [5,8].The primary information in OMs is based on a difference in the reflectivity of early and late wood (EW and LW, respectively).Alternating annual growth rings (GR) on cross sections/cores represent a kind of chronicle of events that reflect the morphology and growth rate of the wood during the growing season.The tree ring width W carries information about growth conditions and indirectly about the quality of wood.Its variations serve as the main source of primary data in problems of dendrochronology and dendroclimatology [3,5,[7][8][9][10][11].The value W can be measured on widely used semi-automatic devices of the LINTAB line from the German company RINNTECH, equipped with TsapWin, Windendro, Coorecorder CDendro image processing and analysis programs.
Since the beginning of the 21st century, analysis of the image of rings in the blue range has been considered more informative and reliable than in other parts of the spectrum [12,13].Following [13], this kind of OM is usually called the blue intensity method and is currently widely used in dendrochronology and dendroclimatology [14][15][16].Virtually all OMs require a skilled operator to decide whether to exclude false rings, which introduces an element of subjectivity into the process.
It is important to emphasize that with all the diversity and development of OMs, the characteristics recovered with their help (anatomical, morphological or geometric, such as the width of the GR, the proportion of EW and LW in them, variations in these parameters from ring to ring) are not directly related to POLYMERIC, BIOORGANIC, AND HYBRID NANOMATERIALS mechanical properties.Some of the OMs depend significantly on subjectively assigned criteria for drawing the boundary between EW and LW.
All of the above together stimulates the search for more informative approaches and techniques for analyzing annual rings, which would be independent of the operator and subjective criteria and would provide quantitative data on the microstructure and mesostructure of wood and its mechanical properties at various scale levels not indirectly, but directly.as a result of direct measurements.This approach will increase the information content of the analysis of the GR structure in the interests of dendrochronology and dendroclimatology, and will provide an opportunity for a deeper understanding of the patterns of formation of the macroscopic mechanical properties of wood based on knowledge of the characteristics of individual microstructural components.
One such nanomechanical/micromechanical method can be scanning nanoindentation (NI) or contact atomic-force microscopy (AFM) [17][18][19][20].They make it possible to achieve a spatial resolution much higher than in optical, X-ray, and isotope methods for studying the structure of wood, and to obtain a complex of multiscale quantitative mechanical characteristics of the material.
The first attempts to use the NI technique for this purpose are described in [21].Then this approach was developed in the series of works [22][23][24][25][26].However, NI performed in a large sequence of discrete points on a surface is very labor intensive and requires expensive equipment [18,19,26].
As an alternative or addition to the NI method, the work proposes a high-performance multifunctional approach to studying the structure and properties of GR, in which the primary data are obtained not with the help of OMs, but by nanomechanical and micromechanical testing of the wood cross section.Along with NI, we use an original method of digital sclerometry, related to NI and tested by us for the first time in [27].In contrast to NI, this method does not continuously record the probe-immersion depth at a fixed point on the sample surface under the action of a growing load, but the vertical and lateral components of the force on the probe as it moves along the sample surface at a given depth.The digital-sclerometry method allows not only determination of the width of the GR and EW and LW layers in the tested wood, but also quantitatively characterization of the local mechanical properties inside the rings with micrometer and, if necessary, nanometer resolution.The transition from the optical characteristics of the wood surface as primary data on the GR structure to their micromechanical properties creates an independent channel of information that is promising for many problems in tree science, dendrochronology and dendroclimatology, growing trees with desired mechanical properties, etc.
It is known that in most tree species the mechanical properties of cell walls, in particular the microhardness H and Young's modulus E measured in EW and LW in any annual growth ring differ by no more than a few tens of percent [28][29][30], and in some cases even by less than 10%.For example, for pine, this difference in H is only about 7% [31].Based on such small differences, it is difficult to construct an accurate method for measuring GR, EW, and LW widths using nanomechanical measurements.At the same time, the effective values of the hardness and Young's modulus (H eff and E eff , respectively), averaged over the cross section of several cells and taking into account the porosity of the cellular microstructure of wood, differ by several times [22][23][24][25][26]32].This creates a more convenient and reliable base of primary data for the subsequent development of nanomechanical methods of dendrochronology and dendroclimatology.However, the measurement H eff and E eff requires careful surface preparation, is time consuming, and is discrete.
In contrast, variations in the normal and lateral forces (F n and F l , respectively) acting on the probe during its movement parallel to the sample surface during scratching, reflect changes in the mechanical properties along the scanning direction continuously and do not require careful surface preparation.When the probe moves at a given depth perpendicular to the annual rings on a cross section of wood, the profile of the change in F n and F l quantitatively and independently of the operator characterizes the ring structure of wood and the local distributions of intraring mechanical properties with the required resolution.This makes it possible to use the scratching technique to determine the GR width and identify the proportion of EW and LW in the interests of dendrochronology and dendroclimatology, as well as to assess both the local and integral mechanical properties of wood and other plant materials.
By varying the predetermined immersion depth of the probe into the material and the geometry of its tip, it is possible to adjust the spatial resolution of the method and investigate size effects in the mechanical properties of wood.Changing the speed of lateral movement of the probe makes it possible to study their speed sensitivity in one device in a very wide range of deformation conditions, from quasi-steady-state to impact.
Taken together, all the features of nanomechanical/micromechanical methods for analyzing the ring structure of wood described above provide a number of advantages over traditional methods based on primary data, which in most cases are obtained using OMs (reviews [33][34][35][36]).
The purpose of this work is the further development of methods for micromechanical testing of the structure and properties of annual rings of wood, their intraring variations with the aim of subsequent adaptation and use for solving problems of dendrochronology and dendroclimatology at a new ideological and technological level.

MATERIALS AND METHODS
The experiment was carried out on samples of coniferous and deciduous wood, typical for the center of European Russia.Scotch pine was chosen as a coniferous tree (Pinus sylvestris L.) 60 years old, growing in the Vernadsky forestry of Tambov oblast.The representatives of hardwoods were pedunculate oak (or common oak, Quercus robur) and small-leaved linden (Tilia cordata) 65 years old, growing on the territory of the Gorelsky forestry enterprise (Tambov oblast).Sample collection was carried out in September 2021.
The samples were sawn from a cross section of wood in the form of parallelepipeds 10 × 30 × 250 mm in size and dried at a temperature of 75°C to a moisture content of 12%.The mode used provides the defectfree drying of wood with full preservation of its natural physical and mechanical properties.The moisture content of the samples during and after drying was periodically controlled by weighing the samples on an analytical balance.The long side of the samples coincided with the radial direction in the tree trunk.All studies of the structure and properties of the GR were carried out on a surface normal to the axis of the tree, and therefore perpendicular to the cell walls and fibers, and the test load was applied along them.This surface was treated with progressively smaller grit size abrasives using an AutoMet 250 grinder and polisher (Buhler, USA).The final surface roughness R a , measured with a DiInnova SPM model 840-012-711 scanning probe microscope (Veeco-Digital Instruments, USA), was about 270 nm for pine and linden, and 160 nm for oak.
Investigation of the cell structure and annual rings in the wood samples by scanning-electron microscopy (SEM) was carried out on a Tescan Vega 3 instrument (Thermo Fisher Scientific, USA).Before that, a layer several tens of micrometers thick was cut from the polished sample surface with an ultramicrotome.The typical SEM images of three types of wood are shown in Fig. 1.
To prepare samples for research by NI methods, layers of the sample deformed during polishing with a thickness of about a hundred micrometers were cut from their surface with the microtome.The nanomechanical properties of the wood were measured by NI methods on a Nanotester Triboindenter TI-950 precision nanomechanical complex (Hysitron, USA) equipped with a Berkovich diamond trihedral indenter with a tip curvature radius of ~30 nm.This tool is able to record the load diagram P-h with a resolution of ~50 nN for force P ~ 0.5 nm along the vertical movement of the indenter h, which is then processed by built-in software to obtain values of the Young's mod- ulus E and hardness H according to the Oliver-Pharr method [37,38] adopted as a basis in the ISO 14577 [39] and GOST [40] standards.
For scratch tests, we used an original specialized device containing a fixed base platform with horizontal guides and a movable carriage with vertical guides (Fig. 2).The carriage with a replaceable force sensor, on which the probe was fixed, was moved parallel to the sample surface at a constant given speed V from 30 µm/s to 8 mm/s with a stepper motor controlled by a computer.A vertical drive on the carriage set a fixed penetration depth d of the probe into the material.As the probe in this work, we used a standard Rockwell indenter made of hardened steel, which has a conical shape with an angle of 120° and a radius of curvature at the apex of R = 200 µm.It was installed using an LF-202M two-coordinate force sensor (Ligent Sensor Tech Co., Ltd., China), which made it possible to continuously measure the normal and lateral components of the probe-sample interaction force.The sensor had a measurement limit of 150 N, and the system resolution was 10 mN for each axis.
To determine the rigidity of the power circuit of the testing machine, scratch tests were carried out on a hardened steel plate with steps of height Δz = 6 µm and the initial minimum pressure of the probe F n = 1-2 N. At the same time, after the test, there were no traces of the probe on the plate, and the force F n on the step increased to 6-7 N (the average value of the jump in the normal component of the force was ΔF n = 5.5 N).Thus, the rigidity of the power circuit of the device was C f = ∆F n /Δz ~ 10 6 N/m.This value exceeded by an order of magnitude the rigidity of the tip-sample contact С с with vertical load on the probe F n = 10-20 N.
Mechanical testing in a "rigid" testing machine means that the probe is preset to a fixed penetration depth d into the material being tested.Value d determines the absolute deformation of the surface, regardless of its elasticity, viscoelasticity, creep, plasticity, etc., and the force sensor measures the resistance to all these types of deformation.The hybrid mode of testing, when both the force and the deformation can be changed at the same time, greatly complicates subsequent interpretation of the experimental results, in which the mechanical properties of the sample and the machine are mixed.
During scanning, components F n and F l of the force applied to the probe were measured; the data stream was digitized by a 24-bit analog-to-digital converter (ADC) at a frequency of 30 Hz and loaded into computer memory.This made it possible to obtain continuous profiles of the physical and mechanical properties of the surface layers of the material with a spatial resolution depending on the shape of the probe and the given scratch depth.At low loads, the resolution could reach a submicron value.The variation in the values V and d made it possible to change the rate of relative deformation ~ V/d during mechanical tests in a very wide range from 0.3 to 1000 s -1 .High deformation rates (>10 s -1 ) completely exclude the influence of creep and viscoelasticity on the test results.Scribing was carried out on transverse sections of the trunk in the radial direction with respect to the annual rings.ε Fig. 2. Scheme of the experimental setup for studying the nanomechanical and micromechanical properties of wood by digital scribing: (1) base platform, (2) movable carriage, (3) rail guides, (4) stepper motor with ball screw for moving the carriage along axis x, (5) a support with a stepper motor for moving the force sensor with the probe along axis z, (6) two-coordinate force sensor, (7) probe, ( 8) sample (transverse saw cut of wood, the radial direction of which coincides with the coordinate x), (9) controller, (10) personal computer.F n and F l are the normal and lateral components of the force acting on the probe during its movement along the sample surface.The operating experience of this installation has shown that it is suitable for testing not only wood and other cellulose-containing composites, but also for a wide range of other materials: cement rock, gas-and oil-containing rocks, ice, ice composites, etc.It makes it possible to carry out multiple nondestructive tests on one sample and obtain a large array of experimental data on the spatial distribution of the strength, elasticity, porosity and other physical and mechanical characteristics, and their size and velocity sensitivity.
An optical method for measuring the geometry of annual rings was used as a reference and was implemented by processing optical images of the surface of samples with a resolution of at least 900 dpi, i.e., no worse than 30 μm.The relative error in determining the width of the rings after averaging the results of four measurements did not exceed 1%.This uncertainty value is close to that of the standard optical technique widely used in wood science and dendrochronology described above.

RESULTS AND DISCUSSION
At the first stage of work, the NI method was used to measure the radial distributions of the effective values of the microhardness H eff and Young's modulus E eff in annual rings of pine, oak, and linden wood (Fig. 3).They are effective, because at the selected maximum load on the indenter P max = 500 mN, the indentation of the Berkovich diamond trihedral indenter had transverse dimensions of more than 100 μm and exceeded the average transverse size of a wood cell by several times.As a result, the data obtained under such deformation conditions refer to the properties of the highly porous cellular cell structure of wood, and not to individual cell walls, which have several times higher mechanical properties and density.The properties of cell walls vary little from layer to layer and from one annual ring to another, which makes them unsuitable for use in dendrochronology and dendroclimatology.
Each point on the graphs in Fig. 3 was obtained by averaging the results of 5-10 independent tests conducted with the same experimental parameters.As can be seen from these figures, in contrast to the mechanical properties of the cell walls, in the effective values H eff and E eff there is a pronounced periodicity of effective mechanical properties.It was in good agreement with the position of the boundaries of the annual rings, which are detected optically by a change in the color of the wood.At the boundary of the rings, in all the studied wood samples, the mechanical properties underwent an abrupt change.When moving from EW to LW inside annual rings H eff and E eff changed in a jumplike manner only in oak, while in pine and linden, it was smooth.
The values H eff and E eff inside each EW layer in different annual rings remained constant from year to year with a deviation of no more than 10%, despite the fact that the weather conditions of growth could differ significantly.For example, 2010 was very dry, which affected the width of the annual ring W (in particular, in pine, the value W decreased by more than half compared to previous years), but this had almost no effect on the value of H eff and E eff in the EW.
The maximum value variations of H eff and E eff from year to year in LW were slightly higher but did not exceed several tens of percent.Thus, variations in the width of the annual rings occur mainly due to the different number of cells in the layer, the transverse size of capillaries, and the porosity of the wood in the layer.
The presence of a sharp jump in H eff and E eff at the boundaries of annual rings (Fig. 3) made it possible to determine their width W NI according to scanning NI.Then they were compared to the value W o , which was determined by the optical method (by the contrast of the photographic image).This was similar to that used in the LINTAB equipment line.Comparison data for these two methods for determining the width of annual rings is shown in Fig. 4, from which it follows that the discrepancies between them do not exceed 2-3% in pine and 4-5% in oak and linden.The average deviation for 10 annual rings was half as much.In fact, this means that the scanning NI method can be used as an alternative to the optical method or supplement it with information about local mechanical properties.
Next, profiling of the mechanical properties of pine, oak, and linden wood was performed using the scratch method (digital sclerometry).Both components F n and F l of the force on the probe as a function of distance traveled x along the sample surface were simultaneously recorded (Fig. 2).These force components are determined by the mechanical properties of the wood, the geometry of the tool tip, and the specified scratch depth d.In this series of experiments d varied in the range from 10 to 100 μm.Depending on d and the mechanical properties of a particular wood, the maximum normal force F n max also changed in the range from 5 to 110 N. Figure 5 shows examples of dependences of the components of the force acting on the probe for each type of wood studied in the work.
When scratching in the specified range of d at a lateral velocity of V = 0.3 mm/s, the relative strain rate was = V/d = 3-30 s -1 (depending on the set value d), which completely eliminates the effect of creep on the results.On the other hand, if it is necessary to study time-dependent properties (viscoelasticity, creep, stress relaxation), the value can be reduced by several orders of magnitude.
The spatial resolution and information content of the method can be improved by optimizing the geometry of the probe tip and the value d.From the obtained data it follows that with an increase in d and  load on the probe, although the signal-to-noise ratio grows, the ratio that carries the main information F max /F min decreases.This is due to an increase in the contact area of the probe with the surface and, as a consequence, greater averaging of the mechanical properties over the bulk of the material, including at the GR boundaries.In addition, at large F max plastic deformation of the material can be replaced by fracture.In pine, when using a Rockwell indenter as a probe with a tip radius of R = 200 μm, this happens at d > 65 μm, which corresponded to F n max > 40 N.A decrease in d up to a few micrometers increases the requirements for surface smoothness, and leads to an increase in interference and a decrease in the signalto-noise ratio.Considering these circumstances, the scratching data at d from 10 to 50 μm were used for analysis and calculations, which corresponded to F n max = 6-25 N. At such a depth of scratching, it was carried out by a small part of the spherical tip of the Rockwell indenter.These conditions made it possible to resolve well not only annual rings, but also intraannular features of the mechanical properties of the wood (Figs.5b, 5d, and 5f).The study of the intraring structure makes it possible to assess, in addition to average annual climate changes, intraseasonal ones, which is of great interest for dendrochronology and dendroclimatology.
From the analysis of scratch profiles, the hardness H s of the EW and LW layers at the mesolevel was determined (Table 1).Here H s = F n /S cont , where S cont is the area of the indenter embedded in the material, determined taking into account its geometry and the depth of the scratch d.To determine the hardness in EW we used F n min on scratch profiles, and in LW, we used F n max respectively.The average ratio of H s in EW and LW was 4.1 ± 0.6 for pine, 3.7 ± 1.3 for oak, and 1.5 ± 0.1 for linden.Similar relationships were typical for the mechanical characteristics measured by NI methods, both for H eff and E eff in EW and LW.For pine, this ratio is 3.1 ± 0.4; for oak, 3.3 ± 0.7; and for linden, 1.6 ± 0.4.
Since the mechanical properties of wood in the EW and LW layers differ significantly, it is technically possible to determine the width of annual rings W s by scratching methods in different ways: (i) by the distance between the maxima (ii) or the minima on the charts F n (x) or F l (x), or (iii) between the maxima of their derivatives with respect to x.   Table 2 illustrates the average spread of the value W s relative to W o determined by the optical method.Table 2 shows that determining W s by the distance between adjacent minima or maxima has a much greater uncertainty compared to the third method.A large error in determining the position of extrema reduces the accuracy of determining W s , and random fluctuations form artifact extrema that enhance the negative effects.Therefore, in the work, the position of the boundaries between the annual rings was determined by the third  x, mm method, i.e., by the position of the maxima of the derivatives on the graphs F n (x) or F l (x).Changing the scribing depth within the limits specified above does not lead to a significant change in the determined position of the boundary.
Figure 6 shows the width of the annual rings W of pine, oak, and linden, determined by two methods: optical method and scratch testing.The relative dis-crepancy between the measured annual-ring widths obtained optically and by scratching is 1.5% for pine and 4% for oak and linden (Fig. 7).The absolute standard deviation of this discrepancy in all cases was several tens of micrometers, which is comparable to the size of a cell in wood.
The results obtained by digital sclerometry, in comparison with climatic data for the same period of time,  make it possible to identify correlations between the mechanical characteristics of annual rings, their intraannular variations in individual layers (in particular, in the EW and LW layers) with the most important weather characteristics for plant vegetation: temperature, precipitation, illumination, etc.Such an analysis makes it possible to propose for dendroclimatology (a retrospective description of climate) a fundamentally new approach in comparison with the traditional one based on the analysis of annual-ring-width variations found using OMs [33][34][35][36].By varying the time intervals at which certain mechanical and climatic charac-teristics are averaged, and the time lag between them, one can obtain a lot of new information about the relationships between such characteristics and identify the most significant weather factors affecting the quality of wood.
As typical examples of such correlations, Figs.8-11 show the results reflecting the degree of influence of temperature and precipitation during the entire growing season, its first and second half in the middle zone of European Russia on the width of annual rings W s , and hardness H s of the most durable LW layers of Scotch pine.It follows from these data that in LW the         3.A more thorough analysis of such relationships requires more statistics on wood samples, as well as weather conditions during its growth.This can be achieved both by increasing the studied time intervals and by expanding the geography of growth of the studied plants.It is of interest to study such correlations for different plant species in order to identify the most representative and accurate species as indicators of climate change.

CONCLUSIONS
A new nanomechanical/micromechanical approach and several methods implementing it for dendrochronology and dendroclimatology are proposed.They are based on the recording and analysis of profiles of changes in the micromechanical properties of wood of annual rings in the radial direction with respect to the axis of the trunk and identification of their correlations with climatic conditions of growth.As convenient local micromechanical characteristics for obtaining primary information, the nanohardness and microhardness, Young's modulus, and the normal and lateral force in contact when the probe moves parallel to the sample surface are used.In fact, in the latter case, an atomic-force probe microscopy scheme was used that was adapted to the problems of wood science, which required the use of much higher contact forces, much higher scanning speeds, and a larger spatial range of probe movements.This approach and methods for obtaining the primary data set are much more informative than those used in traditional optical techniques.In addition to the geometric and anatom-ical characteristics of the ring structure of wood, they allow one to extract information about the distributions of micromechanical and physical properties, and then find their correlations with climatic characteristics and, on this basis, reconstruct the climate in the past.Scribing methods do not have such a high spatial resolution as NI or AFM, but they are much more productive, less labor intensive, allow one to work in a very wide range of relative deformation rates of materials on large spatial scales, and do not require careful surface preparation and expensive equipment.
In the field of dendrochronology, digital scribing can be considered as an alternative or complementary independent method to standard optical and X-ray methods based on measuring the width of annual rings.But with comparable labor intensity and accuracy, the micromechanical approach is able to provide much more information than just the width of annual rings.Continuous profiling of the micromechanical characteristics of wood brings it closer in terms of information richness to surface mapping using NI or AFM, while the labor intensity, time, and cost of the necessary equipment are at least an order of magnitude less.
Knowing the distributions of local mechanical properties and their dependence on the growth conditions of trees of various species will allow a better understanding of the nature and patterns of formation of mechanical, acoustic and other practically useful macroproperties of wood.And when plants are cultivated under controlled conditions, this knowledge will help grow wood with predetermined properties.To clarify the functional and metrological capabilities of the digital scribing method, systematic studies are needed with different types of probes on samples of different types of wood growing in different climatic conditions.

Fig. 1 .
Fig. 1.SEM images of a cross section of pine (a), oak (b), and linden (c) wood.The arrows indicate the boundaries of the annual rings.

Fig. 3 .
Fig. 3. Radial distributions of effective values of the microhardness H eff and Young's modulus E eff in the annual rings of scotch pine (a), pedunculate oak (b), and small-leaved linden (c) for ten successive annual rings, measured by NI at the maximum load applied to the Berkovich indenter, P max = 500 mN.x is the distance across the annual rings.The boundaries of the annual rings are shown by dotted lines.Numbers from 2004 to 2013 indicate the years of wood growth (dry year 2010 highlighted in red).

Fig. 4 .
Fig. 4. Results of measurements of the width of annual rings by the method of nanoindentation W NI and the optical method W o (a) and discrepancies between these methods (b).

Fig. 5 .
Fig. 5. Profile of the normal F n (1) and lateral F l (2) component of the force acting on the probe during the scratching of pine wood (a, b) at d = 50 μm, oak (c, d) at d = 33 μm, linden (e, f) at d = 40 μm at different scales along the horizontal axis.

Fig. 6 .
Fig. 6.Correlation of data on the width of annual rings W of pine (1), oak (2), and linden (3) obtained by the optical W o (large circles) and scratch W s method (green squares, orange triangles, yellow circles).
influence on both W s and H s is the average daily temperature throughout the growing season and especially in the second half.The average daily precipitation in the first half of the growing season has a noticeably smaller effect, and in the second half it has almost no effect on the result.The combination of variations of various, not completely independent factors and their deviation from the norm can further

Fig. 8 .
Fig. 8. Correlation of the width of annual growth rings W s in pine with the average temperature T for different time intervals: (a) May-June, (b) July-August, and (c) May-August.An asterisk indicates characteristics for the unique dry year 2010.

Fig. 9 .
Fig. 9. Correlation of the width of annual growth rings W s in pine with the average daily rainfall p in different time intervals: (a) May-June, (b) July-August, and (c) May-August.An asterisk indicates characteristics for the unique dry year 2010.

Fig. 10 .
Fig. 10.Correlation of the maximum hardness H s of late wood in pine with the average temperature T for different time intervals: (a) May-June, (b) July-August, and (c) May-August.An asterisk indicates characteristics for the unique dry year 2010.
H s = 378 12.9T 3 enhance the effects.Thus, a unique combination of climatic characteristics in 2010 for several decades led to the loss of corresponding points (they are indicated by asterisks in Figs.8-11) from the general long-term trend for all analyzed pairs of parameters.Correlation coefficients and linear-regression parameters corresponding to these pairs are summarized in Table

Fig. 11 .
Fig. 11.Correlation of the maximum hardness H s of late wood in pine with the average daily rainfall p for different time intervals: (a) May-June, (b) July-August, and (c) May-August.An asterisk indicates characteristics for the unique dry year 2010.

Table 1 .
Hardness of wood at different scale levels

Table 2 .
Average scatter (%) upon determining the width of annual rings W s from the scratch method in different ways relative to the width of annual rings W o determined by the optical method

Table 3 .
Linear regression parameters and correlation coefficients between wood properties and climatic factors the relationships for linear regression between the wood properties and climatic factors; r i is the correlation coefficients between the wood properties and climatic factors; W s (mm) is the width of the annual ring; H s (MPa) is the maximum hardness within the annual ring; T i is the average daily temperature; p i (mm/day) is the value of average daily precipitation during the growing season.