Edited by: Cristina Nabais, University of Coimbra, Portugal
Reviewed by: Walter Oberhuber, University of Innsbruck, Austria; Alicia Forner Sales, Museo Nacional de Ciencias Naturales-CSIC, Spain
*Correspondence: Jonatan F. Siegmund
This article was submitted to Functional Plant Ecology, a section of the journal Frontiers in Plant Science
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Observed recent and expected future increases in frequency and intensity of climatic extremes in central Europe may pose critical challenges for domestic tree species. Continuous dendrometer recordings provide a valuable source of information on tree stem radius variations, offering the possibility to study a tree's response to environmental influences at a high temporal resolution. In this study, we analyze stem radius variations (SRV) of three domestic tree species (beech, oak, and pine) from 2012 to 2014. We use the novel statistical approach of event coincidence analysis (ECA) to investigate the simultaneous occurrence of extreme daily weather conditions and extreme SRVs, where extremes are defined with respect to the common values at a given phase of the annual growth period. Besides defining extreme events based on individual meteorological variables, we additionally introduce conditional and joint ECA as new multivariate extensions of the original methodology and apply them for testing 105 different combinations of variables regarding their impact on SRV extremes. Our results reveal a strong susceptibility of all three species to the extremes of several meteorological variables. Yet, the inter-species differences regarding their response to the meteorological extremes are comparatively low. The obtained results provide a thorough extension of previous correlation-based studies by emphasizing on the timings of climatic extremes only. We suggest that the employed methodological approach should be further promoted in forest research regarding the investigation of tree responses to changing environmental conditions.
During the past 15 years the systematic installation and operation of dendrometers and analysis of the obtained data has received increasing interest in forestry sciences. While the first attempts (Friedrichs,
Beyond the fundamental understanding of tree functioning, dendrometer data can also indirectly provide important information on the carbon cycle at the local, regional or global level. Even though stem radius does not allow estimates of total cell numbers, it is an important proxy for a forest's above ground biomass (Schulte-Bisping et al.,
To the authors' best knowledge, almost all above-mentioned studies have investigated dendrometer data using classical statistical tools like linear correlation analysis or linear multiple regression. These powerful methodological approaches have led to an understanding of the relationship between stem size changes and various environmental parameters. Yet, correlation-based approaches generally take all parts of the distributions of two variables of interest into account and therefore describe the joint behavior of these variables. A crucial question only sporadically addressed so far is how tree stem radius variations (SRVs) are linked to extreme weather conditions. This question gains special importance, since recent climate projections suggest a rising frequency and severity of meteorological extreme events for many parts of the world (Barriopedro et al.,
An important study addressing the response of stem-size fluctuations and tree radius growth to climatic extremes using a large number of dendrometer data sets was recently published by Butt et al. (
In this study, we employ the novel methodological approach of event coincidence analysis (ECA) to quantify possible simultaneities between extraordinary daily stem variations and extraordinary meteorological conditions. Here, the commonly used term
Taking into account the existing literature on SRVs and their relation to meteorological conditions we expect that extraordinary climatic events, specifically temperature events, and extraordinary dendrometer variations should occur simultaneously. Additionally, it can be expected that there are clear inter-species differences concerning the reaction to extraordinary meteorological events.
The study site was close to Lake Hinnensee (53.33°N, 13.19°E) in the northeastern part of Germany. The site is located within the Müritz National Park. Large parts of this protected area have been classified as UNESCO World Natural Heritage in 2011. The park is characterized by 200–300 years old mixed beech, pine and oak stands. The climate is semi-continental, typical for central Europe, with a mean annual temperature of about 8°C and an annual precipitation between 550 and 650 mm. The soil at the study site as well as at the meteorological station (see Section 2.2.2) is a brunic arenosol on sand of outwash plains, characterized by strong hydraulic permeability Müller (
The dendrometer data were collected for three tree species: European beech (
For each tree species, 10 individuals were equipped with Ecomatik DR point radius dendrometers (Ecomatik GmbH,
After a comprehensive quality check, the raw dendrometer data were pre-processed using the following three steps:
In a first step, the 30-min resolution dendrometer data were used to calculate daily SRVs. Rather then using a stem cycle approach (Deslauriers et al., As a second step, a two-sided sliding window mean (window size of 15 days) was subtracted from the resulting daily SRVs in order to account for the seasonal cycle. The resulting residuals represent the daily stem increments of a tree as deviations the from the 15-day mean. Finally, the investigation period was defined from April 1st to September 30th of each year to cover the entire growth period for each species. A sliding window approach (see Section 2.3) was applied to produce comparable results which are not shifted against each other by species or year. In order to transform the dendrometer time series into event time series, we applied a 90th and 10th percentile threshold to the daily increments. Values exceeding the 90th percentile of all days of the investigation period were defined as extraordinary positive SRV events, whereas days lower than the 10th percentile were defined as negative events. This event definition results in 55 positive and 55 negative events during the 3-years period for each individual tree. Due to the usage of residuals with respect to the “normal” seasonal behavior, these events are approximately homogeneously distributed within each year (not shown) and the specific timings of the individual events are determined by environmental conditions. An important exception is a very dry period during the summer of 2013 during which only a few strong positive precipitation events were observed.
In order to define days with extraordinary meteorological conditions, data from a nearby meteorological station in Serrahn (at a distance of less than 2 km from the study site) were used. The soil conditions at the dendrometer site and the meteorological station site are comparable, but not identical. Systematically differing soil temperatures, for example, can not be excluded. In addition to air temperature and precipitation, the station provides information on (relative air) humidity, soil temperature, air pressure and incoming solar radiation. The data set is available starting January 2006 at a temporal resolution of 1 h. Similar to the daily SRVs, the meteorological data were pre-processed in order to identify events of extraordinary daily meteorological conditions:
The hourly information was aggregated to daily minimum, mean, and maximum values. Observations of air pressure and minimum radiation were not used since no meaningful results are expected by using these variables. The daily meteorological information was transformed to Finally, the resulting z-scores were transformed to event time series by applying a 90th and 10th percentile threshold as in the case of the dendrometer data. Due to the application of these percentiles for threshold definition, the number of events in each meteorological variable is also 55 (each negative and positive).
The following meteorological variables were used: air temperature at 2 m (
In order to investigate the simultaneity of events in meteorological variables and SRV, we apply
Since the statistical analysis described above is not symmetric, ECA defines two distinct types of coincidence rates,
In addition to the simple calculation of coincidence rates, the R package
As a thorough extension of the basic ECA method for two event sequences, in this work, we introduce new multivariate generalizations of ECA termed
The conditioning of events of type B by events of type C can be described by the precursor coincidence between B and C. Therefore, the
Using the definitions in Equations (1) and (3), the conditional precursor coincidence rate describes the fraction of events in series A, that appear simultaneously with C-conditioned events of type B, and the conditional trigger coincidence rate is the fraction of C-conditioned events of type B that are followed by at least one event in series A. In the special case of a simultaneous occurrence of events of types B and C (i.e., τ
For the application of ECA and CECA/JECA, we dissect the 1095 days period from 2012 to 2014 by sliding windows. For the (bivariate) ECA, the window length is chosen as 61 days with a step size of 5 days, resulting in 75 windows per growing season (1 April to 30 September), where each window contains six events on average. The window length of 61 days is a compromise between a desired high temporal resolution and a possible large window size necessary to produce robust statistics. The step size of 5 days was selected in order to mimimize the computational demand. For the (multivariate) CECA/JECA, the window length is extended to 91 days including nine events on average, since due to the additional conditioning, the number of events in the meteorological variables decreases markedly. In order to cope with the high computational demand of CECA/JECA for 15 variables, the window step size was increased to 10 days, resulting in 15 windows per season.
As a first step, using the sliding window approach, ECA was performed between each of the 15 individual meteorological variables and each tree's SRV series across each window separately. For every window, the fraction of trees with a significant number of coincidences was taken as a proxy describing the reaction of the species to the considered meteorological events. Subsequently, JECA was performed between the dendrometer data and all pairs of meteorological variables. As a consequence, the chosen analysis setting results in 15 × 14/2 = 105 different variable combinations. Note that for τ
In all analyses discussed in the remainder of this work only the (conditional) precursor coincidence rates are considered unless stated otherwise.
In order to analyze the simultaneity of event timings between the individual trees, we additionally use the well established approach of hierarchical cluster analysis with complete linkage. Core of the concept of cluster analysis (in this case for dendrometer time series) is a similarity measure, calculated between all possible combinations of individual time series. This similarity measure is, classically, a correlation coefficient. In this study, we additionally introduce the application of event coincidence rate as similarity measure for the cluster analysis. The calculation of the event coincidence rate between each pair of dendrometer event time series follows along the above mentioned approach, using τ = Δ
Figure
For positive SRV events (Figure
In comparison to positive SRV events, negative events clearly show fewer significant coincidences with extraordinary meteorological conditions (Figure
In addition to the consideration of exactly simultaneous coincidences as described above, Figure
Due to the large number of possible combinations between meteorological variables, the figures showing the results of JECA are provided in the supplementary material. The following analysis concerns
Figure
The investigation of negative beech SRV events using JECA shows hardly any significant coincidences (see Figure
The results of JECA for oak SRV events are provided in Figure
For joint coincidences between negative oak SRV events and pairs of meteorological variables (Figure
The features (i), (ii), and (iii) indicated in Figure
Negative pine SRV events (Figure
As already mentioned in Section 3.1, when comparing the results of ECA without time lag and tolerance window with the results using Δ
Beech | 0.53 | 0.39 | 0.44 | 0.49 | 0.38 | 0.55 |
Pine | 0.64 | 0.54 | 0.45 | 0.57 | 0.58 | 0.50 |
Oak | 0.60 | 0.45 | 0.31 | 0.51 | 0.42 | 0.34 |
To further investigate this question, we additionally used JECA with the same setup, where the positive SRV events (series B) have been observed in parallel with extraordinarily high rH values (series C). Table
Beech | 0.69 | 0.60 | 0.58 | 0.28 | 0.28 | 0.25 |
Pine | 0.83 | 0.66 | 0.48 | 0.42 | 0.40 | 0.26 |
Oak | 0.77 | 0.58 | 0.31 | 0.35 | 0.23 | 0.13 |
When comparing the results of both bi- and multivariate ECA between the three tree species, the differences are relatively small. Altogether, oak seems to not favor wet conditions as strongly as beech and pine, but systematic inter-species differences appear to be absent. In turn, for the mean behavior (of daily as well as subdaily features), the growth characteristics are widely known to differ markedly between different tree species (Drew and Downes,
The two broadleaved species show a positive response to temperature as well as LST while little positive response is found for pine. This positive growth response is likely due to the sufficient supply of water; possibly by reaching groundwater reservoirs. Similar relationships have been found earlier for the mean values (i.e., using correlation-based analyses) by van der Maaten et al. (
Only few coincidences were found between SRV events and soil temperature extremes. It is likely that this observation is due to the location of the meteorological station 2 km from the dendrometer site. Due to the variability in soil type and ground cover throughout in the study area, actual soil temperatures beneath the sampled trees may systematically differ from the values measured at the station.
A positive instantaneous (lag zero) correlation between air humidity and SRV has been observed in previous studies (Downes et al.,
The significant coincidences between low radiation values and positive SRV events can interpreted in a twofold way: One the one hand, low radiation decreases transpiration leading to water replenishment. On the other hand, low radiation days commonly correspond to cloudy and foggy conditions and are therefore often characterized by high relative humidity as well. A general negative dependency in terms of negative correlations between radiation and stem radius variability was reported earlier by Downes et al. (
Our analysis revealed some counter-intuitive significant coincidences between days with extraordinary high air humidity and negative SRV events in beech stems during 2014 (Figure
The results of bivariate (Figures
The counter-intuitive negative beech SRV events found in Figure 2 and discussed in Section 4.1 could also be explained by a statistical artifact due to the co-occurrence between negative SRV events and positive SRV events of the previous day. Such a phenomenon of contradicting climatic signals in tree rings has also been reported for high resolution tree-ring isotope data (Schollän et al.,
The various cycles of swelling and shrinkage shown by dendrometer data have been addressed in several recent studies (Downes et al.,
The JECA revealed six main findings common to all three investigated tree species. (i) The combination of high minimum temperature with high relative humidity events coinciding with positive SRV events describes situations of warm nights followed by moist days. This feature was most clearly visible for pine which is to be explained by pine having the highest potential for water storage due to its larger amount of xylem Pfautsch et al. (
The observations found in Section 3.4 are in fact not trivial, since very different reactions of the analyzed species to environmental conditions have been well documented by, e.g., Gonzalez-Munoz et al. (
We have used high-resolution dendrometer data to investigate tree species-specific responses to extraordinary meteorological conditions. For the first time joint event coincidence analysis as well as a hierarchical clustering analysis based on coincidence rates have been used. This new approach allowed a detailed analysis of the timing of observations falling in the upper and lower tails of the empirical distributions of daily SRVs. This opens new possibilities for interpreting tree-specific responses to meteorological extremes. Our method is able to provide relevant complementary information beyond what has been known from previous correlation-based analyses. Further potential applications of this method include the investigation of dendrochronological data or intra-annual density fluctuations (IADF).
For future investigations, it will be crucial to put additional efforts into disentangling tree stem radius growth from stem swelling, using novel data analysis approaches. Additionally, integrated studies including dendrometer and wood density measurements, as well as an up-scaling across a larger area will be necessary to draw reliable conclusions on tree or forest carbon storage dynamics in relation to meteorological extreme events.
JS Study's Design, Data Analysis, Figures, Writing. TS Study's Design, Proofreading. IH Data Production and Preprocessing, Proofreading. EV Proofreading. SS Data Production and Preprocessing. GH Study's Design, Proofreading. RD Study's Design, Writing, Proofreading.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This study was conducted within the framework of the Young Investigators Group “CoSy-CC2 : Complex Systems Approaches to Understanding Causes and Consequences of Past, Present and Future Climate Change” (grant no. 01LN1306A) funded by the German Federal Ministry for Education and Research (BMBF), the COST Action FP1106 STReESS supported by COST (European Cooperation in Science and Technology), the Virtual Institute of Integrated Climate and Landscape Evolution Analysis—ICLEA—(grant no. VH-VI-415), and the Terrestrial Environmental Observatories project—TERENO—of the Helmholtz Association. Jonatan Siegmund acknowledges financial support by the Evangelisches Studienwerk Villigst e.V. Ingo Heinrich received support from the Deutsche Forschungs-Gemeinschaft (DFG project number He 7220/1-1). The authors wish to thank Jonathan Bauermann and Jonathan Donges for fruitful discussions on the notation of CECA. Thanks to Daniel Balanzategui for proof-reading the manuscript. All presented analyses have been performed using the R package CoinCalc, available at
The Supplementary Material for this article can be found online at: