60◦S 30◦S 0◦ 30◦N 60◦N
125◦W 105◦W 85◦W 65◦W 45◦W
Figure 6.1.: Locations of the archives providing the different proxy time series used in this chapter. The location of the tree ring archive is denoted in green, of the lake sediment archive in blue, of the speleothem archive in red, and of the ice core archive in magenta.
6.2. Palaeoclimate archives and proxy data
6.2.1. Tree rings
Many trees form annual rings whose characteristics depend on environmental factors such as temperature and soil moisture (Bradley, 2015b). In fact, those trees constitute the most important palaeoclimate archive for temperature reconstructions of the past millennium (Bradley, 2015b; IPCC, 2013; St. George, 2014; St. George and Esper, 2019). Still, obtaining and interpreting chronologies from tree ring measurements poses many challenges. For example, it has been shown that the quality of the available data sets varies in terms of data homogeneity, sample replication, growth coherence, chronology development, and climate signal (Esper et al., 2016). Also, modern accelerated tree growth might lead to biases in palaeoclimate reconstructions that need to be accounted for (Scharnweber et al., 2019).
We study a local tree ring width index chronology from eastern Canada (Gennaretti et al., 2014). It is compound of 292 subfossil and 25 living trees and located at a lake (54.2◦N, 70.3◦W) corresponding to the green star in figure 6.1. The proxy time series of tree ring width indices is visualised in the top panel of figure 6.2. It has N = 1102data points, is annually sampled, and covers the period 910 − 2011 AD.
This local tree ring width index chronology is part of a millennial temperature reconstruction of annual summer temperatures in eastern Canada exhibiting responses to volcanic activity (Gennaretti et al., 2014). In fact, the region has been found to
trwindex(a.u.) tree ring data
RCI(a.u.)
lake sediment data
δ18Ospt(a.u.) speleothem data
0 500 1000 1500 2000
year AD δ18Oice(a.u.) ice core data
Figure 6.2.: Proxy time series of tree ring width (trw) indices, red colour intensity (RCI) of the lake sediment data, and oxygen isotope ratios (δ18O) of the speleothem and the ice core data (top to bottom). The vertically shaded areas correspond to the episodes of outstanding climate variability as introduced in section 6.1.
6.2. Palaeoclimate archives and proxy data be more sensitive to volcanism than, for example, Eurasia as complex sea-ice-ocean feedbacks in combination with explosive volcanic eruptions can cause or extend cold episodes. Particularly, the Samalas eruption (1257 AD) and the Tambora eruption (1815 AD) have been identified to influence tree growth in eastern Canada (Gennaretti
et al., 2014).
Tree rings have so far not been studied using recurrence based approaches, mainly because corresponding time series usually show unbalanced variability across the different frequencies (Briffa et al., 1996). As the data set provided in Gennaretti et al. (2014) is classified as good in Esper et al. (2016), we expect it to be a suitable exemplary data set to start exploring this proxy with our framework of wRNA and wssRNA.
6.2.2. Lake sediments
Another important archive for past climate reconstructions are lacustrine sediments which stand out because of their global distribution over all climatic zones, their high resolution, and because they cover long time spans (Bradley, 2015e; Cohen, 2003). They contain a plethora of different proxy variables that can be considered for inferring information on past climate variability as, for example, sedimentary proxies, physiochemical proxies, and biological proxies (Zolitschka and Enters, 2009).
We study the red color intensity (RCI) data from Laguna Pallcacocha (Moy et al., 2002) which is a high-altitude lake in southern Ecuador (2.8◦S, 79.2◦W) marked by the blue star in figure 6.1. We use the most recent part of the available time series covering the interval −50 − 1950 AD. As the original time series is non-uniformly sampled, we interpolate it to uniform sampling using linear and cubic spline interpolation.
The average sampling rate is given as ⟨dt⟩ = 0.51 years corresponding to a length of N = 3901 data points. The linearly interpolated time series is displayed in the second panel of figure 6.2.
The red color intensity has been used as a proxy for rainfall intensity. In particular, higher values of the RCI represent lighter coloured laminae in the sediment and can be associated with strong rainfall events (Moy et al., 2002). In Moy et al. (2002), it was also found that this time series can be related to the strength of historical El Niño Southern Oscillation (ENSO) events as the recorded strong rainfall events were triggered by moderate to strong warm ENSO episodes, i. e., El Niño events.
6.2.3. Speleothems
Speleothems are formations in caves mainly consisting of calcium carbonate which incrementally grow from drips of groundwater passing through the ambient rock of the cave, that is, the karst (Bradley, 2015d). The isotopic composition of speleothems is an important high-resolution palaeoclimate proxy due to the archive’s global distribution in areas where other archives are less represented, the possibility to obtain precise chronologies, and the preservation of many time scales in the records (Wong and Breecker, 2015; Atsawawaranunt et al., 2018). In the lower latitudes, the archive
is mostly sensitive to changes in precipitation amount, while in higher latitudes, temperature is the more important driver for the variability of the speleothem’s isotopic composition (Bradley, 2015d; Oster et al., 2019). Still, including information about the complex local boundary conditions of and the microclimate in the caves is of major importance for interpreting the proxy signals (Lechleitner et al., 2018).
To study oxygen isotope ratios (δ18O) of speleothems, we use data from the stalagmite JX-6 from Juxtlahuaca cave (Lachniet et al., 2012) which is located in southern Mexico (17.4◦N, 99.2◦W) as indicated by the red star in figure 6.1. Again, we use linear and cubic spline interpolation to obtain uniform sampling with average sampling rate ⟨dt⟩ = 1.8 years, thus, the resolution of the data is lower than for the lake sediment data. The time series covers the period −250 − 2000 AD and consists of N = 1218 data points. The third panel of figure 6.2 shows the corresponding linearly interpolated time series. This data set has also been found to be precipitation sensitive and thus to characterise the rainfall variability in the region where smaller values of the oxygen ratios are related to more rainfall and larger values correspondingly to less rainfall. In the study area, rainfall is mostly affected by the strength of the North American summer monsoon which, in turn, is modulated by ENSO with warm ENSO episodes weakening the summer monsoon and vice versa (Lachniet et al., 2012).
6.2.4. Ice cores
Ice cores consist of accumulated snow that transforms to firn and later to ice by a de-and reformation of the snow crystals due to the increasing weight of subsequently fallen snow (Bradley, 2015c). They are one of the most important archives for reconstructing past atmospheric conditions as they provide, for example, information on past temperatures and the atmospheric composition via the isotopic composition of the ice and air contained in closed bubbles, respectively (Jouzel, 2013). In the last decades, data from high-elevation ice cores in the low latitudes have become increasingly available and offer the possibility to study past climate variability in the context of recent climate change (Thompson et al., 2005). To obtain reliable results from those high-resolution cores, some challenges still have to be addressed in more detail. For example, dating of the tropical ice cores becomes difficult for times in which the seasonal cycle is no longer resolved and also the interpretation of the isotopic composition in such cores is debated (Vimeux et al., 2009).
To explore the ice core archive, we use a data set of oxygen isotope ratios (δ18O) from the Quelccaya ice cap (Thompson et al., 2013). The cap is located in the Peruvian Andes (13.9◦S, 70.8◦W) and lies at an altitude of 5670 m above sea level.
The location of Quelccaya ice cap is denoted by the magenta star in figure 6.1. The time series is annually sampled and spans the interval 226 − 2009 AD, thus it consists of N = 1784 data points. A visualisation of the time series can be found in the bottom panel of figure 6.2.
The variability of the δ18O in this data set has been found to be related to sea surface temperatures in the tropical eastern Pacific (Thompson et al., 2013). Similar relationships between Pacific sea surface temperatures and the δ18O in tropical ice
6.3. Results cores have been found, for example, in Vuille et al. (2003) and could be explained by an influence of Pacific sea surface temperatures on upper-level wind anomalies that force the moisture flow over the Andes.
6.3. Results
We now apply the developed analysis framework to the four proxy time series in order to characterise past climate variability on the American continents. First, we start by presenting the results for the varying phase space reconstruction approaches from publication P1. Afterwards, we use uniform time delay embedding in combination with wRNA and wssRNA and the areawise significance test following the framework summarised in chapter 5. The corresponding results for the tree ring width index time series follow those described in publication P2.
6.3.1. Phase space reconstruction
To study the dependence of wRNA on different phase space reconstruction approaches for real-world data, we analyse the lake sediment data set from Laguna Pallcacocha and the speleothem oxygen isotope ratios from Juxtlahuaca cave. We compare the results for the network transitivity of wRNA when reconstructing the phase space of the systems using uniform time delay embedding for varying delay times τ, derivative embedding with the discrete Legendre polynomials for varying numbers p of neighbours taken into account for derivative estimation, and derivative embedding with moving Taylor Bayesian regression (MoTaBaR) for varying numbers Nmtb of points taken into account for the local Taylor approximation. For the derivative embeddings, the resulting time series are scaled to have unit variance. The embedding dimension is chosen to be m = 4 in accordance with the false nearest neighbour criterion. In fact, when varying the embedding dimension, we observe similar results (not shown). The windowed analysis is performed for five values of the window width, W ∈ [100, 150, 200, 250, 500] ⟨dt⟩with offset dW = 1 ⟨dt⟩. The pointwise significance test is based on random shuffling surrogates with significance level spw = 0.95. The results are visualised in figure 6.3.
For the Laguna Pallcacocha data set and time delay embedding, we observe four to five periods with significantly high and one to two periods of significantly low values of the network transitivity. For larger window widths, the timing shifts to more recent times which can be explained by recalling that we assign the time to a window such that it represents the dynamics of the W previous observations. For derivative embedding with discrete Legendre polynomials, we get similar results as for time delay embedding though for larger W , the periods of significant transitivity values get wider and neighbouring periods can no longer be separated. Also, we observe a higher number of significant points. For derivative embedding with MoTaBaR, we see a very stable behaviour of the identified anomalies for varying Nmtb and more but shorter periods of significant values of the network transitivity. Additionally, the
Figure 6.3.: Network transitivity (colour coded) as a function of time for Laguna Pallcacocha ((a), (c), (e)) and Juxtlahuaca cave ((b), (d), (f)) data for different phase space reconstruction approaches and varying embedding parameters: ((a), (b)) time delay embedding for varying delay times τ, ((c), (d)) derivative embedding
6.3. Results
0.40.5 0.6 0.70.8
T
time delay embedding τ = 15hdti
0.40.5 0.60.7 0.80.9
T
discrete Legendre polynomials p = 6
−500 0 500 1000 1500
Figure 6.4.: Network transitivity for window width W = 200 ⟨dt⟩ of Laguna Pallcacocha data for the three considered phase space reconstruction approaches. The grey bars represent the confidence bounds derived from the random shuffling surrogates.
Reproduced from P1, with the permission of AIP Publishing.
maximum values of the resulting network transitivity are lower and the minimum values are higher than for the other two approaches.
To explore the similarities and differences between the different approaches in more detail, figure 6.4 shows the network transitivity for time delay embedding with delay time τ = 15 ⟨dt⟩, for derivative embedding with the discrete Legendre polynomials for p = 6, and for derivative embedding with MoTaBaR for Nmtb= 20. Those parameter choices are motivated by the results described in chapter 3. We observe that the results for time delay embedding and derivative embedding with the discrete Legendre polynomials generally agree well. Some of the significant periods are more or less pronounced depending on the chosen phase space reconstruction approach. The results from MoTaBaR show less agreement with the other results and sometimes even exhibit opposite behaviour. This highlights the importance to consider more than one approach in order to check whether the results are robust and confirms the results from chapter 3 that uniform time delay embedding and derivative embedding with discrete Legendre polynomials can give comparable results. We discuss the relation of the detected anomalies to past climate variability in subsections 6.3.2 and 6.3.3 in combination with the areawise significance test.
In the results from the Juxtlahuaca cave data set, we cannot identify consistent anomalies within the different phase space reconstruction approaches and the corre-sponding parameter variations. Generally, we observe some elevated values of the network transitivity for the recent past and the oldest part of the time series as well as some low values of the transitivity around 1500 AD. However, the timing varies for the different methods and choices of the window width. For derivative embedding with discrete Legendre polynomials and large values of p, we see a different pattern
with many significant high values of the network transitivity. This can possibly be related to the fact that for larger p, the smoothing of the time series is stronger.
In general, we do not expect the results for different values of p to be equally well suited for the analysis and our results confirm that a choice of p of the order of the embedding dimension is reasonable. For MoTaBaR, the results are more robust than for the other two approaches but not as much as for the corresponding results of Laguna Pallcacocha. Again, we observe that the range of transitivity values obtained with MoTaBaR differs from the range of the other approaches. In this case, we find very high values of the network transitivity. With respect to these results, the Juxtlahuaca cave data set does not seem to be equally well suited for the wRNA as the Laguna Pallcacocha data set.
6.3.2. Windowed recurrence network analysis
Next, we apply wRNA for varying window widths in combination with the areawise significance test to all four data sets introduced in section 6.2. We use uniform time delay embedding with delay times τ = 25 ⟨dt⟩ for the tree ring data, τ = 15 ⟨dt⟩ for the lake sediment data, τ = 11 ⟨dt⟩ for the speleothem data, and τ = 2 ⟨dt⟩ for the ice core data. For the lake sediment data, we choose the embedding dimension to be m = 4, while for the other three data sets, we use m = 3 which can be seen as a compromise between the results of the false nearest neighbour method and the length of the available data sets. The windowed analysis is performed as outlined in chapter 5 for window widths varying in the interval [100, 300] ⟨dt⟩ with step size
∆W = 1 ⟨dt⟩and offset dW = 1 ⟨dt⟩. The pointwise significance test is again based on random shuffling surrogates with confidence level spw = 0.95 and the areawise significance test is performed as detailed in chapter 4 using the data-adaptive null model based on the iterative amplitude-adjusted Fourier transform surrogates. The fitting parameters and the confidence levels of the areawise significance test for the four data sets can be found in appendix C.
Figure 6.5 shows the results of the wRNA as a function of time. The vertical lines denote the episodes of documented climatic variations as discussed in the introduction. First, we note that we do not get any areawise significant patches of the network transitivity for the speleothem oxygen isotope ratios from Juxtlahuaca cave, confirming the expectations from subsection 6.3.1 that pointwise detected anomalies are not robust in this data set. For the lake sediment data from Laguna Pallcacocha and the oxygen isotope ratios from the Quelccaya ice cap, we find some patches of areawise significant values of the network transitivity, most of them corresponding to anomalously low values. For the tree ring data from eastern Canada, we find one patch of anomalously low values of the network transitivity around the Samalas eruption in 1257 AD possibly marking the end of the MCA in this region. Interestingly, for smaller delay times, we find areawise significant anomalies around the Tambora eruption in 1815 AD, which is discussed in more detail in appendix C.2.
With respect to the different episodes of documented climate variations of the past 2000years, we find that for the RWP, there is not sufficient data coverage in order to
6.3. Results
Figure 6.5.: Network transitivity (colour coded) obtained from wRNA as a function of time for varying window width W for the four different proxy time series in combination with the areawise significance test (hatched contours). The vertical lines again denote the episodes of outstanding climate variability introduced in section 6.1.
make any statements. The first centuries AD that have been associated with increased climatic variabilities, are covered by the lake and speleothem data, and partially also by the ice core data. We find both low and high values of the network transitivity within this period and one patch of areawise significant low values in the lake sediment data set corresponding to anomalously high-dimensional dynamics. During the LALIA, we do not find areawise significant analysis results but observe low values of the network transitivity. The same holds for the period between the LALIA and the MCA, where we also observe an areawise significant patch of low transitivity values in the data from Laguna Pallcacocha. During the MCA, and particularly towards its end for larger choices of the window width, we find areawise significant anomalously low values of the network transitivity indicating increasingly higher-dimensional dynamics.
In Europe, the MCA has been characterised by relatively stable climatic conditions, thus, we would expect the dynamics to be lower-dimensional. Our findings point to a different manifestation of the MCA in North and South America or represent the reordering of the climate system towards the beginning of the LIA. The onset of the LIA is then characterised by higher values of the network transitivity with downward trend during the LIA for the tree ring and the lake sediment data, while the speleothem and the ice core data show lower values at the onset and elevated values during the LIA. Both for the lake and the ice core data, the beginning of the LIA also corresponds to areawise significant anomalies. For more recent times, we observe areawise significant low values of the network transitivity for the ice core and areawise significant high values for the lake sediment data.
To get another perspective on the obtained results, we analyse data of the last millennium reanalysis project version 2 (Hakim et al., 2016; Tardif et al., 2019) which provides reconstructed temperature and precipitation data of the past 1500 years for the different locations of the proxy time series (appendix C.3). We find less areawise significant patches of the network transitivity than for the proxy data and also observe local differences in the variability of the network transitivity.
Taken together, these results show that dynamical anomalies in the past climate are recorded differently at the different locations, thus they indicate different local manifestations of climate variability on the American continents. The fact that the speleothem data do not show areawise significant patches points to the role that local
Taken together, these results show that dynamical anomalies in the past climate are recorded differently at the different locations, thus they indicate different local manifestations of climate variability on the American continents. The fact that the speleothem data do not show areawise significant patches points to the role that local