Description: The Indian Ocean Zonal Mode (IOZM) has gained considerable attention in the past decade due to its role in causing widespread flooding and droughts in the continents and islands surrounding the Indian Ocean. The IOZM has also been observed to vary on a low-frequency (multi-decadal) basis, making its behavior important to understand both for mid-range 21st century climate prediction and for paleoclimate studies. Despite efforts to reconstruct the IOZM using corals and other high-resolution proxies, nonstationarities in the response of paleoclimate proxies to the IOZM have also been noted, raising the possibility that the IOZM may be difficult to reconstruct or to predict in the long-term. It is therefore critical to assess the low-frequency component of the IOZM in observed, modeled, and paleoclimate data from the Indian Ocean region in order to identify nonstationary behavior and to assess its role in low-frequency climate variations. We present an analysis of low-frequency and nonstationary behavior in the IOZM on multi-decadal to centennial timescales using a combination of modeled, observed, and proxy reconstructions of δ18O/δDprecip. In order to assess multiple timescales of low-frequency variability, we focus on two key time periods: the historical period (1870–2003), and the past millennium (1000 C.E.-present). We find significant nonstationarities in the relationships between the IOZM, precipitation amount, and δ18Oprecip/δDprecip during the historical period. These relationships vary on a multi-decadal basis in our model and in observed/reanalysis datasets. Air-sea interactions in the Indo-Pacific Warm Pool and teleconnections to the Pacific Ocean, as well as the phase of the IOZM itself, may contribute to this nonstationary behavior. We examine the potential ramifications of nonstationary IOZM behavior using a synthesis of spatially distributed proxy archives of δ18Oprecip/δDprecip from both sides of the IOZM region spanning the past millennium. Our findings indicate that during the past millennium, a strong IOZM-like connection exists in the proxy data network, with anti-correlation between East Africa and Indonesia. However, the links are spatially limited and in some cases timescale-dependent. Nonlinear behaviors in these links suggest that the IOZM may be difficult to detect on a consistent basis in proxy records from the past millennium. Based on our modeling results, the inconsistent links in the IOZM proxy network may arise from temporally and spatially variable relationships between the IOZM, precipitation, and δ18Oprecip/δDprecip. We conclude that the IOZM's potential to influence the climate of the Indian Ocean region is inconsistently reflected in proxy data, and that due to the changing strength of the IOZM/δ18Oprecip/δDprecip relationship, its spatial “footprint” may be restricted on multi-decadal to multi-centennial timescales.

Description: Internal variability of the Asian monsoon system and the relationship amongst its sub-systems, the Indian and East Asian Summer Monsoon, are not sufficiently understood to predict its responses to a future warming climate. Past environmental variability is recorded in Palaeoclimate proxy data. In the Asian monsoon domain many records are available, e.g. from stalagmites, tree-rings or sediment cores. They have to be interpreted in the context of each other, but visual comparison is insufficient. Heterogeneous growth rates lead to uneven temporal sampling. Therefore, computing correlation values is difficult because standard methods require co-eval observation times, and sampling-dependent bias effects may occur. Climate networks are tools to extract system dynamics from observed time series, and to investigate Earth system dynamics in a spatio-temporal context. We establish paleoclimate networks to compare paleoclimate records within a spatially extended domain. Our approach is based on adapted linear and nonlinear association measures that are more efficient than interpolation-based measures in the presence of inter-sampling time variability. Based on this new method we investigate Asian Summer Monsoon dynamics for the late Holocene, focusing on the Medieval Warm Period (MWP), the Little Ice Age (LIA), and the recent period of warming in East Asia. We find a strong Indian Summer Monsoon (ISM) influence on the East Asian Summer Monsoon during the MWP. During the cold LIA, the ISM circulation was weaker and did not extend as far east. The most recent period of warming yields network results that could indicate a currently ongoing transition phase towards a stronger ISM penetration into China. We find that we could not have come to these conclusions using visual comparison of the data and conclude that paleoclimate networks have great potential to study the variability of climate subsystems in space and time.

Description: Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.

Description: Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.

Description: Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ18O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.

Description: Paleoclimate proxy data cover large sections of the Earth's past dynamics and hold information that is crucial to improve climate models on timescales from decades to millennia. The heterogeneous origins of the proxy data e.g. from marine or terrestrial archives, biologically growing or proxies resulting from (inorganic) sedimentation processes amplify reconstruction uncertainty due to proxy specific challenges such as record sparsity, age uncertainty and sampling time irregularity. The attribution of proxy variability to different climate parameters, such as temperature or precipitation is necessary for most model-data intercomparisons. This is, however, complicated by the time-scale dependent and mostly unknown signal-to-noise ratio and underdeterminacy and short overlapping periods in the calibration to modern-day data. We investigate the agreement between terrestrial paleoclimate proxy records in Asia using linear and nonlinear time series analysis methods to identify potential archive-dependent biases and local vs. regional climate variability. While a single archive or proxy is unlikely to capture climate variability sufficiently well in time and space, we aim to identify archive-proxy combinations that improve the representation of annual to centennial timescales and separate temperature from precipitation variability.

Description: The last glacial period was characterised by a highly var- iable climate including abrupt changes such as Heinrich and Dansgaard-Oeschger events. In contrast, the Holocene time period was observed as relatively stable. This variabi- lity change is often discussed based on data from polar ice cores, particularly from Greenland. Here, we contrast the polar ice core-based variability change with the variability change recorded by a global compilation of multi-proxy records. Estimated spatial patterns of changes point towards mechanisms generating glacial and Holocene climate variability. Furthermore, our analysis allows insight into the abilities of the different pro- xy sensors concerning the recording of climate variability.