The objective of this study is to provide a comprehensive review and characterization of selected climate variability indices. While we discuss many major climate variability mechanisms, we focus on four principal modes of climate variability related to the dynamics of Earth’s oceans and their interactions with the atmosphere: the El Niño–Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), Pacific Decadal Oscillation (PDO), and Atlantic Multi-decadal Oscillation (AMO). All these oscillation modes are of broad interest and considerable relevance, also in climate impact studies related to teleconnections, i.e., relationships between climate variations at distant locations. We try to decipher temporal patterns present in time series of different oscillation modes in the ocean–atmosphere system using exploratory analysis of the raw data, their structure, and properties, as well as illustrating the quasi-periodic behavior via wavelet analysis. With this contribution, we hope to help researchers in identifying and selecting data sources and climate variability indices that match their needs.

The hypothesis of this study was one of existence of spatially organized links between the time series of river runoff and climate variability indices, describing the oscillations in the atmosphere–ocean system: ENSO (El Niño–Southern Oscillation), PDO (Pacific Decadal Oscillation), AMO (Atlantic Multidecadal Oscillation), and NAO (North Atlantic Oscillation). The global river flow reconstructions (ERA-20-CM-R) for 18 study areas on six continents and climate variability indices for the period 1901–2010 were used. The split-sample approach was applied, with the period 1901–2000 used for training and 2001–2010 used for testing. The quality measures used in this paper were mean absolute error, dynamic time warping, and top extreme events error. We demonstrated that a machine learning approach (convolution neural network, CNN) trained on climate variability indices can model the river runoff better than the long-term monthly mean baseline, both in univariate (per-cell) and multivariate (multi-cell, regionalized) settings. We compared the models to the baseline in the form of heatmaps and presented results of ablation experiments (test time ablation, i.e., jackknifing, and training time ablation), which suggested that ENSO is the primary determinant among the considered indices.

<p>Interpretation of flood hazard and its variability remains a major challenge for climatologists, hydrologists and water management experts. This study investigates the existence of links between variability in high river discharge, worldwide, and inter-annual and inter-decadal climate oscillation indices: El Niño-Southern Oscillation, North Atlantic Oscillation, Pacific Interdecadal Oscillation, and Atlantic Multidecadal Oscillation. Global river discharge data used here stem from the ERA-20CM-R reconstruction at 0.5 degrees resolution and form a multidimensional time series, with each observation being a spatial matrix of estimated discharge volume. Elements of matrices aligned spatially form time series which were used to induce dedicated predictive models using machine learning tools, including multivariate regression (e.g. ARMA) and recurrent neural networks (RNNs), in particular the Long Short Term Memory model (LSTM) that proved to be effective in many other application areas. The models are thoroughly tested and juxtaposed in hindcasting mode on a separate test set and scrutinized with respect to their statistical characteristics. We hope to be able to contribute to improvement of interpretation of variability of flood hazard and reduction of uncertainty.</p>