Hydrologic regionalization deals with the investigation of homogeneity in watersheds and provides a classification of watersheds for regional analysis. The classification thus obtained can be used as a basis for mapping data from gauged to ungauged sites and can improve extreme event prediction. This paper proposes a wavelet power spectrum (WPS) coupled with the self-organizing map method for clustering hydrologic catchments. The application of this technique is implemented for gauged catchments. As a test case study, monthly streamflow records observed at 117 selected catchments throughout the western United States from 1951 through 2002. Further, based on WPS of each station, catchments are classified into homogeneous clusters, which provides a representative WPS pattern for the streamflow stations in each cluster.

Sea surface temperature (SST) patterns can – as surface climate forcing – affect weather and climate at large distances. One example is El Niño-Southern Oscillation (ENSO) that causes climate anomalies around the globe via teleconnections. Although several studies identified and characterized these teleconnections, our understanding of climate processes remains incomplete, since interactions and feedbacks are typically exhibited at unique or multiple temporal and spatial scales. This study characterizes the interactions between the cells of a global SST data set at different temporal and spatial scales using climate networks. These networks are constructed using wavelet multi-scale correlation that investigate the correlation between the SST time series at a range of scales allowing instantaneously deeper insights into the correlation patterns compared to traditional methods like empirical orthogonal functions or classical correlation analysis. This allows us to identify and visualise regions of – at a certain timescale – similarly evolving SSTs and distinguish them from those with long-range teleconnections to other ocean regions. Our findings re-confirm accepted knowledge about known highly linked SST patterns like ENSO and the Pacific Decadal Oscillation, but also suggest new insights into the characteristics and origins of long-range teleconnections like the connection between ENSO and Indian Ocean Dipole.

The climate is a complex dynamical system involving interactions and feedbacks among different processes at multiple temporal and spatial scales. Although numerous studies have attempted to understand the climate system, nonetheless, the studies investigating the multiscale characteristics of the climate are scarce. Further, the present set of techniques are limited in their ability to unravel the multi-scale variability of the climate system. It is completely plausible that extreme events and abrupt transitions, which are of great interest to climate community, are resultant of interactions among processes operating at multi-scale. For instance, storms, weather patterns, seasonal irregularities such as El Niño, floods and droughts, and decades-long climate variations can be better understood and even predicted by quantifying their multi-scale dynamics. This makes a strong argument to unravel the interaction and patterns of climatic processes at different scales. With this background, the thesis aims at developing measures to understand and quantify multi-scale interactions within the climate system. In the first part of the thesis, I proposed two new methods, viz, multi-scale event synchronization (MSES) and wavelet multi-scale correlation (WMC) to capture the scale-specific features present in the climatic processes. The proposed methods were tested on various synthetic and real-world time series in order to check their applicability and replicability. The results indicate that both methods (WMC and MSES) are able to capture scale-specific associations that exist between processes at different time scales in a more detailed manner as compared to the traditional single scale counterparts. In the second part of the thesis, the proposed multi-scale similarity measures were used in constructing climate networks to investigate the evolution of spatial connections within climatic processes at multiple timescales. The proposed methods WMC and MSES, together with complex network were applied to two different datasets. In the first application, climate networks based on WMC were constructed for the univariate global sea surface temperature (SST) data to identify and visualize the SSTs patterns that develop very similarly over time and distinguish them from those that have long-range teleconnections to other ocean regions. Further investigations of climate networks on different timescales revealed (i) various high variability and co-variability regions, and (ii) short and long-range teleconnection regions with varying spatial distance. The outcomes of the study not only re-confirmed the existing knowledge on the link between SST patterns like El Niño Southern Oscillation and the Pacific Decadal Oscillation, but also suggested new insights into the characteristics and origins of long-range teleconnections. In the second application, I used the developed non-linear MSES similarity measure to quantify the multivariate teleconnections between extreme Indian precipitation and climatic patterns with the highest relevance for Indian sub-continent. The results confirmed significant non-linear influences that were not well captured by the traditional methods. Further, there was a substantial variation in the strength and nature of teleconnection across India, and across time scales. Overall, the results from investigations conducted in the thesis strongly highlight the need for considering the multi-scale aspects in climatic processes, and the proposed methods provide robust framework for quantifying the multi-scale characteristics.

The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-) processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.

In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson’s correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson’s correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.