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The quantification of spatial propagation of extreme precipitation events is vital in water resources planning and disaster mitigation. However, quantifying these extreme events has always been challenging as many traditional methods are insufficient to capture the nonlinear interrelationships between extreme event time series. Therefore, it is crucial to develop suitable methods for analyzing the dynamics of extreme events over a river basin with a diverse climate and complicated topography. Over the last decade, complex network analysis emerged as a powerful tool to study the intricate spatiotemporal relationship between many variables in a compact way. In this study, we employ two nonlinear concepts of event synchronization and edit distance to investigate the extreme precipitation pattern in the Ganga river basin. We use the network degree to understand the spatial synchronization pattern of extreme rainfall and identify essential sites in the river basin with respect to potential prediction skills. The study also attempts to quantify the influence of precipitation seasonality and topography on extreme events. The findings of the study reveal that (1) the network degree is decreased in the southwest to northwest direction, (2) the timing of 50th percentile precipitation within a year influences the spatial distribution of degree, (3) the timing is inversely related to elevation, and (4) the lower elevation greatly influences connectivity of the sites. The study highlights that edit distance could be a promising alternative to analyze event-like data by incorporating event time and amplitude and constructing complex networks of climate extremes. [ABSTRACT FROM AUTHOR]

Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively, intrinsic predictability delivers the highest level of predictability for a time series and informative in unfolding whether the system is unpredictable or the chosen model is a poor choice. We introduce a novel measure, the Wavelet Entropy Energy Measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. To investigate the efficiency and reliability of the proposed measure, model forecast performance was evaluated via a wavelet networks approach. The proposed measure uses the wavelet energy distribution of a time series at different scales and compares it with the wavelet energy distribution of white noise to quantify a time series as deterministic or random. We test the WEEM using a wide variety of time series ranging from deterministic, non-stationary, and ones contaminated with white noise with different noise-signal ratios. Furthermore, a relationship is developed between the WEEM and Nash–Sutcliffe Efficiency, one of the widely known measures of forecast performance. The reliability of WEEM is demonstrated by exploring the relationship to logistic map and real-world data. [ABSTRACT FROM AUTHOR]

• Accounted for temporal variability and magnitude to identify homogeneous regions of precipitation in India. • Coupling of self-organizing map with SVI reveals unique seasonal distribution of precipitation for each cluster. • South-central India; South-eastern coastlines; Konkan Coast exhibit stable clusters independent of temporal variability. • The temporal evolution of clusters unravels a new emerging pattern of Indian Summer Monsoon across Central India. Precipitation regionalization deals with an investigation of the seasonality and its temporal variability and is useful for a wide variety of applications in hydro-meteorology. The d homogeneous regions can be used as a basis for transforming the information from gauged to ungauged sites and can reduce the uncertainty in estimating the seasonal characteristics of precipitation across India. Despite several studies stressing the importance of seasonality and temporal variability to the environment, there is a lack of studies on accounting for temporal variability in regionalization. Precipitation regionalization must account for both the precipitation magnitude and its temporal variability at multiple time-scales to extract the seasonality of a region representing coherent local and inter-annual variability. Therefore, in this study, we propose a framework for precipitation regionalization, considering both precipitation magnitude and its temporal variability. High resolution (0.25° × 0.25°) gridded daily precipitation time series over the period 1901–2013 from Indian Meteorological Department (IMD) was used for the evaluation of the framework. First, the historical daily time series was transformed into multiple time scales, i.e., annual, seasonal, and monthly time scales. Entropy-based standardized variability index was used to measure the inter-annual variability of precipitation at each time scale. Regionalization of grid points was performed using self-organizing maps, an artificial neural network. Ten distinct regions were identified that can be tied back to two general categories, such as climate characteristics and physical characteristics. Coupling of the self-organizing map with standardized variability index reveals unique seasonal distribution of precipitation for each region. The temporal evolution of clusters unravels a new emerging pattern across Central India. Consideration of temporal variability plays an insignificant role in the shape, size and stability of south-central India, south-eastern coastlines, and Konkan Coast. Intriguingly, separate Rain-belt and Rain-shadow Western Himalayas are formed due to the difference in topography and seasonal characteristics of precipitation. The temporal evolution of clusters unravels a significant change in the occurrence of the 50th percentile monsoon after the 1940s across the north-western region; a significant increase in the 50th percentile monsoon after the 1940s across western India, and decrease in the 50th percentile monsoon after the 1980s in the north-central Region. [ABSTRACT FROM AUTHOR]