ALBERT

Description: Extreme hydrological events are often triggered by exceptional co-variations of the relevant hydrometeorological processes and in particular by exceptional co-oscillations at various temporal scales. Wavelet and cross wavelet spectral analysis offers promising time-scale resolved analysis methods to detect and analyze such exceptional co-oscillations. This paper presents the state-of-the-art methods of wavelet spectral analysis, discusses related subtleties, potential pitfalls and recently developed solutions to overcome them and shows how wavelet spectral analysis, if combined to a rigorous significance test, can lead to reliable new insights into hydrometeorological processes for real-world applications. The presented methods are applied to detect potentially flood triggering situations in a high Alpine catchment for which a recent re-estimation of design floods encountered significant problems simulating the observed high flows. For this case study, wavelet spectral analysis of precipitation, temperature and discharge offers a powerful tool to help detecting potentially flood producing meteorological situations and to distinguish between different types of floods with respect to the prevailing critical hydrometeorological conditions. This opens very new perspectives for the analysis of model performances focusing on the occurrence and non-occurrence of different types of high flow events. Based on the obtained results, the paper summarizes important recommendations for future applications of wavelet spectral analysis in hydrology.

Description: We examine a statistical model for the description of the seasonal variation of extreme daily precipitation at 689 stations across the UK. The probability distribution for monthly maximum precipitation intensity is modelled with a generalised extreme-value distribution (GEV). Instead of modelling the distribution of precipitation maxima separately for every month, we propose an overall model with seasonally-varying location and scale parameters and a constant shape parameter. This model is tested against an augmented version with the shape parameter allowed to vary as well. Furthermore, we compare model adequacy for block length of one and two month and found no major improvements for the longer block-length. Based on this model, the 10 and 100-year return levels are calculated conditioned on the month of the year. The interpolation of return levels to a complete coverage of the UK allows for an identification of spatial patterns and their temporal evolution. These patterns suggest that different mechanisms for extreme precipitation are dominant in different regions of the UK.

Description: We propose an equivalence class of nonstationary Gaussian stochastic processes defined in the wavelet domain. These processes are characterized by means of wavelet multipliers and exhibit well-defined time-dependent spectral properties. They allow one to generate realizations of any wavelet spectrum. Based on this framework, we study the estimation of continuous wavelet spectra, i.e., we calculate variance and bias of arbitrary estimated continuous wavelet spectra. Finally, we develop an areawise significance test for continuous wavelet spectra to overcome the difficulties of multiple testing; it uses basic properties of continuous wavelet transform to decide whether a pointwise significant result is a real feature of the process or indistinguishable from typical stochastic fluctuations. This test is compared to the conventional one in terms of sensitivity and specificity. A software package for continuous wavelet spectral analysis and synthesis is presented.

Description: We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We study the difference of the phase dynamics between El Niño/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. We identify distinct epochs, especially two intervals of phase coherence, 1886–1908 and 1964–1980, corroborating earlier findings from a new point of view. A significance test shows that the coherence is very unlikely to be the result of stochastic fluctuations. We also detect so far unknown periods of coupling which are invisible to linear methods. These findings suggest that the decreasing correlation during the last decades might be a typical epoch of the ENSO/Monsoon system having occurred repeatedly. The high time resolution of the method enables us to present an interpretation of how volcanic radiative forcing could cause the coupling.

Description: We present a modern method used in nonlinear time series analysis to investigate the relation of two oscillating systems with respect to their phases, independently of their amplitudes. We overcome the difficulties coming along with low frequency fluctuations typical for climate data by a novel geometric approach, that efficiently filters out variations of the mean. The potentials of this concept in comparison to conventional methods are illustrated by an application to a paradigmatic example from climatology: We study the difference of the phase dynamics between El Niño/Southern Oscillation (ENSO) and the Indian Monsoon on inter-annual time scales. Distinct epochs can be identified, especially two intervals of phase coherence, 1886-1908 and 1964-1980, corroborating earlier findings from a new point of view.We also detect so far unknown periods of coupling which are invisible to linear methods. The high time resolution of the method reveals a possible dependency of the coupling on volcanic radiative forcing. We study this hypothesis utilizing a conceptual model.