What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology

TLDR: It is shown how wavelet spectral analysis, if combined to a rigorous significance test, can lead to reliable new insights into hydrometeorological processes for real-world applications and how this opens new perspectives for the analysis of model performances focusing on the occurrence and non-occurrence of different types of high flow events.

About: This article is published in Advances in Water Resources.The article was published on 2007-12-01 and is currently open access. It has received 125 citations till now. The article focuses on the topics: Wavelet.

Figures

Fig. 5. Squared wavelet sample coherence calculated with a Morlet wavelet, x0 = 6: same as Fig. 4a, but zoom on the years 1993–1994 (top) and on the year 1999–2001 (bottom).

Fig. 1. Wavelet periodogram of a Gaussian white noise realization with the Morlet wavelet, x0 = 2p. Thin lines: pointwise test on 95% level, thick lines: additional areawise test on 90% level.

Fig. 4. Squared wavelet sample coherence calculated with a Morlet wavelet, x areawise significance test (thick contour line); top: precipitation versus temp discharge of the Vispa River.

Fig. 3. Wavelet spectrum of daily precipitation; values above the cone of infl black contour lines delineate pointwise significance patches, the thick black lin

Fig. 2. Observed daily time series of discharge (m3/s), precipitation (mm/d) and temperature ( C).

Frequently asked questions

Q1. What are the contributions mentioned in the paper "What drives high flow events in the swiss alps? recent developments in wavelet spectral analysis and their application to hydrology" ?

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. 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. Based on the obtained results, the paper summarizes important recommendations for future applications of wavelet spectral analysis in hydrology. 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. 

Q2. What are the future works in "What drives high flow events in the swiss alps? recent developments in wavelet spectral analysis and their application to hydrology" ?

Such more quantitative applications of wavelet spectral analysis require however further research into the interpretation of continuous wavelet spectra for hydrological processes and should be completed in close collaboration with time series analysts from other fields. 

Q3. What is the common method for a time-scale resolved analysis?

One method for such a time-scale resolved analysis is wavelet analysis: it decomposes a signal into a superposition of scaled and translated versions of an original (mother) wavelet (a fast-decaying oscillating function). 

Q4. Why does the areawise test always denote a true deviation from the Null hypothesis?

Due to its high specificity, an areawise deviation almost always (depending on the significance level of the areawise test) denotes a true deviation from the Null hypothesis. 

Q5. What is the width of the kernel for averaging over a range of scales?

For averaging over a range of scales, the width of the kernel should be proportional to scale, i.e. for the common logarithmic scale axis, the width would be constant. 

Q6. What causes a significant coherence in a short time interval?

A significant coherence in a short time interval can be due to spurious common oscillations; i.e. a short coherence interval alone is not necessarily indicative of a physical relationship. 

Q7. What is the significance of the wavelet spectral analysis?

Wavelet spectral analysis enables the inference of time and scale resolved correlations between two time series through the estimation of wavelet coherences; as for the sample spectra, their significance should be tested. 

Q8. Why is the simulation of extreme high flow events difficult?

The simulation of extreme high flow events in Alpine catchments is particularly difficult due to the high spatial variability of the main system inputs, i.e. of the precipitation and of the temperature. 

Q9. How can one estimate the length distribution under the Null hypothesis?

The length distribution under the Null hypothesis (i.e. of randomly common oscillations) can be estimated by a bootstrap approach. 

Q10. What is the significance of the areawise test?

As they showed, in comparison to the conventional pointwise test, the areawise significance test is slightly less sensitive but more specific, i.e. the probability of obtaining misleading false positive results has been reduced dramatically.