A review on the applications of wavelet transform for streamflow and suspended sediment analysis

Abstract

Preliminary communicationAnalysis and modelling of discharge and suspended sediment time series is of great importance in hydrology and water management. Discharge and suspended sediment time series are the result of complex physical processes and characterized by non-stationarity. Wavelet transform enables representation of non-stationarities in time-frequency domain, decomposition and reconstruction of series and de-noising of series, and therefore represents powerful tool for analysis of hydrological time series. Overview of mentioned wavelet transform advantages is given in this paper with focus on discharge and suspended sediment time series, presented through: (i) multi-temporal scale analysis of series variability; (ii) multi-scale trend analysis; (iii) prediction and forecasting of series with wavelet based hybrid black-box models, and (iv) wavelet-aided simulation of synthetic series. Keywords: discharge; suspended sediment; wavelet transform Pregled primjene valićne transformacije u analizi protoka i suspendiranog nanosaPredhodno priopćenje Analiza i modeliranje vremenskih serija protoka i suspendiranog nanosa je vrlo važan zadatak u hidrologiji i gospodarenju vodama. Vremenske serije protoka i suspendiranog nanosa uvjetovane su složenim fizikalnim procesima i karakterizirane su nestacionarnošću. Valićna transformacija omogućava prikaz nestacionarnosti u vremensko-frekvencijskoj domeni, rastavljanje i rekonstrukciju serija te potiskivanje šuma u serijama, te time predstavlja moćan alat za analizu hidroloških vremenskih serija. U ovom radu je dan pregled primjene spomenutih prednosti valićne transformacije s fokusom na vremenske serije protoka i suspendiranog nanosa prikazan kroz: (i) viševremensku skalenu analizu varijabilnosti serija (ii) analizu trenda na više skala; (iii) predviđanje i prognoziranje serija hibridnim modelima crne-kutije baziranim na valićima te (iv) simulaciju sintetičkih serija potpomognutu valićnom transformacijom.

Wavelet Transform Application for/in Non-Stationary Time-Series Analysis: A Review

“…The XWT and the WTC, which were respectively introduced in Sections 2.1.1 and 2.6 as two derivatives of CWT, have been also used to illustrate and quantify the associations between the different parameters o 56-year TS obtained from 323 Snow Telemetry (SNOTEL) sites. Potocki et al [49] have presented an overview of the different wavelet applications for discharge and suspend sediment analysis. Four different objectives have been presented in their study: wavelet-based multi-temporal scale, trend analysis, forecasting, and wavelet-aided simulation of synthetic series.…”

Lake-land breezes over a small elongated lake (Kozjak, Plitvice Lakes, Croatia)

“…To verify how well the above conditions define LLB events, wavelet analysis (Torrence andCompo, 1998 andGrinsted et al, 2004, with wavelet bias corrections from Liu et al, 2007 andVeleda et al, 2012) was applied. Wavelet analysis is widely used for analyzing nonstationary time series (e.g., Flinchem and Jay, 2000;Mihanović et al, 2009;de Alcântara et al, 2011;Šepić et al, 2012;Vilibić et al, 2014;Potočki et al, 2017;Schmidt et al, 2018;Chang et al, 2019;Valerio et al, 2019), as it detects frequency and time signals. In other words, it points to time intervals that are characterized by an elevated energy content for a particular frequency where energy content evolves over time.…”