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Application of Continuous Wavelet Transform for Analysis of Discharge and Precipitation Variability on the Three Stations in the Sava River Basin

Analysis of hydrological time series variability and identification of the processes that caused them is a very important task in hydrology because it gives input for the water management projects and activities, such as flood and drought forecasting, design of hydraulic structures and water quality modeling. Hydrological time series, e.g. discharges and water levels, have complex structure that is a product of non-linear and non-stationary processes. Traditional methods for hydrological time series analysis, such as models based on analysis of serial correlations in time domain or Fourier analysis in the frequency domain, are focused on decomposition of series on deterministic components such as trend, seasonal variations and other periodic changes. The remaining part of time series is considered a noise that “pollutes” data and makes detection of deterministic components more difficult. Hydrological series are non- stationary and therefore application of mentioned traditional methods is limited. In contrast, wavelet analysis, based on wavelet transform enables representation and analysis of non-stationarities in time-frequency domain and therefore is a powerful tool for analysis of hydrological and climate series [1]. Continuous wavelet transform (CWT) is used in hydrology for representation of wavelet coefficients variations with respect to time and scale that also indicates the change in seasonal dry and wet periods. Elaborate analysis of the statistical significance of the wavelet coefficient was developed and with this CWT became widely applicable to hydrological and climate time series [2]. Previous research of the multi-temporal variability of the discharges on the Sava River have been done with CWT and showed strong 0.5, 1 and 2-year periods (scale) in discharge and suspended sediment load spectrum but climate indices have not been examined [3]. Precipitation is one of the main climate drivers of the hydrological process on the river basin and therefore is related to the variability of river discharges. The goal here is the application of CWT for preliminary analysis of variability in river discharge on the Sava River and precipitation time series in the city of Zagreb wider area, i.e. identification and comparison of periods between analyzed series. Input signal for this analysis is daily discharge from two hydrological gauging stations (GS) on the River Sava and daily precipitation recorded at meteorological station (MS) Maksimir in the city of Zagreb, obtained from Croatian Meteorological and Hydrological Service. Distance between the two GS located on the Sava River, upstream (GS Podsused Žičara) and downstream from Zagreb urban area, (GS Rugvica) is 39.1 km. The daily data is gathered from 1970. to 2016., and data from the GS Podsused Žičara and MS Maksimir is complete for analyzed measurement period. However, data obtained from GS Rugvica is incomplete, with several data gaps up to four years which resulted in exclusion of years following 1995 from the analysis of this GS. Excessive noise in the daily precipitation signal did not give appropriate results and daily raw data were transformed into monthly by calculating (i) average and (ii) maximum for discharge and (iii) sum for precipitation series. Finally, time series consists of 564 observations (47 years data) for stations Podsused-Žičara and Maksimir and 312 observations (26 years data) for station Rugvica. Two separate analysis were done due to different length of the continuous measurements: 1970-2016 and 1970-1995. Detection and comparison of changes in variations on inter- and intra-annual time scales (periods) was conducted on time series applying CWT with Morlet wavelet function. Code for the analysis was tailored on an example provided by Torrence and Compo [2]. Significant wavelet power spectra (WPS) levels are compared against red-noise background designed as a univariate lag-1 autoregressive process. Global wavelet spectra (GWS) showed averaged WPS for analyzed measurements time span. Precipitation GWS is characterized by 1-year period peak, while discharge GWS has several expressed peaks: 0.5-year period, 1-year period and 2- year periods for both, mean and maximum series. GWS for mean discharge has stronger 2-year periods and weaker 0.5-year periods in comparison to maximum discharge series. All stations have in common regions of high-power spectra for 1-year periods and relatively high- power spectra for semi-annual periods. The comparison of results in WPS between discharge on GS Podsused-Žičara and precipitation on MS Maksimir for a period of 47 years indicates similar patterns for 1-year period, especially in the years 2010 and 2014 when Zagreb encountered significant high discharges passing through Zagreb area that were related to flood events in the Sava River Basin wider area. Presented preliminary analysis was conducted to explore possibilities of wavelet analysis application on the hydrological and climate series for the large lowland rivers in Croatia. Method and results could be highly applicable in following research steps for better understanding of correlation and coherence between parameters such as discharge, precipitation, floods waves analysis, etc. Better understanding of relationships between hydrological parameters and conclusions about periodical patterns in discharge and precipitation in the Sava basin could be of great help in the future research connected to the R3PEAT project (“Remote Real-time Riprap Protection Erosion Assessment on large rivers”) supported by Croatian Science Foundation under the project number UIP-2019-04-4046.

wavelet analysis, precipitation, discharge, Sava River Basin

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