Aquifer Responses to Rainfall through Spectral and Correlation Analysis

Abstract

The response time of hydrological components is an important feature for establishing the connections within a hydrological system and for characterizing it. This study proposes a quantitative and qualitative assessment on the response times of river discharge components, especially the baseflow, regarding the impulse provided by precipitation, using time series analyses of time and frequency domains. To this end, a set of complementary methods including correlation and spectral approaches was used, which are: autocorrelation, cross correlation, continuous wavelet transform, and cross wavelet transform. Such framework was applied in multiple and nested basin scales (53, 1,867, and 3,519 km2), located in the Jacaré‐Guaçu River Basin (Southeastern Brazil). Based on a digital filtering technique, it was found the baseflow contributes more than 80% of the annual streamflow, revealing a major role of the aquifer in regulating the river discharge in all three studied basins. In addition, we found baseflow represents a range of 24%–27% of the annual precipitation. The uniform results are mainly due to the similar physical characteristics found in those areas. Overall, our framework indicates a baseflow response time for a precipitation of approximately two years for the smaller basins and three years for the biggest one. Such results can support the water allocation in conjunctive water management, by providing estimates of future surface water availability.

Empirical rainfall‐based model for defining baseflow and dynamical water use rights

“…The geological formations (sandstone) is extensive, underlying large areas in southwestern Brazil. However, in the study area, the groundwater recharge, storage, and release to the draining stream occurs in the shallower Cenozoic sediments that cover the outcrop zones of the Guarani Aquifer System, as discussed by Gómez et al (). In this sense, the system behaves as an unconfined aquifer and, in general, the groundwater divides coincide with the surficial basin limits.…”

“…The ground‐based gridded rainfall product developed by Xavier et al () and updated by Gómez et al () was used to derive mean daily rainfall data from 1974 to 2013 (~ 40 years). The time spans with available streamflow data are from 1974 to 2004 (LJGB) and 1971 to 1991 (UJGB), respectively.…”

“…Different methods can provide insights regarding specific types of responses by the system. For example, the autocorrelation function expresses the linear dependency of successive values over time; hence, it has been used to assess rainfall randomness over a region or the influence of an impulse signal on the corresponding response signal (Buytaert et al, ; Gómez et al, ). Among the various possible approaches, the use of correlation and spectral analysis has been shown to be a solid option to better understand the regulatory capacity of aquifers by evaluating the relationship between rainfall and hydrographs (Padilla and Pulido‐Bosch, ; Zhang et al, ; Gómez et al, ).…”

“…This study builds on the paper by Gómez et al (), who evaluated time lags of river baseflow to rainfall using time domain techniques (autocorrelation and cross‐correlation), as well as time and frequency domains (discrete wavelet transform and cross wavelet transform). The overall objective of that study and the present one is to contribute to the establishment of an integrated (surface water and groundwater) and dynamic (time varying) water allocation policy in Brazil, by providing quantitative estimates regarding the hydrologic system responses.…”

“…Gómez et al () determined the slow (long‐term) response of the groundwater system. To complement the analyses in Gómez et al (), we apply a frequency domain technique (Fourier transform) to time series of rainfall and baseflow seeking to identify fast (short‐term) responses in the same study areas considered in that study. We assume that the groundwater storage change is related to rainfall and such a relationship can be studied by adopting an empirical modelling approach.…”