Analysis and interpretation of natural variations in water table and groundwater recharge of coastal aquifer system in the coastal plain of Rio Grande do Sul, Brazil

This paper presents the results of recharge estimation and water table variation analyses of the Coastal Aquifer System, located in the Rio Grande do Sul Coastal Plain (Brazil). Water-level data from 11 wells were processed and analyzed, applying autocorrelation and cross-correlation methods to evaluate the aquifer memory effect and mean response time to rainfall events. The seasonality of the response time was evaluated through splitting the data series in windows of 90 days, overlapped by 45 days. Recharge rates were obtained with the water table fluctuation (WTF) daily applications (RISE and MRC), considering specific yields of 20%, 25% and 30%. Water-level data smoothing with moving averages and time series filters were necessary, to remove level rises not associated with precipitation events within the aquifer average response time, The autocorrelation and cross-correlation displayed a variability of responses through the wells, with median response times of level to precipitation from 0, 1 and 2 days (wells in aquifer layers of fine to medium sands) to 10 days (wells in aquifer layers of higher clay content). The recharge rates of 0.74 to 2.42 mm day−1 and Recharge/Precipitation ratios from 19% to 46% were obtained (Sy = 25%, mean between RISE and MRC results). From these applications, the study presents the importance of level data processing and filtering to daily WTF applications and displays the differences in the behavior of the wells in the Coastal Aquifer System.


Introduction
The evaluation of water table fluctuation and groundwater recharge is central to improve the knowledge about aquifer systems and to promote the integrated water resources management, which is increasingly demanded from pressures imposed upon water availability, such as urbanization, changes in land use and increases in agricultural activity. These issues are associated with the increase in polluting loads and climatic change, with potential of harming water security in Brazilian watersheds (Maziero and Wendland 2005). Thereby, it is important that water resources managers consider hydrogeological studies to support estimates of groundwater availability and guide the sustainable usage of this resource (Feitosa 2008).
In the study of groundwater, measuring variables such as water availability, reserves, and recharge is generally difficult, given the geological complexity and the difficulty of understanding the spatial variation of the properties of aquifer systems. Thus, instead of calculating an exact number, one should estimate the recharge rate (Feitosa 2008), presenting ranges of values of its occurrence in the study area. However, estimating recharge remains a challenging task, which involves uncertainties in the measurements and the difficulty in validating the results of the different methods applied. In the coastal region of the Brazilian state of Rio Grande do Sul, there are additional challenges to estimate the groundwater recharge, associated with existence of lagoons, connected by swamps and channels with reduced flows (Tomazelli and Villwock 2005), which can hinder the 1 3 330 Page 2 of 17 application of methods based on flow measurements in surface water bodies.
In this regard, this paper aims to contribute to the study of recharge and groundwater dynamics of the Coastal Aquifer System (CAS), in the Rio Grande do Sul Coastal Plain (PCRS), for which there are few studies on this theme. Therefore, data from 11 monitoring wells of the Brazilian Geological Survey's Integrated Groundwater Monitoring Network (RIMAS-CPRM) were analyzed, from 2012 to 2020. The study involved the application of autocorrelation and cross-correlation to evaluate the behavior of water-level oscillations, as well as the development and application of filters to remove level variations not related to precipitation. These methods were already applied in data from Karst Aquifers (Larocque et al 1998;Delbart et al 2014;Cai and Ofterdinger 2016) and Shallow Granular Aquifers (Neto et al 2016;Gómez et al 2018;Boumaiza et al 2021), providing information about groundwater trends and behavior, but still lack application in data from the CAS.
Recharge estimates were obtained based on the application of the water table fluctuation (WTF) method, which relates water-level variations to the amount of water stored in the aquifer (Healy and Cook 2002), analyzed jointly with the results of the statistical methods to present indications about the recharge processes. Thus, the study also aimed to fill a gap in knowledge in the estimates of water resources in the CAS, considering there are just a few studies of recharge in this region, which are focused on the Northern side of the coastal region of Rio Grande do Sul (Troian et al 2017;Senhorinho et al 2021).

Study Area
The Rio Grande do Sul Coastal Plain (PCRS) is a Brazilian geological unit, composed predominantly by unconsolidated sediment deposits, that cover the entire coastal strip of the state of Rio Grande do Sul. This unit has an area of 33 thousand km 2 and a length of 622 km in the N-S direction, between the latitudes of 28° S and 33° S, from the border with the Brazilian state of Santa Catarina (SC) to the border of Brazil with Uruguay. The PCRS covers important freshwater lagoons (Patos and Mirim Lagoons) and the outflow of a large watershed (Guaíba Lake), which are associated with a regional flow towards the ocean, that also supports a stable freshwater aquifer composed of sediment barriers on the Coastal Plain (Schafer et al. 2017).
There are important municipalities located in the PCRS, including Rio Grande (which has more than 200,000 habitants and an regionally relevant seaport) and the coastal cities in the Northern Coast, which has a seasonal migration flux of around 1 million habitants between December and March (SCP-RS 2015). The groundwater in this region is important for domestic use and for the productive activities of the region, especially irrigation. The water extraction in the CAS occurs through drilled, driven and dug wells, many installed irregularly (Reginato et al. 2008), which makes it difficult to estimate the actual flow extracted from the CAS.
The climate in the PCRS is classified as Subtropical, with the absence of a dry season and the presence of hot summers (Alvares et al. 2013). The Pluviometric Atlas of Brazil (Pinto et al. 2011) shows that the Northern Coast region presents higher average precipitation, between 1600 and 1700 mm year −1 , and in the municipality of Osório, a little further south, there is in an average rainfall zone around 1400 mm year −1 . At lower latitudes, the wells are in lower average rainfall zones: around 1500 mm year −1 in Arambaré, around 1400 mm year −1 in Rio Grande and around 1300 mm year −1 in Tavares, Mostardas and Santa Vitória do Palmar.
The hydrological context of the Coastal Plain is distinguished by the presence of coastal lagoons and lakes (with high residence time) and the absence of extensive and large flowing rivers (SEMA-RS 2019). To the north, the plain is characterized by a series of small and medium coastal lagoons. The middle section is mainly covered by the Patos Lagoon, with approximately 10,000 km 2 , and the Peixe and Estreito Lagoons. To the south, the largest water body is the Mirim Lagoon, with approximately 3770 km 2 , connected through the Taim wetland with the Mangueira Lagoon, closer to the coastal strip.
The lithological composition in the PCRS consists of unconsolidated sediments associated with processes of erosion, transport and deposition resulting of coastal mechanisms, in which medium to fine sands predominate, interlayered with fine lenses of clay (Troian et al. 2020). Sediments in the PCRS date to the Tertiary and Quaternary and are associated with alluvial fans and four lagoon-barrier depositional systems, originated from sea-level oscillations during the Pleistocene and Holocene (Tomazelli and Villwock 2005).
In the PCRS region, the Coastal Aquifer System (CAS) is found, associated with layers of sandy and clayey sediments, which can constitute unconfined, semi-confined, and confined aquifers (Troian et al. 2020). Recently there have been identified five hydrostratigraphic units that compose the SAC in the PCRS: the most superficial is characterized by sandy unconsolidated sediments, with a depth of 20-40 m, followed by the intercalation of clay and sandy sedimentary units, with different hydraulic and water quality properties (Troian et al. 2020).
The Hydrogeological Map of Brazil (Diniz et al. 2014) describes the CAS as two aquifer units with distinct characteristics (Fig. 1). The first unit follows the coastline and presents moderate productivity (specific flow between 1 and 2 m 3 /h/m), with layers of fine to medium sand, interlayered by layers with lower clay content. The second unit, west of the first, on the margins of the lagoon bodies and further inland, presents generally very low productivity, but locally low (specific flow between 0.04 and 0.4 m 3 /h/m) and is composed of finer sands with higher clay content.
The main source of hydrogeologic data on the CAS is the Brazilian Geological Survey's Integrated Groundwater Monitoring Network (RIMAS/CPRM), with data available on the project website (http:// rimas web. cprm. gov. br/). The 11 RIMAS monitoring wells at PCRS considered in this study can be observed in Fig. 1 and Table 1.
Shallow aquifers and wells with low depths are found in the PCRS, considering the 11 RIMAS wells from the Northern Coast region (in Arroio do Sal, Terra de Areia, Capão da Canoa and Xangri-lá, latitudes around 29° 40′ S) to the far south of the state (in Santa Vitória do Palmar, latitude 33°35'S). These monitoring wells present an average water table level of 3.52 m (0.55-7.36 m) and an average total depth of 65 m (42-100 m). As displayed in Fig. 1, these wells are located in granular aquifer units of moderate productivity (3 Gr), with the exception of the well in Osório (well 4300020530), which is located in a unit of locally low productivity (5 Gr).
The mapping of groundwater recharge in the PCRS still lacks studies that consider the entirety of its extension, the diversity of characteristics in the aquifer layers, and the application of different methods. The recent study by Troian et al. (2017) evaluated groundwater recharge from monitoring five wells located in the CAS, in the Northern Coast of Rio Grande do Sul, applying the WTF method for monthly averages of water table-level data, which estimated recharge/precipitation ratios between 21% and 40%, for a specific yield of 30%.

Data collection and processing
Water-level data, representing the depth from the top of the well to the water table, were collected with the 11 monitoring wells of the RIMAS/CPRM Network displayed in Table 1, located in the Coastal Plain of Rio Grande do Sul, in the Coastal Aquifer System. The data were downloaded from RIMAS/CPRM public website on 08/01/2021 and represent a daily data series of water level between May 2012 and April 2020. The level variations in RIMAS wells are recorded with pressure transducers equipped with a datalogger, consolidated, and made available for download at daily frequency.
The analysis of the monitoring wells design diagrams, available at RIMAS website, displayed that the screens for every well are positioned at more than one of CAS layers. Therefore, the water table fluctuations are related to the overall behavior of the Aquifer System and the measures of levels cannot be associated to a specific hydrostratigraphic unit. Figure 2 displays the availability of groundwater-level data for the wells considered in this study, which have at least two hydrological years of water-level data, with measures available (data not missing) from 98% to 100% of the period considered. The hydrological year considered in this study is the time period from May 1st to April 30th, a typical interval for the state of Rio Grande do Sul (Tucci 1993;Silva Júnior et al. 2001). The gaps in the data series occurred in a maximum of 5 consecutive days and were filled using linear interpolation, observing the behavior of the waterlevel hydrographs. The replacement of outliers was also performed, through visual analysis of the hydrographs, adopting a substitution by the linear trend of the data around these values.
The rainfall data in daily frequency were obtained from the National Hydrometric Network (RHN), available on the HidroWeb Portal (http:// www. snirh. gov. br/ hidro web/ apres entac ao). The selected data were collected in rainfall stations near the wells, operated by the Brazilian Geological Survey (CPRM) and the Brazilian National Institute of Meteorology (INMET), as shown in Table 2.
The rainfall stations near the wells displayed availability of daily rainfall measurements from 96.2% to 99.5% over the hydrological years. The gaps were complemented by daily measurements at stations near the wells (nearest neighbor method), operated by CPRM, INMET, Brazilian Center for Monitoring and Early Warnings of Natural Disasters (CEMADEN) and the Brazilian Agrometeorological Monitoring System (AGRITEMPO), and the few remaining gaps in data, of no more than 5 consecutive days, were filled through linear interpolation.

Evaluation of water-level variations and recharge estimation
The methods applied for the evaluation of water-level variation and the estimation of groundwater recharge were categorized into: (1) statistical methods for data series analysis, used for water level and precipitation data and (2) recharge estimation methods, through the proposed WTF applications.

Data series analysis
The first method adopted to evaluate water table variations was autocorrelation, which can quantify the linear dependence of successive water-level values over an arbitrated period (Larocque et al. 1998). The expression for the autocorrelation function is as follows: (1)  where C(k) is the correlogram, n is the length of the time series, k is the time lag, x t is a single event, x is the mean of the events and γ(k) is the autocorrelation function. Autocorrelation coefficients are obtained over time lags, considering relevant values as those above a predefined range, usually 0.2 (Cai and Ofterdinger 2016). A slow decline of the autocorrelation values up until high values of lag times indicates a greater memory effect (data with greater interrelation over time), which can be associated with the storage characteristics of the soil matrix that constitutes the aquifer system under analysis (Bortolin 2018). Cross-correlation analysis was also applied, considering rainfall data as inputs and water-level data as outputs, to obtain an average response time for the water level measured in the wells in relation to the precipitation events. Since lower values in water-level data (depth to the water table) are expected to be related to higher values of precipitation measurements, the study focused on the negative cross-correlation values, detailed below: where C xy is the cross-correlogram, n is the length of the time series, k is the time lag between x and y, x t and y t are the input and output events, respectively, x and y are the mean of input and output events, respectively, γ xy is the autocorrelation functions and x and y are the standard deviations of input and output events, respectively. The method can result in a maximum absolute value for a positive lag time of the output with respect to the input (when the input precedes the output)¸ indicating the average response time between the two variables.
The cross-correlation analysis was also applied on intervals of the data series, to evaluate the variability of response times and investigate seasonal effects. The application selected for this study is described in Delbart et al. (2014), which sliced the water level and precipitation data series into 90-day windows, overlapped by 45 days, and applied the cross-correlation function for each division.

Applications of water table fluctuation
The method selected for recharge estimation was the water table fluctuation (WTF). This application attributes waterlevel rises (∆H) to aquifer recharge, assuming that the x y available water in a column of water is equivalent to the specific yield (S y ) multiplied by its height (Healy 2010). Therefore, recharge (R) can be estimated over a specific time interval (∆t) as This application is best suited for fast level changes associated with precipitation events, more frequent in shallow, unconfined aquifers in regions with high precipitation rates and low slopes (Healy and Cook 2002), consistent with the CAS. The method has spatial representativeness of hundreds of square meters and does not contemplate slow and steady state flows from the subsurface layer into the aquifers, which is generally not a problem for aquifer depths less than 10 m (Delin et al. 2007).
WTF applications need to relate positive variations in water level with precipitation events, since other phenomena can lead to sudden oscillations in level not necessarily related to groundwater recharge (Healy and Cook 2002). In the case of the wells located in the CAS, with water levels close to the surface and many oscillations, it was proposed a time series application with daily data, that considers level rise events that can be associated with the occurrence of precipitation events, from the adaptation of the approach proposed by Crosbie et al. (2005): where R t is recharge at time t, h t is water level at time t, S y is the specific yield, P t′ is the sum of precipitation over the aquifer response time, which is t′ (the time required to observe a rise in water level after a rainfall event, estimated by cross-correlation analysis). The term D is associated with the recession of the hydrograph and has been adapted to be estimated with the RISE and MRC approaches, with daily data.
The RISE method is an application of WTF that calculates daily level rises from the difference between the level on two successive days, discarding negative values (Rutledge 1998). This approach is expected to underestimate recharge rates, because it disregards recession and equals the D term in Eq. (6) to zero. However, the method has advantages in allowing the automation of recharge estimation and dismiss the need for estimation or graphical extrapolation of recession curves (Delin et al. 2007).
The master curve recession (MRC) method estimates the parameters for a recession curve that relates levelto-level variation in the absence of recharge, assuming a otherwise characteristic functional relationship between water level and recession rate (Heppner and Nimmo 2005). Compared to the RISE approach and manual extrapolation of recession curves, the application of MRC is expected to overestimate the recharge rates (Delin et al. 2007). The estimation of the recession curves (H vs. dH/dt) was obtained through polynomial fitting, for each hydrological year of the consolidated data series, through the MRCfit program, developed in the R programming language (Nimmo et al. 2014).
To implement the recharge estimation, it was performed a smoothing of the level data using a 5-day simple moving average (Yang et al. 2018;Melati et al. 2017;SRH-CE 2017). Applying this filter is important to correct small oscillations in level measurements, that can occur from a series of mechanisms besides recharge, such as evapotranspiration, changes in atmospheric pressure, air trapping, ocean tide changes, pumping near the well, and others (Healy and Cook 2002). This process contributes to the removal of noise that could lead to an overestimation of recharge rates (Labrecque et al. 2019).
Another component evaluated was the specific yield, which represents the aquifer storage capacity associated with the water instantaneously discharged in recharge and discharge processes (Healy and Cook 2002). Considering that recharge rates estimated through WTF vary greatly from changes in specific yield values (Healy 2010), a sensitivity analysis with S y values of 20%, 25%, and 30% for all wells was adopted. This approach was based on the study by Troian et al. (2017), who evaluated geophysical profiles in wells in the PCRS and adopted these three values, which are compatible with specific yields observed in layers of fine and medium sands (Johnson 1967).
Thus, the following workflow was applied to estimate recharge: (1) obtain and sum the recession value (0 for RISE or estimated by MRC) to the daily ∆H; (2) select the positive terms; (3) zero the terms not preceded by precipitation in the aquifer response time; (4) aggregate the remaining terms for each hydrologic year, resulting in an annual ∆H; (5) multiply the ∆H by the three proposed S y values; (6.a) divide the S y .∆H term by the number of days in the hydrologic year to obtain the average recharge rate (mm day −1 ) and; (6.b) divide the S y .∆H term by the cumulative rainfall in each hydrologic year to obtain the R/P ratio.

Data series analysis
The water-level fluctuations during the study period (2012-2020) are visible for each RIMAS/CPRM monitoring well in Fig. 3. The water table levels (in meters) are displayed in blue lines and the rainfall during each period are displayed in grey columns (in daily millimeters).
These hydrographs indicate a difference in behavior between the levels in the wells. Some wells present a high daily variability of levels, with values between 0 and 2 m and no distinct seasonal variations, especially in wells 4300020526, 4300020527 and 4300020529. Diversely, wells 4300020530 and 4300022136, with levels around 3 and 4 m, displayed less daily variability and more long-term fluctuations, noticing that the other wells are in an intermediate situation between those described. Table 3 presents the results of the autocorrelation analysis.
The application presented that level data from wells 4300020526, 4300020527, 4300020528 and 4300020529 generally resulted in shorter periods with high autocorrelation coefficients (greater than 0.2), the minimum being 14 days for well 4300020529, in the hydrological year from May 2017 to April 2018 (Fig. 4). Nonetheless, even in these wells there can be periods with higher ratio between levels, associated with the repetition of daily values, especially when a longer period is considered. The first periods before reaching an autocorrelation coefficient lower than 0.2 were considered and displayed in Table 3, because water-level time series for most of the wells demonstrated a behavior of long-term increases in coefficients after a decline, and thus generating more than one interval with high coefficients, what can be associated to a repetition of level values over the hydrological years.
Autocorrelation applied in data from other wells, such as 4300020530, 4300020531, 4300022136, 4300022137 and 4300022639, indicated a greater memory effect, for example, the 59-day period with autocorrelation coefficient greater than 0.2 between 2017 and 2018 for well 4300020530 (Fig. 4). These differences can be associated with the soil and aquifer layer matrix, as these five wells are in regions with finer sediments, which are results of deposition processes associated with the proximity with lagoons. These characteristics can result into aquifers with reduced transmissivity and higher stability to disturbances in the water system. In the other hand, wells with faster declines in autocorrelation coefficient are closer to regions, where fineto-medium sands prevail, constituting aquifers with higher permeability and more prone to oscillations. Table 4 features response times of the water level in relation to precipitation (time lag for higher cross-correlation coefficient), over the hydrological years considered.
This analysis allowed to differentiate the average responses between water table-level time series collected in the CAS. The results displayed that wells 4300020526, 4300020527 and 4300020529 present fast responses (between 0 and 1 days) and absolute maximums of cross correlation coefficient between 0.2 and 0.4, indicating greater relation in the variation of levels to precipitation. These responses can be associated with the presence of fine to medium sands around these three wells, that have a faster infiltration of water from land surface to the saturated zone, considering the low depths to the water table.
A faster response is also observed in levels from well 4300022639, but with lower cross-correlation coefficient values, indicating a less intense relationship between the variables. This well is located near the Taim Ecological Station, a region with the presence of wetlands (complex natural systems) and close to the Peixoto Lagoon, which can imply in the differences observed in the hydrological responses.
Wells with less variability in levels (4300020530, 4300022136, and 4300022137) also showed a less intense relationship between levels and precipitation, with absolute maximums of cross-correlation coefficient around 0.08-0.25 for lags between 1 and 31 days. Figure 5 exemplifies the differentiation between the responses in the wells from the data in hydrological years 2017-2018 at wells 4300020529 and 4300020530. These results can be associated with the presence of clayey sediments and the proximity with lagoons, that can be in a dynamic equilibrium with the coastal aquifers (discharge and recharge processes can both happen over time, as observed in Caitano and Andrade 2020). In addition, in the surroundings of these wells there is also more natural vegetation landcover (Souza et al. 2020), that may contribute with more soil water holding capacity, slowing the response of the water table.
The application of the sliding windows cross-correlation (Table 5 and Fig. 6) consolidates the characterization of the responses in the wells in the Coastal Aquifer System.
Sliding windows cross correlation also resulted in different behavior for the 11 water table-level data series. Wells  , with less intense relationship between level and precipitation and lower percentage of significant peaks. The slowest responses are observed in wells 4300022136 and 4300022137, fluctuating between 0 to 16 days, with medians of 10 days. Two wells on the Northern Coast, 4300020528 and 4300020530, presented median response times of 4 for the constructed intervals, but in well 4300020528 there are lower water levels and a slightly more intense relationship between level and precipitation, from the percentage Table 3 Result of the autocorrelation analysis for the water-level data in the 11 RIMAS/CPRM wells analyzed Values displayed in bold represent analysis of complete time periods available for each well, and the remaining values are related to single hydrological years a The period of r (auto correlation coefficients) higher than 0.2 represents the average estimated time, where linear relationship between water levels over time is considered relevant (Cai and Ofterdinger 2016), i.e., the higher this value, the "memory-effect" is more predominant The longer response times in some wells are coherent with the results observed in autocorrelation, that indicated long-term stability in levels measured that can extend close to or further than 90 days (window size selected). As discussed above, some factors that may contribute to this matter are the proximity to lagoons, the presence of clayey sediments and natural vegetation in the surroundings. Even though there can be differences in the magnitude of the cross-correlation coefficients through the windows, the stable response in some wells may be associated with the high permeability and presence of fine to medium sands, aspects that do not have seasonal impacts. Table 6 presents the recharge rate estimates after smoothing the water-level data and applying the time series filter (which considers the medians of the response times for each well presented in table). Recharge rates between 0.55 and 2.97 mm day −1 or between 199 and 1083 mm year −1 were obtained.

Estimates of recharge
In the RISE method, recharge rates range from 0.55 and 1.89 mm day −1 for S y = 20%, from 0.68 to 2.37 mm day −1 for S y = 25%, and from 0.82 to 2.84 mm day −1 for S y = 30%. As expected, the values for MRC are consistently higher than those estimated through RISE, ranging between 0.62 and 1.98 mm day −1 for S y = 20%, between 0.77 and 2.47 mm day −1 for S y = 25%, and between 0.93 and 2.97 mm day −1 for S y = 30%.
The maximum observed rate occurred in well 4300020527 (in Capão da Canoa), of 2.47 mm day −1 (S y = 25%, MRC), in the aggregate period 2013-2016 and 2018-2020. Wells 4300020526, 4300020528 and 4300020529 (on the Northern Coast) and well 4300022639 (in Rio Grande, near the Taim Ecological Station) also show high recharge rates, between 1.75 and 2.22 mm day −1 (MRC, S y = 25%). Intermediate values (between 1.40 and 1.50 mm day −1 , MRC, S y = 25%) were observed in well 4300009528, on the Middle Coast, in a Pleistocene barrier deposit with eolian sediments, and in well 4300020566, on the Northern Coast, but in a region with predominant geology composed of lagoon plain sediments (Wildner et al. 2006). The lowest recharge values were estimated for wells 4300020530, 4300022136 and 4300022137, of 0.90, 0.77 and 0.84 mm day −1 , respectively (MRC, S y = 25%). Figure 7 presents the estimated recharge rates for each hydrological year with data available, considering the values obtained with the application of MRC and S y = 25%.
In general, there is relevant variability in the estimated recharge rates, although there are no sharp trends of declining or increasing values for the complete periods, the analysis is made more difficult given the reduced availability of level data over time. It is important to note that wells with higher recharge rates also show greater overall fluctuations in these rates over the years, especially wells 4300020527, 4300020528 and 4300020529. The peak followed by a fall in recharge rate between 2015-2016 and 2016-2017 at well 4300020528 is noteworthy, associated with the declining in levels between these hydrologic years (as depicted in Fig. 4), which may indicate near well interference in the aquifer, some problem in the measuring equipment, or another issue during this period. Table 7 presents the ratios of recharge to precipitation estimated with the WTF method. For the average between RISE and MRC results, values were obtained between 15% (well 4300020530) and 37% (well 4300020527) for S y = 20%, between 19% and 46% for S y = 25%, and between 23% and 55% for S y = 30%. The importance of this R/P evaluation was reinforced through the preliminary estimate of recharge without water-level data smoothing and time series filtering, which for several wells in the CAS resulted in implausible values, such as R/P ratios close to or even greater than 100%, also justifying the necessity of these filters. The estimated ratios are generally high, but compatible with Brazilian aquifers in similar conditions, especially in the Northern Coast, where the wells have filter packs installed to a greater extent in aquifer layers composed of fine sands (4300020526, 4300020527, 4300020528 and 4300020529). These high values are associated with the geological conditions as well as water tables being very close to the ground level and the highest rainfall rates in the PCRS, which is an overall plain region with low slopes, allowing for fast infiltration and recharge, configuring aquifers very responsive to rainfall events. Table 4 Result of cross-correlation analysis for rainfall and water-level data in the 11 RIMAS/CPRM wells analyzed Values displayed in bold represent analysis of complete time periods available for each well, and the remaining values are related to single hydrological years *Significance at p equal to 0.05 a Highest absolute r (cross correlation coefficient) indicates the maximum level of relationship between water level and precipitation through the time lags evaluated (− 100 to 100 days), and the time lag associated with the highest value represents the average response time of the water   The estimated recharge for this Northern region is close to the same range of values obtained using monthly data in Trojan et al. (2017), from 21% to 40% (S y = 30%), although the estimated values in the present study are somewhat higher. This can be associated with the fact that applications of WTF considering daily data tend to be superior to evaluations of monthly data, which can underestimate recharge rates (Delin et al. 2007).
The lower recharge rates in well 4300020530 may be related to the fact that the well is in an aquifer unit of lower productivity and in a region with a greater presence of clayey sediments (Diniz et al. 2014). The constructive profile of this well, available in the RIMAS/CPRM portal, indicate the presence of a superficial layer of clayey sand, which can influence the subsurface water flow and delay the recharge of the aquifer, as pointed out by the statistical methods. Well 4300022137 has a surface layer of coarse sand, which can decrease water retention and favor infiltration and recharge processes. However, both wells 40300020530 and 4300022137 are in a region of beach deposits and ridges parallel to the lagoon banks and well 4300022136 is in a lagoon deposit (Wildner et al. 2006), which can be associated to the contribution of clayey sediments to the aquifer layers.
As mentioned, there is a visible association of higher recharge rates with wells in regions with higher rainfall rates in the PCRS, as occurs in the Northern Coast (average rainfall of 1914 mm year −1 for the period of analysis), with an exception to this observation being well 4300022639, located in Rio Grande, close to a wetland in Taim Ecological Station. Wells in regions, where precipitation is lower, presented in general lower recharge rates, as occurs in the south of the state, with the minimum average precipitation considered to be 1258 mm year −1 , for the period 2014-2020, in the region of well 4300022136 (which also presents the deepest average water table, of 7.36 m). More detailed assessments with field precipitation gauges closer to wells can deepen this evaluation.
It is important to note that the recharge rates estimated in this study with the WTF method include uncertainty which is difficult to quantify. This is associated with the necessity of the further estimation of specific yield values considering the hydrogeological context of each well. Another limitation that demands deeper evaluation is to compare responses and recharge rates of this study with results estimated on wells with screens in specific aquifer layers from the CAS, important for a more refined understanding of the hydrological processes. The surrounding conditions of the wells and its relationship with different recharge mechanisms can also instigate further studies. Therefore, this study proposes to be a starting point for understanding level variations and recharge in the PCRS, considering the lack of flow and level data and the few studies developed in the region.

Conclusions
In this paper we examined groundwater-level data sets from 11 wells located in the Coastal Aquifer System, in the Coastal Plain of Rio Grande do Sul. The study was able to characterize the response of wells through cross-correlation and autocorrelation analysis, obtaining fast responses to precipitation (0-2 days) in some wells, related to shallow and unconfined aquifers, composed predominantly of fine to medium sands. However, slower responses (medians of 10 days) and weaker relationships between level and precipitation are observed for wells with lithologies composed of sediments with higher clay content. These differences are also detected through the results of autocorrelation, displaying a weaker memory effect in water levels from wells in regions with soils and geologic units more permeable, pointing to more variability in levels.
The paper also presented estimates of recharge, assessed with the WTF method, obtaining overall high recharge rates, which indicates that the Coastal Plain of Rio Grande do Sul, a plain region with low slopes and shallow water tables, has fast responses and favorability to natural recharge through rainfall events. The highest values (R/P greater than 40%, avg. between RISE and MRC, S y = 25%) were observed in wells with water table closer to land surface, in regions with predominance of fine to medium sands associated with eolic and coastal processes, as well as some proximity to urban areas, in the Northern Coast of Rio Grande do Sul. Relatively lower recharge rates (R/P lower than 30%, avg. between RISE and MRC, S y = 25%) were observed in some wells close to coastal lagoons, in regions with presence of soils and sediments with high percentage of clay, as well as higher percentage of natural areas in their surroundings. This information is relevant for the adequate management of groundwater resources in the Coastal Plain of Rio Grande do Sul, which needs studies to support its advance.
An important issue highlighted in the study is the correction of noise in the measurements of water levels in wells of the Coastal Aquifer System, which was achieved through the application of a time series filter considering the water table response time to precipitation and the smoothing of data with a moving average filter. In this type of aquifers this issue is very relevant, due to the high permeability, low average water levels, and the proximity of wells to lagoons and the ocean, which can lead to level oscillations not necessarily related to recharge, highlighting the importance of the methodologies applied. Obtaining larger historical series with fewer data gaps, associated with the maintenance and improvement of the RIMAS/CPRM, and comparing the results with recharge rates estimated by other methods can contribute to complement this study in the future.