QUALITY OF GROUNDWATER DISTRIBUTED BY COLLECTIVE ALTERNATIVE SOLUTION IN RURAL AREAS INTERFERES WITH WEATHER VARIABLES

Theoretical benchmark: The seasonal and spatial variability of a spring can be monitored by physical, chemical and microbiological parameters, to ensure access to the population of drinking water, managed in a safe manner, since alternative and unsafe sources of water supply, and sometimes without treatment, pose risk to human health. Method: Quantitative, retrospective study of water samples collected monthly by monitoring the quality of water for human consumption in rural and urban areas from collective supply from January 2018 to December 2019. Results and conclusion: Precipitation interfered with all water quality indicators except free residual chlorine; and temperature interfered with turbidity, free residual chlorine, and fluoride. There was a correlation between fluoride and temperature; total coliforms and free residual chlorine, which suggests the possibility of antimicrobial action. Cross-sectoral actions to improve the quality of water supplied in rural areas are therefore proposed, through the adoption of continuous disinfection of all water sources. Research Implications: Presents important indicators on the quality of water


INTRODUCTION
Water is essential to life on the planet, to the conservation of ecosystems (Bicudo, Tundis & Scheuenstuhl, 2010) and to socio-economic development, and therefore it is a strategic asset (Carvalho, Lacerda, Carvalho, Lopes & Andrade, 2020).Groundwater has great storage capacity and resistance to long periods of drought, mainly due to climate change, the growth in the use of well as an important source of human supply is outstanding (Krolow, Krolow, Santos, Casali & Mulazzani, 2018;Hidrata, Suhogusoff, Marcellini, Villar & Marcellini, 2019;Machado et al, 2022).
Groundwater quality is conditioned by natural variables such as precipitation, surface runoff, geology and vegetation cover, and by anthropic actions such as effluent discharge, soil management, use of fertilizers and agro-chemicals (Feitosa, Filho, Feitosa & Demetrio, 2008).
The water quality of a spring should be assessed by its physical, chemical and microbiological parameters, as well as monitoring its spatial and seasonal variability (Bertossi, Menezes, Cecílio, Garcia & Neves, 2013).Global climate change can lead to changes in rainfall, evaporation and humidity in relation to the historical values of a region (Bicudo et al. 2010).
In Brazil, the form of collective supply responsible for the distribution of drinking water, most frequent in the rural environment, is the collective alternative solution (SAC), (Guerra & Silva, 2018;BRAZIL, 2021) and of this 63% of SAC do not have treatment in the country (BRAZIL, 2015), which favors the proliferation of pathogenic organisms and demonstrates vulnerability and exposure to health-related risks (BRAZIL, 2015;WHO, 2017).
Given the need to provide access to the population of drinking water, submitted to safe and efficient treatments without risks to human health and the possibility of interference of climatic factors in its quality, the present research aims to evaluate the interference of air temperature and rainfall rainfall on the quality of water consumed by the rural population, coming from SAC of underground abstraction.

METHOD
This is a retrospective, quantitative study, based on the analysis of water samples collected by the monitoring of the quality of water for human consumption (VIGIAGUA), registered in the Laboratory Environment Manager (GAL).
The study area corresponds to the rural area of two small municipalities, intentionally selected, that are part of the Diversity Health Region, located in the Northwestern part of the state of Rio Grande do Sul.Both municipalities have about 7000 inhabitants (SISAGUA, 2019), with a proportion of the rural population between 43 and 48% and a municipal human development index (MHDI) of 0.743 and 0.753 (IBGE, 2010).The rural population is supplied by SAC and individual alternative solutions (Sisagua, 2019), from underground abstraction.The municipalities studied have high agricultural activity, whose main crop is soybeans and occupies about 60% of the territorial area (IBGE, 2017).The climate of the region is temperate subtropical with seasonal variation of temperature, with hot summers and harsh winters.Average temperatures range from 15 to 18°C, with a minimum of -10°C and a maximum of 40°C.With regard to rainfall, the state presents a relatively balanced distribution of rainfall throughout the year and the average is between 1,500 and 1,800 mm (RIO GRANDE DO SUL, 2019).
Of the total of nine monthly samples collected by the Vigiagua servers of each municipality, established according to this Guideline, 214 were sampled in SAC, located in the rural area, that is, 107 samples in 2018 and 107 in 2019.These samples come from underground collection and were collected in the period from January 2018 to December 2019.To obtain this data, a primary database, extracted from the LAG, was used.
At each sampling point, two aliquots of the same sample were collected: one in a sterile 100 mL bag for microbiological analysis (total coliforms and Escherichia coli) and another in a 500 mL bag for turbidity and fluoride.These sterile bags are supplied by the Central Laboratory of Public Health (Lacen) to the municipalities.Collections followed the standard operating procedures established by Lacen.
With the laboratory samples, the analysis of the basic parameters of water quality was carried out: free residual chlorine, turbidity, fluoride, total coliforms and E. coli.The samples were collected monthly by the municipal Vigiagua and sent to the Regional Laboratory of Public Health of the 17th Regional Coordination of Health (Lacen-Ijuí), to carry out the analyzes of the basic parameters, except the free residual chlorine, which was carried out in the field, at the time of collection, by the municipal Vigiagua, with the results recorded in the LAG.
The free residual chlorine dosage was performed after bag sampling by the colorimetric method with the DPD (diethylphenylene diamine) reagent powder, expressed in mgL-1 (Soares et al. 2016).In Lacen, the tests were carried out according to Standard Methods for Examination of Water and Wastewater (APHA, 2012) for turbidity (nephelometric method 2130 B), fluoride (potentiometric method with selective ion electrode 4500-F-C) and for the presence or absence of total coliforms and E. coli (chromogenic/enzymatic substrate method 9223 B, Colilert system).The basic parameters were evaluated according to the GM/MS Ordinance No. 888/2021.
The samples were grouped according to the seasons of the year: summer (January, February, March), autumn (April, May, June), winter (July, August, September) and spring (October, November and December).In the microbiological analysis, number of samples with presence of total coliforms/E.coli were identified; and for total coliforms, percentage of detectable samples was calculated.In the present study, it is not possible to determine the potability in relation to the total coliforms of the SAC analyzed, since only one monthly collection occurred per form of supply, which does not allow to define the standard of potability, according to the relevant legislation.The assumptions of normality and homogeneity were verified via Bartlett's test.Comparison between average and percentage values required data transformation.Afterwards, a comparison analysis of averages by Fisher was carried out, at a level of 5% probability of error.Pearson's correlation analysis was performed by associating indicators of water quality with meteorological elements during the two years of data use for research.Multivariate analysis was used for a more global study involving all the variables in the study together.Analyzes of descriptive statistics, Fischer's mean test, multivariate analysis with grouping and Pearson's correlation were carried out using the Genes program.
The meteorological data of air temperature and accumulated precipitation were obtained by the total automatic station installed at the Regional Institute of Rural Development/IRDeR-Unijuí in Augusto Pestana-RS (28° 26' 30" latitude S and 54° 00' 58" longitude W).
As this is research involving primary data, extracted from the LAG, authorization was obtained from the State Center for Health Surveillance (CEVS) through the Office n°14/2020, CEVS/SES/RS, of 28/04/2020.

RESULTS AND DISCUSSIONS
Of the total samples analyzed (214) for free residual chlorine, 91.6% were PPF in the two years analyzed.The spring of both years showed 100% of the free residual chlorine FPP samples and the winter had the lowest proportion.It is also noted that winter 2019 was the only season that showed significant difference in the proportion of free residual chlorine samples less than 0.2 mgL-1 when compared to the other seasons of the same year.It is also evidenced that fluoride was DPP in all the analyzed samples and in the different seasons of the year.It should also be noted that only two samples had the turbidity FPP among the 214 analyzed: one in spring 2018 (10 uT) and another in autumn 2019 (7.4 uT).
In the current legislation, a minimum of 0.2 mgL-1 of free residual chlorine is mandatory throughout the water distribution (Brazil, 2021), to maintain microbiological quality (WHO, 2017), regardless of weather conditions or the season.Thus, the majority of free residual chlorine analyzes (91.6%) presented values lower than those recommended by GM/MS Ordinance No. 888/2021.This index of water samples with unsatisfactory residual free chlorine content demonstrates the vulnerability of the analyzed SACs to microbiological contamination.The absence of free residual chlorine was also identified in rural SAC in RS (Fioravanti et al. 2020).Differently, in MG, adequate values of free residual chlorine were found (Souza;Frade & Soares, 2018).
Winter was the season that had the lowest percentage of non-compliant free residual chlorine samples, there was a strong negative correlation between free residual chlorine and minimum and average temperature in 2019.According to the authors, it is influenced by climate, environment, type and soil cover.It is known that free residual chlorine concentrations are influenced by the increase in temperature in the distributed water, and is an important parameter to be assessed in water quality, by reducing gas solubility, accelerating chemical reactions (Monteiro;Viegas;Covas & Menaia, 2015) and stimulating the growth of opportunistic pathogens (WHO, 2017).Regarding the identification of total coliforms, 69.6% of the total samples analyzed were present.It can be said that they were detected in higher percentages in autumn (81.3%), followed by spring (74.2%) 2018; and in summer (76.2%) and spring (75%) 2019.The percentages of total coliforms, on the other hand, were lower in winter, in both years analyzed.
The percentage of detection of total coliforms in the samples was above 60% in all the seasons of the two years evaluated, and it meets studies developed in Brazil: 100% of the samples with the presence of total coliforms in the State of Espírito Santo-ES (Menezes;Bertossi;Santos & Neves, 2013), in Rio Grande do Norte-RN (Gregório; Brito; Oliveira; Paiva & Mascarenhas, 2020) and 61.3%, in SP (Santos et al. 218).Other studies are in line with the results of the present study: in the State of Ceará-CE, 40% of the samples were found with the presence of total coliforms (Costa;Lima;Paixão & Pantoja, 2012).It also supports the study by Aguirre et al, 2020.It should be noted that the high detection of total coliforms in the SACs studied, warns against insufficient disinfection in the distributed water and/or exposure to sources of environmental contamination (WHO, 2017;Fioravanti et al. 2020).The winter of both years assessed was the season with the highest proportion of adequate free residual chlorine samples, which may have favored lower detection of total coliforms.The kinetics of inactivation of microorganisms by free residual chlorine is also influenced by the increase in temperature (BRAZIL, 2016), by changing its rates of degradation of disinfectant in the distribution of drinking water (Monteiro et al. 2015).
As for seasonality and occurrence of total coliforms, winter differed from autumn 2018 (Table 1), and autumn was the season with the highest percentage of detection of total coliforms (Table 5).Autumn was the driest season (217 mm) of 2018, which suggests that low natural recharge may create a more concentrated percolating liquid, as the dilution effect does not occur (Feitosa et al. 2008).A study in the rural area of the MA, obtained the same finding (Coelho et al. 2017).
E. coli was found to be present in 23.8% (51/214) of samples, with the highest percentage in spring, followed by autumn 2018; and in summer and spring 2019.There was no presence of E. coli in the winter of 2018, and the winter and autumn of 2019.
Regarding the occurrence of E. coli, it was present in 23.8% of the total samples analyzed in this study, and in 2019 it was 27.1% compared to the year 2018 (20.6%), i.e., it was found to be worse of this indicator.Some studies have found higher contaminations, such as E. coli detection in 100% of samples (Gregório et al. 2020;Rego;Bezerra & Pinto Filho, 2020) and 85.7% (Scalizeet al. 2014).Others have seen lower percentages of E. coli: 14.8% (Teixeira et al. 2012), and no detection (Souza. et al. 2018).These surveys took place in different regions of the country with different characteristics, where fecal contamination was found to be related to precarious sanitation: either by the absence of disinfection (Souza et al. 2018;Fioravanti et al. 2020), or by poor structural conditions of wells and lack of proper management of domestic waste and animal excrement, which make groundwater highly vulnerable to anthropic pollution (Gregório et al. 2020;Rego et al. 22222020) (2) In this investigation, there was a positive correlation between E. coli and total coliforms in 2018 (r = 0.89; p < 0.05).One study found a positive correlation between these two biological parameters (Mottin;Silva;Rocha & Neto, 2016).Yet another study found no such correlation (Castro;Cruvinel & Oliveira, 2019).
Sequentially in Table 2, it is found that the mean values of free residual chlorine, fluoride and E. coli did not show significant differences between the seasons of the year.In the comparison between averages of turbidity, summer differed from other seasons (p < 0.05), with the lowest mean.It is also noted that summer was the season with the highest average rainfall accumulated in the year 2019.As regards the detection of total coliforms in 2018, autumn had the highest average and summer the lowest (p < 0.05).In the same year, too, the average accumulated precipitation was higher in summer, and lower in autumn.
As for the seasonality of E. coli, the spring and autumn of 2018 showed the highest percentages of samples.This result shows the seasons that showed greater fecal contamination of the distributed water, and also showed percentages above 95% of FPP samples of free residual chlorine.In the year 2018, it also found a strong negative correlation between these two indicators (r = -0.94,p > 0.05), which suggests that the higher the quantification of free residual chlorine, the lower the detection of E. coli.Investigations demonstrate the importance of adequate free residual chlorine values in rural SACs associated with the absence of detection of E. coli (Souza et al. 2018;Fioravanti et al. 2020).To guarantee this condition, it is necessary to implement integrated public sanitation policies, involving actions to monitor the quality of the distributed water, added to the guidance and legal requirement by the monitoring bodies to the companies responsible for the supply of treated water in the maintenance of adequate values of free residual chlorine (Teixeira et al. 2012;Scalize et al. 2014).And research shows that most of these investments and infrastructure are concentrated in urban centers when compared to rural areas (Scalize et al. 2014;Souza et al. 2018).
Table 3 of the correlation analysis, considering the year 2018, free residual chlorine showed a significant negative correlation between turbidity and E. coli, which indicates that the increase in free residual chlorine effectively improves water clarity and decreases fecal microbiological contamination.The turbidity of the water is determined by the suspended solids.It may have aesthetic implications, affecting appearance and acceptability for consumers, and drinking water safety (Feitosa et al. 2008;WHO, 2017).Regarding the turbidity analyzes in the present study, only 0.01% of the samples analyzed were PPF in the years studied.Similar findings, in which point samples were non-compliant, were found in rural communities: in RO (Oliveira et al. 2015), in MA (Coelho et al. 2017) and in MG (Souza et al. 2018).Other studies found higher percentages of non-compliance in this parameter: 11% in SP (Fioravanti et al. 2020), and 20% in RS (Zerwes et al. 2015).These investigations found that the highest detection of turbidity occurred due to the high levels of iron (Fioravanti et al. 2020) and total solids (Zerwes et al. 2015) present in groundwater, as well as structural problems of wells (Menezes et al. 2013).
As for seasonality and turbidity, summer differed from other seasons in 2019, with the lowest average of turbidity concentrations.Summer was the rainiest season of 2019 (538 mm), as was the summer of the previous year (542 mm), however, the number of rainy days was lower (37 days in 2018; and 28, in 2019).A similar finding occurred in the State of Pará, with lower turbidity values in the rainy period than in the dry season, which indicated that the greater percolation of the water allows the dilution of solids present in the water (Silva;Barbosa & Silva, 2018).However, other investigations have found that the rainy season presented greater turbidity than in dry weather (Santos et al. 2018), which can be explained by poor structural conditions of wells, which allows infiltration and surface runoff of the precipitated water (Santos et al. 2018).
In the present study, analyzed here, there was a positive correlation between turbidity and average/maximum temperature (r = 0.91/0.87;p < 0.05) in 2018.Temperature increase in non-chlorinated or poorly disinfected aquatic environments may increase turbidity due to the multiplication of microorganisms present in water (WHO, 2011).It should be noted that there was also a negative correlation between turbidity and free residual chlorine (r =-0.95; p < 0.05) in 2018.When free residual chlorine is added to water, different chemical reactions occur, as well as its immediate consumption by the organic matter present in water (BRAZIL, 2016;WHO, 2017).Turbidity alone does not pose a risk to public health, however, it may indicate the presence of pathogenic microorganisms and be an effective indicator of problems in drinking water distribution (BRASIL, 2016;WHO, 2017).
With regard to fluoride, also in the year 2018, a high positive correlation was identified with the number of rainy days.There were associations between turbidity and maximum/average temperature with high positive correlation (p >0.05).The total coliforms, on the other hand, showed association with fluoride with a high negative correlation, which suggests that the higher the fluoride, the lower the environmental contamination.
Also in Table 3, in the year 2019, a high negative correlation between fluoride and minimum/average temperature and accumulated precipitation was found, a positive correlation between fluoride and free residual chlorine was found.Negative correlation with temperature (minimum and average) was also identified for free residual chlorine.E. coli showed an association with the number of rainy days with a high positive correlation.
The presence of fluoride in groundwater is due to the chemical composition of the rocks, alkaline hydrological environment, climatic conditions, residence time in aquifers and geochemical processes (Edmunds & Smedley, 2013).It should be noted that the present study assesses the fluoride doses coming from natural waters, since there is no guidance of fluoridation (fluoride addition) in SAC in Brazil (BRAZIL, 2021).
Fluoride was DPP in the two years evaluated.It is often found in low concentrations in groundwater (Edmunds & Smedley, 2013).However, studies have reported high concentrations of fluoride in aquifers (Ezaki;Aguilar;Hypolito & Shinzato, 2016).In the water distributed for human consumption, the presence of fluoride, within the standard of potability, is a protective factor in the prevention of caries; however, it can be a risk to dental and bone fluoroses, depending on their concentration (Venturini;Narvai;Manfredini & FRazzie, 2016;BRAZIL, 2021).Therefore, the presence of this chemical, less in the absence of fluoridation, should be monitored by water quality monitoring (BRAZIL, 2016;WHO, 2017;Fioravanti et al. 2020).
In the multivariate analysis, of the weather elements in the different seasons of the year, the maximum temperature and accumulated precipitation were the variables that most contributed to differentiate the seasons of the year 2018; and in 2019, it was the average temperature, and minimum.
There was a positive correlation between the number of rainy days and E. coli in 2019.This finding suggests that the increase in surface water runoff, in contact with contaminated environments, may carry microorganisms to the point of abstraction (Silva et al. 2018;Fioravanti et al. 2020) or greater percolation of these towards the groundwater (Oliveira et al. 2015;Silva-Et al. 2018).Other authors also found a higher occurrence of E. coli in the rainy period than in the dry one (Oliveira et al. 2015;Silva et al. 2018), which demonstrates precipitation interference in this biological variable and these correlations may change, since meteorological variables are dependent on the climatic conditions of the period analyzed.The relative contribution of water quality indicators to the seasons of the year, it was observed that total coliforms were the variable that contributed, mostly, to differentiate the seasons of the year in 2018; and turbidity, free residual chlorine and fluoride, in 2019.In the formation of the groups of similarities of the seasons, according to the indicators of water quality, in 2018: there was the formation of two groups: I (autumn, winter and spring) and II (summer); already, in 2019, there were three groupings: autumn and spring formed the first group, which were distinct from both summer and winter.
With respect to fluoride and accumulated precipitation, negative correlation was found between them in the year 2019 (r = -0.97;p > 0.05).Naturally, fluoride concentrations are controlled by rock-water interaction and percolated water volume, which increases groundwater flow rate, which decreases contact time and reduces fluoride concentration (Ezaki et al. 2016).
A positive correlation was found between fluoride and number of rainy days (r = 0.97; p < 0.05) in 2018, i.e., the higher the intensity of precipitation, the higher the fluoride levels found.The summer of 2018 was the season with the highest number of rainy days and the highest average fluoride concentrations.This correspondence suggests that there may be anthropogenic groundwater fluoride contamination, through surface runoff or percolation in the unsaturated zone and in aquifer recharge areas (Fantong et al. 2010).Studies indicate that poor structural conditions of the well, such as lack of sanitary protection, orifices and deterioration of the pipe, allow the entry of chemical, physical and biological contaminants in the occurrence of greater precipitation (Oliveira et al. 2015;Fioravanti et al. 2020).The area studied has high agricultural activity with the use of fertilizers and pesticides (IBGE, 2017).
Interestingly, fluoride showed negative correlation with total coliforms (r = -0.98;p<0.05) in 2018 and with minimum and average temperature in 2019 (r =-0.98 and r =-0.93, respectively).Also, fluoride was found to correlate positively with free residual chlorine in 2019 (r = 0.98, p > 0.05).No studies have been found that show similar findings in the distribution of water for human consumption, whether through simplified systems or distribution networks.It has already been established that fluoride possesses antibacterial properties this characteristic does not occur exclusively in the human oral cavity, but also in soil and waste water (Herrera et al. 2009).Groundwater geochemistry has a substantial impact on untreated water microbiota (Kaestli et al. 2019).Thus, the hypothesis arises of the possibility of antimicrobial action of fluoride in bacteria present in simplified distribution systems, a question to be elucidated in longer studies, since these conditions were observed in only two years of studies, which does not allow to make inferences.
Table 5, 2018 (1647 mm) was rainier than 2019 (1605 mm), and summer, followed by spring, were the seasons with the highest accumulated rainfall in the two years analyzed.In the multivariate analysis, the maximum temperature (38.14%) and accumulated precipitation (30.27%) in the year 2018; and the average temperature (52.98%) and minimum temperature (34.23%) in the year 2019 were the meteorological elements that most contributed to differentiate the seasons from the years studied.This result shows that the seasons do not, by themselves, change the indicators of water quality, but rather the meteorological conditions that occur within these seasons, such as air temperature and precipitation, which are dependent on the condition of the year analyzed.It should also be noted that 2018 showed greater climate divergence than the following year, since winter and autumn were thought to be similar (Varejão-Silva, 2005), which did not occur.This demonstrates that 2018 was atypical and reinforces that meteorological conditions change the physico-chemical and microbiological indicators analyzed in this study and suggests that longitudinal temporal investigations may help to elucidate which variable(s) would have the greatest contribution potential.
When considering the indicators of water quality in multivariate analysis, the total coliforms had the largest relative contribution (72.5%) in the formation of the 2018 season groups that showed similarity: autumn, winter and spring (group I) and summer (group II).In 2019, turbidity (36.06%), free residual chlorine (35.09%) and fluoride (23.05%) were the variables that contributed to the formation of the groupings: autumn and spring (group I); summer (group II) and winter (group III).Although turbidity, fluoride and free residual chlorine had similar magnitudes in the contribution to the pools in 2018, they were stronger than E. coli and, when analyzed in 2019, this proportionality is practically maintained between those indicators.

FINAL CONSIDERATIONS
The present study shows that meteorological elements, such as air temperature and rainfall, interfere with the dynamics of relationships of all variables of water quality studied, since they alter elements linked to the environment, biology and chemical reactions.
Rainfall interference was observed in all water quality indicators except free residual chlorine.Increased accumulated precipitation reduces turbidity, fluoride concentrations and the detection of total coliforms.The higher rainfall intensity favors anthropic contamination, either by E. coli and/or fluoride.High temperatures contribute to increased turbidity and reduced free residual chlorine concentration, as the increase in temperature favors the multiplication of micro-organisms.These interferences vary according to the conditions of the year, indicating the need for longer longitudinal studies.Although it is a result found in the two years analyzed, it is a question to be clarified in future investigations.
Maintaining adequate concentrations of free residual chlorine can reduce meteorological influences, especially with regard to microbiological indicators, which showed nonconformities throughout all seasons of the year in this study.Thus, in the search for the microbiological safety of SACs, cross-sectoral actions are proposed to improve the quality of water supplied in the rural area, through the adoption of continuous disinfection of all water sources and reinforcement of monitoring actions carried out by surveillance, as well as improvements in structural conditions of wells.
One of the limitations of the study is its restriction to two municipalities and the exclusive use of a database, the aim of which is to increase the number of municipalities researched, as well as the variables included in the analyzes, and to add data collection in locu.

Table 1 -
Descriptive statistics and comparison between the percentages of PPF samples of the indicators of groundwater quality in the rural area, in different seasons of the year.Number of samples analyzed; SD = Standard deviation; DPP = Within potability standard; FPP = Outside potability standard; Samples + = Samples with presence of total coliforms or E. coli.PPF (%) followed by different capital letters in the same row between seasons of the same year, differ from each other by Fisher's test, and denote significant difference (p < 0.05).

Table 2 -
Average values of indicators of water quality in the rural area, from underground abstraction and meteorological elements in different seasons of the year.

Table 3 -
Correlation between the meteorological elements with the indicators of groundwater quality in the rural area, second year evaluated.

Table 4 -
Relative importance of meteorological elements and indicators of water quality for human consumption and similarities between seasons.Quality of Groundwater Distributed by Collective Alternative Solution in Rural Areas Interferes with Weather Variables Prepared by the authors (2023).

Table 5 -
Values of air temperature, accumulated precipitation and number of rainy days, by season, from 2018 to 2019.Regional Institute for Rural Development/IRDeR-Unijuí.Prepared by the authors (2023).