Meteorological and hydrological patterns are being considerably perturbed because of anthropogenic climate global warming (O’Gorman 2015; Pfahl et al. 2017). Therefore, water resources systems and are being rapidly transformed (Allan and Soden 2008; Chang et al. 2015; Kalra et al. 2013; Trenberth 2011; Al-Rawas et al., 2019). In this sense, stationarity in traditional stationary hydrological time series (rainfall-runoff-aquifer recharge) is not prevalent anymore (Back, 2011; Donat et al. 2016; Huff, 1990; Wasko and Sharma 2015). In this sense, extreme events such as floods (Vogel et al., 2018) or droughts (Marcos-Garcia, 2017) and their impacts, are increasingly recurrent (Jyrkama and Sykes 2007). Consequently, there is a strong demand of developing potent and reliable analytical methods to build accurate models that simulate and predict/forecast the hydrodynamics of a water system (Hao and Singh 2016; Xu et al. 2015). Accuracy in predictive modelling comprises, first, dealing with the inherent hydrological time series randomness and variability and, second, to incorporate uncertainty (Kong et al. 2017). There is also a strong need to build predictive models considering the sudden behaviour of hydrological systems. In this sense, methods/models based on minutal, hourly or daily data and time steps are required for this.
Marotzke et al. (2017) define “weather” as the result of the “interplay of thermodynamic and dynamic processes which determine circulation and rainfall patterns”. Furthermore, Nobre et al. (2017) define Climatic variability as “the natural fluctuations of the climate system around the long-term trend”. However, those variations are being increasingly altered due to the impact of Climate Change (CC). Currently, CC drives several hydrological processes: a) larger-scale climate structures such as El Niño–Southern Oscillation (ENSO), anti-ENSO called La Niña, North Atlantic Oscillation (NAO) mainly, b) extreme hydrologic events, c) sea level rise, d) melting of mountain glaciers and polar ice, e) thermal expansion of sea water and f) decrease of general water availability and increase of groundwater extraction (Chang et al. 2015; Kalra et al. 2013). This worldwide phenomenon is strongly related to the effect of global warming (IPCC 2021), which is highly intensified by anthropogenic actions (Marotzke et al. 2017). Min et al. (2011) and Zhang et al. (2013) O’Gorman (2015), provide evidence for an anthropogenic contribution to observed changes in precipitation extremes. NAO is the major cause of seasonal and interdecadal variability of atmospheric circulation on the European continent (Qian et al. 2000). Rodrigo et al. (2000) determined that NAO is the most likely cause of alterations on the precipitation in the south of Spain. Rodriguez-Puebla et al. (2001) show that NAO is main source of interannual variability over Iberian Peninsula.
Uncertainty, randomness, and variability are own features of hydrological time series. Regarding local meteorological processes, their recurrency is also being altered showing greater picks and frequency of massive rainfall-runoff processes in reduced territories. The occurrence of heavy rainfall often leads to flooding episodes that may have a greater or lesser socio-economic impact depending on the degree of vulnerability of societies. Better infrastructure planning in general will make it possible to reduce the degree of vulnerability to these extreme events determining their probability of occurrence and, therefore the greater or lesser risk of exposure to the phenomenon. The case study where this research has been developed is in the Segura Hydrographic Demarcation (DHS), located in SE Spain. This DHS with a relatively small area, presents a complex orographic configuration marked fundamentally by two extensive plains or depressions, that of the Segura and the Guadalentín, as well as by important mountain chains belonging to the foothills of the subbetic system and other pre-coastal mountain ranges. The morphology of the basin and the intense rainfall that tends to occur in the region (CHS, 2018; Melgarejo-Moreno et al., 2021)) increase its risk level in the event of flooding episodes. Over the last 70 years, the average annual precipitation for the entire DHS has not undergone any significant change, although there has been a decrease in the annual number of rainy days and, therefore, in the number of days of rainfall and therefore of the average daily intensity of precipitation, as well as a greater frequency of events greater than 40 mm in 24 hours (Lizondo-Osset and García Valero, 2020). This last change is in line with the increase in the frequency and intensity of the most intense precipitation events in the on the Mediterranean basin of the Iberian Peninsula obtained at Oria (2021), as well as in the southeastern peninsular observed in Acero et al. (2011). Both results are compatible with the increase in the occurrence of Isolated High-Level Depressions observed in Muñoz et al. (2020). Attributing these changes to anthropogenic climate change is not straightforward mainly due to the high interannual variability of precipitation observed over the region (Lizondo-Osset and García Valero, 2020), which is indicative of high internal variability, and much more so if it is referred to intense precipitation events. However, some of these changes are in line with climate change projections (Cardoso et al., 2020; Donat et al., 2016), which are not exempt from great uncertainty and low confidence when it comes to intense events (Stocker, 2014). The maximum annual 24-hour precipitation is a variable considered as unlikely and has traditionally been used as an index to assess risk by using its series to determine return periods of certain thresholds after adjustment to a distribution function of extreme values of a general type, Gumbell, SQRT-ET max (Ministerio de Fomento, 1999), etc. Knowing the possible existence of trends in this variable could be an indication that it maybe the risk is changing and therefore needs to be re-evaluated. Several studies have been analyzed within this research aimed to evaluate possible trends of maximum annual precipitation in the different sub-basins of the DHS and the analysis of possible changes in the return periods associated with this variable (CHS, 2018; García-Valero, 2021).
Predicted changes on meteorological variables such as temperature or rainfall can provoke significant variations on aquifer hydrodynamics such as recharge rates (Jyrkama and Sykesa, 2007), or piezometric levels. There is not a clear consensus on the Climate Change impact on aquifers´ behaviour. In this sense, several studies forecast decreases in aquifer recharge (Herrera-Pantoja and Hiscock, 2008; Merritt et al., 2006; Molina et al., 2013; Molina et al 2021;), whilst others predict increases (Döll, 2009; Green et al. 2007; Gurdak and Roe, 2010; Jyrkama and Sykes, 2007; Kovalevskii (2007); Yusoff et al., 2002). Furthermore, other contributions cast doubt about it (Molina et al., 2013; Pulido-Velázquez, 2015). Especially in arid and semiarid regions, water resource availability can be reduced, modifying stream-aquifer interaction, pumping cost rates and, eventually, leading to aquifers contamination.
Mathematical groundwater flow models are needed to simulate and predict future groundwater dynamic variability under different management scenarios. There are many developments of numerical simulation models worldwide. Of course, there are different type of numerical models, but they all have something in common which is the power and ability to physically represent the high spatio-temporal variability of aquifer properties and inherent conditions (Coppola et al. 2005; Molina et al 2009). However, the way the uncertainty is analyzed, quantified and integrated to those models is still a non-resolve topic and challenge, especially for predicting developments. Furthermore, mathematical physical codes and developments are often limited by the data volume required and to the anisotropy and intermixture of physical features that need to be represented by too many parameters to which the data is scarce. Consequently, the cost for developing these physical models is a challenge in many contexts The unavoidable and inherent significant error and uncertainty generated within the different iterations of those models´ development make, in many cases, these models not to be as effective and useful as desired (Szidarovszky et al. 2007).
Today, Artificial Intelligence (AI) techniques, due to the progress in computer science, is the most popular paradigm of techniques for implementing massive data analysis. In this sense, Artificial Neural Networks (ANNs) are one of AI techniques (Derbela and Nouiri, 2020; Yang et al. 2017a). ANNs that has been used for many purposes such as forecasting drinking water demand (Ghiassi et al. 2008), predicting extremal precipitation (Bodri and Cermak 2000), characterizing and predicting illnesses (Khan et al. 2001), predicting electricity demand (Kandananond 2011), assessing civil aviation safety (Zhou et al., 2017), modeling river flow (Aichouri et al. 2015), predicting reference evapotranspiration (Mosavi and Edalatifar 2019), estimating dam capacity (Üneş et al. 2019), or for hydrodynamic prediction of groundwater level. In this sense, many studies have used ANNs to resolve hydrogeological research problems at different temporal scales (Banadkooki et al. (2020); Chitsazan et al. (2015); Coppola et al. (2005); Feng et al. (2008); Sun et al. (2016). Üneş et al. (2017); Üneş et al. (2019). The greatest limitation of ANN is that does not incorporate uncertainty in its analysis because it is a deterministic technique. Consequently, stochastic processes cannot be analyzed or modelled in a realistic and accurate way.
Furthermore, recently, a large amount of data sources is available and a rapid emergence of new techniques in hydrology based on Information Theory and Artificial Intelligence have emerged. In this sense, other important techniques and applications may comprise the study of dependence relationships through Entropy Theory (Singh 2011), or forecasts improving by Bayesian approach (Zhao et al. 2015) or Machine Learning techniques (Lima et al. 2016), drought predictions (Kousari et al. 2017), and reservoir operations through data mining and artificial intelligence (Hejazi and Cai 2011; Yang et al. 2017b, 2016), among others. The relationship between hydrological variables and their time series can be captured through many ways from the main basic analysis (Pearson Coefficient) to much more rigorous based on AI techniques such as probabilistic conditional dependence. This organization comprises a set of trivial and non-trivial (induced and diffused) dependence relationships that explain its general temporal behavior (Hao and Singh 2016; Wang et al. 2009). Furthermore, dependence structures among different random variables should be quantified and considered for the analysis, modeling and prediction of hydrological events. (Hao and Singh 2016). Relationship between variables can be also analyzed through dependence. This has been analyzed for hydrologic studies through many methods (Hao and Singh 2016). The most conventional measure of dependence is the Pearson’s correlation coefficient based on the normal distribution hypothesis to measure the linear dependence. However, in many cases the normal behaviour is not valid, and the linear dependence is too simplistic to characterize much more complex dependence configurations (Hao and Singh 2016). Another common technique is the Spearman and Kendall correlations. It has also been traditionally implemented as complementary dependence indicator to characterize the nonlinear dependence of hydrological variables, as demonstrated recently with copula models (Nelsen 2006). In Hydrology, copula applications started after the work (De Michele and Salvadori 2003), where Frank copulas were tested for a joint study of the negatively associated storm intensity and duration. Other research works such as (Zhang and Singh 2006, 2007) incorporated copulas for an extreme analysis of rainfall and drought events. Dependences´ modelling for and between extremes events is currently strongly studied (Davison and Huser 2015; Dutfoy et al. 2014; Vogel, 2018). Dependence in extreme events should be evaluated through techniques designed as extreme distribution like the tail dependence coefficient. This has been commonly used in investigating hydroclimatic extremes, such as precipitation and temperature (Serinaldi et al. 2014). These extreme events drive the aquifers recharge main processes and they must be considered as a major source of aquifers´ income in water budgets.
Another important and recent area of research is the construction of a multivariate distribution in modelling different dependence structures (Sarabia-Alzaga and Gómez-Déniz 2008). This is applied to hydrology and in the form of frequency analysis, downscaling, streamflow or rainfall simulation, geo-statistical interpolation, bias correction, etc. Other methods, such as multivariate parametric distribution (Balakrishnan and Lai 2009), entropy (Molina et al. 2016; Singh 2013), copula (Nelsen 2006), have been developed to model various dependence structures of multivariate variables through the construction of joint or conditioned distribution.
Bayes´ rule implemented through Bayesian Inference and Bayesian Networks (BNs) or Dynamic Bayesian Networks (DBNs) can be considered as popular AI technique (Molina et al. 2013; 2016; 2020). Other techniques related to the previous one is the multinomial logistic regression (Wu et al. 2015) and Markov Random Field (MRF; Lee et al. 2012). MRF or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. BNs are directed and acyclic (Not possible close feedback loops), whereas MRF´s are undirected and may be cyclic (possibility of close feedback loops). Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it cannot represent certain dependencies that a Bayesian network is able to, such as induced and diffused dependencies (del Sagrado Martínez 2003). The identification and quantification of these dependences is not a minor issue and causal analysis is a very good method for capturing these relations (Molina and Zazo, 2017). The demand of skills for working with complex relations and building probability distributions make these new approaches appropriate. Those skills can be summarized as follows: The ability of using field raw-data (Zounemat-Kermani and Teshnehlab 2008) that can be calibrated within the same analysis; then, “a priori” information of the process is not needed (Nourani et al. 2011); then, they are able to process a great amount of data. Consequently, they are useful for identifying physical relationships which are not completely either identified or understood. In this sense, BNs have been largely used for groundwater management as Decision Support System for the Integrated Water Resources Management. BNs are being used to model diverse problems of high complexity for water management applications (Molina et al 2010). However, BNs, Bayesian Inference (BI) or Bayesian Causal Reasoning (BCR) have not been exclusively used so far to reproduce physical hydrodynamic behaviour in groundwater hydrology. In this sense, being able to develop technical tools based on BCR implemented by BNs is an unexplored field that this research aims to cover for the groundwater hydrology field.
Common approaches do not incorporate any causality in their computations. Classic return period approaches just comprise an average value that represents the inverse of the probability of a certain temporal period, generally called recurrence interval. To better perceive the differences and the accuracy of results, this study is applied to a monitored system that comprises a pluviometry station and a piezometric level station in real time. The proposed methodology may be applicable to any other aquifer system as a suitable alternative and appropriate complement to traditional approaches.
This study is mainly aimed to provide a quantitative assessment through BCM of the hourly dependence relationship between temporal evolution of rainfall and groundwater level and its implications on aquifers´ hydrodynamics. Using those time series, a causal analysis (Bayes Theorem) that computes, shows and define the probabilistic interaction of two variables is developed. This analysis provides the knowledge of the level of dependence relationship among those variables at an hourly time step. This approach differs over traditional approaches such as Pearson correlation coefficients or Spearman rank correlation coefficient that measures the dependence in the main data body without fully considering Uncertainty (Hao and Singh 2016).
This manuscript is organized as follows. Following section is dedicated to show a state of the art that comprises the main existing approaches and techniques in which this study is based on. Next section comprises the description of the case study. Later on, the applied methodology is described. Next section shows the main results drawn from the research. Final section is devoted to the discussion and conclusions generated from the study.