Precipitation plays a paramount role in the drainage of watersheds, especially in those depending on rainfall for the persistence of the flows, considered intermittent streams. These types of watercourses, occasionally dry, are already a large-scale phenomenon (Acuña et al., 2005; Larned et al., 2010; Datry et al., 2014) and could be potentially increased under climate change conditions (Nabih et al., 2021; Brunner et al., 2020; Skoulikidis et al., 2017; Brooks, 2009). Thus, the intensity and magnitude of rainfall events are a key part of hydrological models for the simulation and prediction of floods in these watersheds (Gioia et al., 2008; Kirkby et al., 2005), and knowing the thresholds required to generate new flows helps to tackle natural hazards from a hydrological modelling perspective (Kampf et al., 2018).

Ephemeral streams are drainage networks remaining completely dry during a variable period of the year, and, owing to rainfall events of certain magnitude, they can discharge relatively high flows that can persist for some time. The western Mediterranean area is especially prone to accommodating watersheds with these types of streams because of the high irregularity of precipitation, both in space and time (Tockner et al., 2009; Datry et al., 2017). In ephemeral streams, this irregularity turns into a great uncertainty in flow generation, affecting not only the stream, but also other parts of the system. For example, the fickleness of flows alters the actual ecological functioning of the watershed at variable scales and, of course, affects the agricultural systems covering lowlands that usually require infrastructures to retain water. Understanding how these watersheds react to precipitation is fundamental for the prediction and forecasting of droughts and floods (Döll and Schmied, 2012; Arnone et al., 2020), but also for erosion potentiality depending on the type of lithology under the soil and the type of vegetation or land cover at surface and for sediment transport assessment (Fortesa et al., 2021). Previous research in ephemeral watersheds in the western Mediterranean (e.g. Camarasa and Tilford, 2002; Camarasa, 2016) showed that rainfall–runoff relationships drive hydrological processes and the dynamics of the rest of the system at basin scale and that they can be modelled to forecast flows based on the rainfall events of different magnitude. These studies highlight that, in the current Spanish Mediterranean scenario of a decrease of the total amounts of precipitation but an increase in intensity (Serrano-Notivoli et al., 2018), hydrological connectivity is more dependent on rain intensity than in the past.

In this work, we explore the rainfall–runoff relationships in two watersheds with ephemeral streams in southeastern Spain: Algeciras (44.9 km2) and Mula (169.4 km2). Daily precipitation and flows from 17 and 24 years, respectively, were analysed at event scale to model the influence of rainfall events in the generation of new runoff in both watersheds. Due to the great irregularity of precipitation, we used a non-linear approach through generalized additive models, and we compared the results in a wider temporal perspective through the calculation of return levels for several return periods. Based on the watershed physical and climatic characteristics, we hypothesize that runoff highly depends on the intensity and amount of rainfall of singular events.

The watersheds of Algeciras and Upper Mula are located within a semi-arid climate that characterizes the southeastern area of the Iberian Peninsula (Fig. 1). Annual precipitation, with a manifest equinoctial regime (maximums in March–April and September–October), rarely exceeds 300 mm (Serrano-Notivoli et al., 2017a), depicting the driest place in continental Europe. Average temperatures range from 10 to 26 ∘C; however, temperatures above 30 ∘C are common during summertime, and absolute values higher than 40 ∘C are not an exception (Serrano-Notivoli et al., 2019). With more than 100 d above 25 ∘C, the evapotranspiration rate is among the highest in Spain (Tomás-Burguera et al., 2020), leading to a negative water balance in the whole region, especially in summer months (June, July, and August), and being highly variable depending on the season and the year. This water balance is sometimes aggravated by types of soil with high rates of infiltration, hampering surface runoff during most of the year

The Upper Mula stream is an intermittent tributary in the headwaters of the Mula River, which directly flows into the Segura River. Algeciras stream is an ephemeral watercourse draining into the Guadalentín River, the main tributary of the Segura River. Both basins belong to the geomorphological Betic and Subbetic domain. Limestone and dolomites, sandstones, siliceous marls, and detrital limestones predominate in their headwaters. However, their middle and lower parts are lithologically quite contrasted: marls and alluvial sediments are abundant in the Algeciras watershed, promoting a badlands landscape, while sandstone, conglomerates, and detrital limestones predominate in the Upper Mula basin (Fig. 2a and b). The land cover in the Algeciras is mainly composed of forest (28 %), bare soil (25 %), and scrubland (24 %), while forest (39 %), agricultural row crop (25 %), and shrubland (20 %) are dominant in the Upper Mula catchment (Fig. 2c and d). Lowlands of the watersheds are occupied by two reservoirs: Cierva-Mula (built in 1929) and Algeciras (built in 1995), both with a defensive function against floods and for irrigation control.

Rainfall–runoff relationships at event scale in Upper Mula and Algeciras showed very different flow dynamics. Although they are located near each other, and precipitation regimes are relatively similar, the response to RE in terms of flow generation had the responsibility of the duration of the event in common, but the magnitude and the intensity played a different role depending on the watershed (Fig. 7). Differences in the lithological setting also explain these dissimilarities, agreeing with previous works in similar environments (e.g. Huza et al., 2014; Merheb et al., 2016; Fortesa et al., 2020; Martinez-Salvador and Conesa-García, 2020). Constrained to the study area of our research, Martínez-Salvador et al. (2021) noted that flows in Upper Mula are sourced from lateral flow and from base flow storage, due to the permeable materials. Conversely, the ephemeral stream in Algeciras is caused by the low values of the saturated hydraulic conductivity, the hydraulic conductivity of the main channel, and the coefficient of roughness for overland flow, since a large part of the basin is dominated by clayey materials, emphasizing the importance of lateral flow within the kinematic storage model. Thus, in addition to the dependence on the lithological and terrain configuration (van Dijk, 2010) and changes in seasonal precipitation regimes (Fakir et al., 2021), the RE duration, intensity, and magnitude have a high probability of changing the available flow, as shown in the results of the GAM. For instance, Camarasa (2021) showed that runoff in ephemeral streams is more dependent on rainfall intensity in the Mediterranean area than in non-arid environments, and Gutierrez-Jurado et al. (2019) and Bull et al. (2000) showed that soil type has the greatest influence on flow generation in intermittent rivers. In summary, rainfall–runoff relationships in ephemeral streams are influenced by topography and soil characteristics (Wooldridge et al., 2003; Chen et al., 2019); however, their flows are heavily dependent on the intensity, which is usually considered using the ratio between the volume of rainfall (magnitude) in a RE and its duration (e.g. Camarasa and Tilford, 2002; La Torre Torres et al., 2011; El Alfy, 2016). In addition to the topographical and climatic characteristics of the watersheds, anthropic interventions, such as irrigation, industrial uses, roads, or any water resources that change at large scale, can modify rainfall–runoff dynamics, leading to increased consequences of flooding (Conesa-García et al., 2016; Betancourt-Suárez et al., 2021).

Most of the previous works based on rainfall–runoff modelling in ephemeral streams were dedicated to runoff forecasting based on rainfall and topographical characteristics at different temporal and spatial scales. Many of these studies used different methods such as transfer-function models (Camarasa et al., 2002), artificial neural networks (Daliakopoulos and Tsanis, 2016; Ahmadi et al., 2019), or hydraulic models (Berardi et al., 2013; Doglioni et al., 2015), amongst others. While they fall into the categories of conceptual or physics-based models (Wheater et al., 1993), our focus is a metric approach using rainfall observations at event scale to characterize the response of flow generation. To this end, we used a GAM method instead of other regression procedures because of its ability to handle non-linear relationships between the response variable (flow generation) and the set of explanatory variables (Paillex et al., 2019). GAMs have already been used to model rainfall–runoff relationships in ephemeral streams (e.g. van Ogtrop et al., 2011; García-Galiano et al., 2015; Rashid and Beecham, 2019), and they are highly appropriate for these semi-arid environments since they involve the usual highly non-linear relationships between rainfall and runoff in this type of intermittent river (Ye et al., 1997; Goodrich et al., 1997). However, the novelty of our research is found in the use of the characteristics of rainfall events (duration, magnitude, and maximums) as explanatory variables, instead of the conventional analysis using all rainfall observations (daily, monthly, or annual) without our proposed distinction. Our approach allows the rainfall–runoff responses to be separated by the occurrence of rainfall events (consecutive rainy days), avoiding inconsistencies in flow generation of consecutive rainy days due to potential lags between rainfall at headwaters and flow at gauges in lowlands. While the event scale is not new in ephemeral stream studies, most of the event-based analyses referred to experimental designs based on single or a few events and/or in sub-daily scales (e.g. De Boer, 1992; Bull et al., 2000; Gutierrez-Jurado et al., 2019). By isolating the rainfall events from daily data over a long period, we provide a general overview of the response of runoff to rainfall. The selection of the explanatory variables was based on the core characteristics of a RE: duration, magnitude (sum of precipitation in the total duration of the event), and intensity (through the sum of hourly maximums). These three variables have been widely used in rainfall–runoff modelling of ephemeral streams (e.g. Camarasa et al., 2002; Kirkby et al., 2005; Hooke, 2016) and represent the rainfall characteristics influencing runoff generation (Martínez-Mena et al., 1998; Ran et al., 2012; dos Santos, 2017). The atmospheric evaporative demand measured in terms of reference evapotranspiration is well known to be a useful climatic factor modelling runoff (Gallart et al., 2002; Goulden and Bales, 2014; Roy et al., 2017). However, we did not use it in our analysis because we pursued the unravelling of the particular contribution of rainfall, at event scale, to the runoff generation, using only precipitation observations to create a reliable model representing that contribution.

Precipitation behaviour over the last decades in both watersheds has been slightly different than the rest of the Iberian Peninsula, where a decrease in the intensity prevailed (Serrano-Notivoli et al., 2018). However, the Mediterranean Spanish coast, and especially the southeast area where Algeciras and Upper Mula are located, experienced a moderate increase of high-precipitation and very high precipitation events from the mid-20th century as well as a remarkable increase in the number of wet days, agreeing with temporal patterns of both watersheds (Fig. 3). While the precipitation total decrease is an already well-known trend (González-Hidalgo, et al., 2011; Homar et al., 2010; Ruiz-Sinoga et al., 2010), southeastern Spain tended toward a more intense precipitation (Mosmann et al., 2004) that is more concentrated in time (de Luis et al., 2011; Serrano-Notivoli et al., 2017c). This scenario increases the chances of flow generation in ephemeral streams of Algeciras and Mula, but the high irregularity and the negative trend of precipitation totals do not envisage a significant change on flow dynamics to less intermittent streams. However, a change in the seasonality of flows is expected under these changing conditions of precipitation, leading to potential alterations that could intensify wet and dry periods (Pumo et al., 2016). In Algeciras and Upper Mula watersheds, climate change scenarios also depict a decrease in water resources caused by the changing seasonality, due to an increased evapotranspiration situation (Martínez-Salvador et al., 2021).

Linear rainfall–runoff relationships were clearly uninformative due to the great irregularity of the RE, and they did not provide a valid approach to derive rainfall thresholds (T) for flow generation. For this reason, we used a GAM approach that takes advantage of non-linear relationships, which are highly representative of the great irregularity of precipitation in the Mediterranean area. This approach represents an advantage among the wide variety of methods that has been previously used to model these thresholds in ephemeral or low-yield streams such as multivariate regressions and machine learning approaches (e.g. Kaplan et al., 2020; Kampf et al., 2018; Shortridge et al., 2016). Furthermore, GAMs allow stationarity assumptions in rainfall–runoff relationships to be avoided (Tian et al., 2020) in comparison with the above-mentioned methods. Using non-parametric smoothed functions as a response curve for each variable has been demonstrated to reinforce the capture of non-linearity between dependent variables (Qbin in our case) and covariates (RE parameters) in hydrological models (Rahman et al., 2018). However, the accuracy of GAMs models is highly dependent on the data since the predictability is jeopardized when the smoothed variables contain outliers, which is precisely the case of the great variability of the RE parameters. The own nature of GAMs, being accurate in the data range, can lead to overfitting and a loss of predictability in uneven datasets. Yet, the rainfall characteristics obtained for Algeciras and Mula are similar to those exposed by Hooke (2016) in a nearby watershed (Guadalentín basin).

Low return periods were shown for events generating new flow at 95 % probability, but they dramatically increased when probabilities were increased until maximum (99.5 % in Algeciras and 98.8 % in Mula). However, the analysis has some limitations to consider. First, we only considered one variable (magnitude or maximum) for each basin when, in fact, they also depend on duration. This means that the return periods could be higher because the degree of reliability provided by the model only considers the situation in which those variables occur in a RE of average duration (1.9 and 2.1 d, respectively). In this regard, further investigation is needed to set more accurate return periods because univariate approaches might lead to inadequate estimation of the risk of a RE (Brunner et al., 2016). It should also be considered that we only used the data of the RE in periods when flow was available (18 years for Algeciras and 25 years for Upper Mula) because hourly maximums were not available outside of the considered periods, meaning that the obtained return periods could be lower if long-term data series were included. Additionally, a non-stationary POT approach would be more appropriate, as made in previous works (e.g. Beguería et al., 2010; Agilan et al., 2021), but longer data series are needed to build reliable fittings of distributions.

Lastly, the non-linear analysis of RE helped to understand the type of event required to generate new flow in both watersheds. Prediction models in hydrology are a useful tool to improve water resources management in ephemeral streams through a deeper knowledge of their rainfall–runoff dynamics, especially in areas vulnerable to the potential effects of climate change and the accelerated degradation of their ecosystems.

We analysed rainfall–runoff relationships of two intermittent streams located in two medium-sized watersheds in southern mainland Spain, Algeciras (2003–2020) and Upper Mula (1996–2020), with the aim of modelling the type of rainfall event required to generate new flow. While a linear relationship was insufficient to derive robust conclusions about flow production and rainfall, a non-linear analysis using GAMs helped to understand that most of the new flow is driven by a similar duration of the rainfall events (4–5 d to ensure a 95 % probability) in both watersheds. However, the magnitude of the event (cumulated precipitation) was a more significant predictor in Algeciras (20.7 mm) than Upper Mula, where cumulated hourly maximums of each day (3.8 mm) showed a higher significance than in Algeciras. These differences could be due to the different orographic and lithological configuration. For example, Algeciras is smaller, with a higher average slope than Upper Mula and less permeable materials prevailing across the watershed, in comparison to Upper Mula, where groundwater plays an important role in water management from rainfall events and produces a different response than Algeciras.

Results showed that the precipitation regime was very irregular, and the observed average event of 1.2 d and less than 1.5 mm was clearly insufficient to generate new flow. Almost a third of the rainfall events were non-contributing for flow generation (flows were similar to or lower than the previous day to the rainfall event). A long-term analysis through the calculation of return levels showed that low rainfall return periods are enough to produce a contributing rainfall event with a 95 % probability, rapidly increasing with rising flow generation probabilities. These results agree with the long-term (70 years) precipitation patterns that showed a highly variable annual water availability alongside a significant increase of wet days, with different behaviour among watersheds. Within the study period, Upper Mula showed 16 of 25 years below average precipitation, while Algeciras remained with the same frequency as previous decades but a higher rate of wet days. A future drier scenario as considered in western Mediterranean climate projections could lead to an increase in the return periods for the required magnitude of rainfall events to generate flows.