Rainfall-runoff relationships at event scale in western Mediterranean ephemeral streams

. Ephemeral streams are highly dependent on rainfall and terrain characteristics and, therefore, very sensitive to 10 minor changes in these environments. Western Mediterranean area exhibits a highly irregular precipitation regime with a great variety of rainfall events driving the flow generation on intermittent watercourses, and future climate change scenarios depict a lower magnitude and higher intensity of precipitation in this area, potentially leading to severe changes in flows. We explored the rainfall-runoff relationships in two semiarid watersheds in southern Spain (Algeciras and Upper Mula) to model the different types of rainfall events required to generate new flow in both intermittent streams. We used a nonlinear 15 approach through Generalized Additive Models at event scale in terms of magnitude, duration, and intensity, contextualizing resulting thresholds in a long-term perspective through the calculation of return periods. Results showed that the average ~1.2-day and <1.5 mm event was not enough to create new flows. At least a 4-day event ranging from 4 to 20 mm, depending on the watershed was needed to ensure new flow at a high probability (95%). While these thresholds represented low return periods (from 4 to 10 years), the great irregularity of annual precipitation and rainfall characteristics, makes 20 prediction highly uncertain. Almost a third part of the rainfall events resulted in similar or lower flow than previous day, emphasizing the importance of lithological and terrain characteristics that lead to differences in flow generation between the watersheds. Results show that the precipitation regime is very irregular, and an average event of 1.2 days and less than 1.5 mm is clearly insufficient to generate new flow. Almost a third part of the rainfall events are non-contributing for flow generation (flows are similar or lower than previous day to the rainfall event). A long-term analysis through the calculation of return levels showed that a 10-year return period for Algeciras and a 4-year for Upper Mula are enough to produce a contributing rainfall 340 event. 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 increase the return periods for the required magnitude of rainfall events to generate flows.

watersheds (Gioia et al., 2008;Kirkby et al., 2005) and knowing the thresholds required to generate new flows helps to 30 tackle with 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 (Donglioni et al., 2015) that can persist for some time. Western Mediterranean area is especially prone to accommodate watersheds with these types of streams because of the high irregularity of precipitation, both in space and time (Tockner et al., 2009;Thibault et al., 2017). In ephemeral 35 streams, this irregularity turns into a great uncertainty in flow generation affecting not only the stream but also to 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 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 40 under the soil and the type of vegetation or land cover at surface. Previous research in ephemeral watersheds on Western Mediterranean (e.g., Camarasa and Tilford, 2002;Camarasa, 2016) showed that rainfall-runoff relationships drive hydrological mechanisms 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.
In this work, we explore the rainfall-runoff relationships in two watersheds with ephemeral streams in southeastern Spain: 45 Algeciras (44.9 km 2 ) and Mula (169.4 km 2 ). 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 nonlinear 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.

Study site 50
The watersheds of Algeciras and Upper Mula are located within the semiarid climate characterizing the southeastern area of the Iberian Peninsula ( Figure 1). Annual precipitation, with a manifest equinoctial regime (maximums in March-April and September-October) rarely exceeds 300 mm (Serrano-Notivoli et al., 2017), depicting the driest place in continental Europe.
Average temperatures range from 10 to 26 ºC, however, temperatures above 30 ºC are common during summertime and absolute values higher than 40 ºC are not an exception (Serrano-Notivoli et al., 2019). With more than 100 days above 25 ºC, 55 the evapotranspiration rate is among the highest in Spain (Tomás-Burguera et al., 2020), leading to a negative water balance in the whole region that persists all over the year. This water balance is sometimes aggravated by types of soil with high rates of infiltration, hampering runoff during most of the year https://doi.org/10.5194/hess-2021-352 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License. The Upper Mula stream is an intermittent tributary at 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 65 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 (Figure 2a and 2b).
Lowlands of the watersheds are occupied by two reservoirs: Cierva-Mula (1929) and Algeciras (1995), both with a defensive 70 function against floods and for irrigation control.

Data
The data series of flows were obtained from the gauging reports supplied by the Center for Public Works Studies and Experimentation (CEDEX) for the Segura basin. We used the data series of the daily average flow (m 3 /s) corresponding to periods 2003(Algeciras) and 1996. Although Algeciras and Mula watersheds are ungauged and there are not direct measures of water discharge, the daily flow series were calculated from the difference between the 80 volume of water stored in the reservoirs and the output of the previous day (Eq. 1).
where is the inflow into the reservoir (m 3 ); , the reserve of the current day (m 3 ); 1 , the reserve of the previous day (m 3 ); and , the output flow of the previous day (m 3 ). While resulting daily series are not a direct measure of the streamflow, they 85 provide the only representation of daily flow variations.
In order to provide single daily precipitation (P) series for each watershed, we created two regional series based on the information of meteorological stations (13 for Algeciras and 14 for Mula) from the Spanish meteorological agency (Aemet), the Agroclimatic Information System (SIAR) of the Spanish Ministry of Agrifood and Fisheries, and the Segura https://doi.org/10.5194/hess-2021-352 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License.
Hydrographic Confederation (CHS) (Figure 1). These sources provided daily sums of precipitation and their hourly 90 maximums. Both series (sums and maximums) were averaged for Algeciras and Mula for all days in which daily flows data series were available (2003in Algeciras and 1996. The original data series of the meteorological stations provided a reliable representation of the real magnitude of precipitation events. Although the use of a spatial interpolation scheme had been useful to look for precipitation differences in a different situation (e.g., larger spatial domain, longer temporal period), the small extent of the study area (approx. 50x50 km) and the watersheds, along with the sizeable 95 number of available observations, made the mean daily precipitation a reliable representation of the precipitation regime at event scale. In addition, the availability of single flow data series for each watershed constrained the analysis to a comparison with unique precipitation series. The complete process resulted in 2 series of daily precipitation and 2 series of hourly maximums in the same period of flows data series. Due to the reduced study area, most of the stations have a similar behaviour regarding precipitation occurrence, however, we considered as dry days those averaging a value lower than the 100 minimum registered by the precipitation gauges (0.1 mm). The series of hourly maximums were built by averaging, for each day in all stations, the maximum precipitation cumulated in one hour. Despite the potential difference between stations, this measure represents the average intensity of daily precipitation. Lastly, we used the SPREAD dataset (Serrano-Notivoli et al., 2017), a daily gridded precipitation dataset covering the whole Spanish territory at a 5x5 km spatial resolution, to analyse long-term trends of annual precipitation since 1950 to 2020 of the two watersheds. This analysis helped to study the low-105 frequency climatic signal of a broader spatial domain, by contextualizing the study period of each watershed since mid-20 th century.

Statistical analyses at event scale
Instead of relating daily precipitation (P) with daily flows (Q), we opted to work at event scale due to consecutive wet days (P > 0) can have a different and more persistent impact on flow generation than single wet days. Rainfall events (RE) were 110 detected from daily data series for the whole period, in both watersheds, by grouping consecutive wet days. We then calculated 4 variables for each event: duration (number of days); magnitude (sum of precipitation of all days); maximum (sum of hourly maximums of all days); and flow contribution (ΔQ, difference between the cumulated flow during the RE and flow of the day before the RE).
We performed, using all events, a simple linear correlation analysis between the four variables for an overview of the general 115 linkage between each other. However, ephemeral streams involve highly nonlinear relationships between rainfall and runoff (Ye et al., 1997) and, for this reason, we used Generalized Additive Models (GAMs) to detect further responses of the flows to rainfall at event scale. GAMs allowed for assessing simultaneous smooth relationships that can be linear or nonlinear as demonstrated in previous research (e.g., van Ogtrop et al., 2011). As the objective was to find out what type of event was necessary to generate flow in both basins, we used as dependent variable the ΔQ codified as a binomial variable (Qbin, 120 ΔQ>0: 1; ΔQ<=0: 0) and duration, magnitude and maximum were treated as smooth predictor variables, specified using shrinkage smoothers (thin plate regression spline). GAMs were used with the logit link and the three variables were included https://doi.org/10.5194/hess-2021-352 Preprint. Discussion started: 13 July 2021 c Author(s) 2021. CC BY 4.0 License.
in the model to predict Qbin, first individually, and then in combination with each other. All the models were compared, and the basis dimension of each smooth term was checked and increased when necessary. The final model was selected, for each watershed, based on the Akaike Information Criterion (AIC). Concurvity (the analogue of multi-collinearity in GAMs) was 125 tested in the final model (Table S1).
To contextualize the different thresholds of the RE for different probabilities of generating flow in both watersheds, we estimated the return levels of the RE for up to 400 years using the generalized extreme value (GEV) distribution for extreme events using the block maxima approach. We used four different methods (Maximum Likelihood Estimation (MLE); Generalized MLE (GMLE); Bayesian estimation (BPE); and L-moments estimation (LMOM)) to establish proper and wide 130 confidence levels in the estimate of maximum rainfall per RE.

Characteristics of flows and precipitation
Average daily flows (Q) in Algeciras and Mula were relatively low in both watersheds (0.29 and 0.15 m 3 /s, respectively) and these values were distant from the median of each month (Figure 3), denoting their great irregularity. However, the specific 135 flow, that considers the size of the watershed, is 6.5 l/s/km 2 in Algeciras and 0.9 l/s/km 2 in Upper Mula (Table 1). Both watersheds had a similar precipitation regime, with a clear minimum in summer, especially in July, and maximums in spring and autumn (March and September are the rainiest months, respectively). However, their flows did not respond in the same way to precipitation. While Mula had a more direct response to incident rainfall, Algeciras showed a different behaviour with their maximums at the end of summer and the beginning of autumn, associated to very high precipitation events. Also, 140 the middle and lower parts of the Algeciras watershed are mainly covered with marls and alluvial sediments, creating an arid landscape consisting of a predominance of badlands and bare soil, where the rates of saturated hydraulic conductivity and hydraulic conductivity of the main channel are very low. Additionally, Algeciras show a higher curve number and slope than Upper Mula and shorter concentration and lag times (Table 1). Thus, terrain characteristics play a key role on rainfall-runoff relationships, but also to the amount of Q per month. For instance, Mula have an average 30% more days per month with 145 Q>0 than Algeciras, reaching almost 50% in summertime.

Rainfall events (RE) over time
The long-term analysis of annual precipitation showed different behaviours of the watersheds in the first two decades of 21 st century ( Figure 4) than in previous periods, coinciding with the period of study (when available flow data series). Algeciras A non-negligible proportion of RE produced a zero (14% in Algeciras and 3% in Mula) or negative (22% and 23%) ΔQ, 175 meaning that the flow contributed resulted in a similar or lower value than the previous day of the event, respectively. These RE, that were very similar in both watersheds, were short and small in terms of amount of rainfall. With a mean magnitude between 0.5 and 1.5 mm and a mean duration from 1.2 to 1.3 days, the generation of new flow is difficult. The reason of why these RE did not produced any flow contribution are related to the flow and precipitation regimes of the watersheds. For instance, a large proportion of non-contributing RE were from June to August (Table 1)

Linear rainfall-runoff relationships 195
The linear correlation between the parameters of the RE and their corresponding ΔQ showed the general agreement between precipitation and flow contribution. As expected, the parameters derived from the RE, duration, magnitude and hourly maximums were highly positively correlated ( Figure 6). An increase in the duration of the events usually led to higher magnitudes of cumulated precipitation (Pearson 0.68 and 0.66 in Algeciras and Mula, respectively), but was the relationship between magnitudes and cumulated hourly maximums the most direct with Pearson correlations of 0.98. These positive 200 relationships between the parameters, which are almost identical in both watersheds, showed that most of the events are torrential (hourly maximums represent a higher proportion of the magnitudes) and of short duration (most of them occur between 1 and 5 days). However, the relationship between the RE parameters and ΔQ was very different between watersheds. Both showed positive correlations, but Algeciras revealed higher values, from 0.53 to 0.68, with a more direct response to the duration of RE and a slightly lower, and very similar, to the magnitude and maximums. In a lesser intensity, 205 Mula showed a similar overall pattern but with lower Pearson values (from 0.44 to 0.49). These results indicated that the flow reaction to the RE was different between both watersheds in terms of the intensity of the relationship and that the linear association is not enough to derive conclusions about it.

Nonlinear rainfall-runoff relationships
In order to assess the nonlinear relationships between the ΔQ and precipitation to extract the required parameters to generate 215 new flow by a RE, we modelled Qbin (ΔQ as a binomial variable where 1 represents new generation of flow by the RE) through a GAM approach. With the aim of evaluating the model accuracy with the selection of the best combination of variables for each watershed, we compared different models using from one to all variables through the estimate errors AIC (Akaike Information Criterion), logLik (log-likelihood), deviance (Residual deviance), and UBRE (Un-Biased Risk Estimator). 220 Results (Table 3)   To evaluate the hit rate of the models, we used a random sample of 75% of the RE in each watershed to set up the models.
Then, predictions were computed for the remaining 25% and classified as probabilities from 0 to 1 as P<0.5: 0 and P>=0.5: 1 to be compared with the observations. Contingency table (Table 4)  While success rates are relatively high in both watersheds, results suggest other variables driving flow generation in RE different than precipitation. Again, topographical and soil characteristics probably play an important role that is difficult to 240 integrate in these types of models. Diagnostic plots of the partial effects (Figure 7) showed the probability of flow generation by a RE as long as the rest of the partial effects remain in their average values. For instance, Algeciras showed that an event of 5 days duration guarantees the flow contribution at a 95% probability (Figure 7a), but the 2-day RE already sum a probability of 50%. On the other hand, in a RE of average duration (1.9 days), the magnitude required to reach 95% probability of flow contribution is 20.7 mm (heavy rainfall), but the 50% probability is reached (Figure 7b) with 0.1 mm, meaning any precipitation record. By 250 comparison, Mula requires a 4-day RE to ensure new flow generation with a 95% probability. However, considering an average duration event (2.1 days), the cumulated hourly maximums needed to fulfil with that probability is 3.8 (not very intense precipitation), being reduced to 0.1 for a 50% probability.
Overall, these results indicate that, despite the new flow generation similarly reacts to RE in Algeciras and Mula, in both watersheds the duration of the event is a critical factor. However, the total amount of precipitation is more important in 255 Algeciras than Mula, where cumulated hourly maximums, ultimately, the intensity of the RE has a more direct relationship.

Return periods of RE 260
We calculated the return levels of magnitude of the RE in Algeciras and of cumulated hourly maximums in Mula for return periods from 1 to 400 years (Figure 8). Based on the fitted models, the most probable situation in which flow could be generated in Algeciras required a magnitude of 20.7, which is approximately a 10-year return period. While not-being a very usual magnitude in the watershed, it does not represent a rare value, meaning that flow generation in Algeciras is relatively easy. A 4-year return period was obtained for the 3.8 mm required in Upper Mula to ensure the flow generation at 95% 265 probability. However, the great variability of this model increased the probabilities until 98.8% with a maximum of 44.6 mm, which represents a return period from 100 to more than 400 years. This large difference reveals the extreme irregularity of flows in Mula and the high uncertainty in prediction based only on the RE.

Discussion
Rainfall-runoff relationships at event scale in Upper Mula and Algeciras showed very different flow dynamics. Although 275 they are located near each other and precipitation regimes are relatively similar, the response to RE in terms of flow generation had in common the responsibility of the duration of the event but the magnitude and the intensity played a different role depending on the watershed. 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 280 flows in Upper Mula source 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, the way in which the watersheds receive rainfall drives the flow generation, which always depends on the lithological and terrain configuration 285 (van Dijk, 2010), and changes in seasonal precipitation regimes or in RE duration, intensity, and magnitude, have a high probability of changing the available flow.
In this regard, precipitation behaviour over the last decades in both watersheds was 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, experimented a moderate 290 increase of high and very high precipitation events from mid-20 th century as well as a remarkable increase in the number of wet days, agreeing with temporal patterns of both watersheds (Figure 3). While the precipitation totals decrease is an already well-known trend (Gonzalez-Hidalgo et al., 2011;Homar et al., 2010;Ruiz-Sinoga et al., 2010), southeastern Spain tended to a more intense precipitation (Mosmann et al., 2004) and more concentrated in time Serrano-Notivoli et al., 2017). This scenario increases the chances of flow generation in ephemeral streams of Algeciras and Mula, but the 295 high irregularity and the negative trend of precipitation totals do not envisage a significant change on flow dynamics to less intermittent streams.
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. Among the wide variety of methods that has been used to model these thresholds in ephemeral or low-yield streams such as multivariate regressions, machine learning 300 approaches, etc. (e.g., Kaplan et al., 2020;Kampf et al., 2018;Shortridge et al., 2016), we used a GAM approach that allows for avoiding stationarity assumptions in rainfall-runoff relationships (Tian et al., 2020). Using nonparametric smoothed functions as a response curve for each variable has been demonstrated to reinforce the capture of non-linearity between dependent variable (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 data sets.
Low return periods were shown for events generating new flow, the analysis have 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 10-year return period for Algeciras or the 2-year for Mula could be higher because the degree of reliability 310 provided by the model only considers the situation in which those variables occur in a RE of average duration (1.9 and 2.1 days, 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 be also 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 out of the considered periods, meaning that the obtained return periods could 315 be lower if including long-term data series. Additionally, the approach that we used for the RE frequency analysis was the bock maxima (BM) instead of the peaks-over-threshold (POT). One drawback of BM series is that they use only one event per year, thus, the second highest, for instance, may be greater than several events of other years (Mkhandi et al., 2005), leading to a loss of information. However, BM method is preferable when observations are not exactly independent and identically distributed (Ferreira and de Haan, 2015). 320 Lastly, the nonlinear analysis of RE helped to understand the type of events 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 vulnerable areas to the potential effects of climate change and the accelerated degradation of their ecosystems.

Conclusions 325
We analysed rainfall-runoff relationships of two intermittent streams located in two medium-sized watersheds in southern mainland Spain: Algeciras (2003) and Upper Mula (1996, 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 nonlinear analysis using GAMs helped to understand that most of the new flow is driven by a similar duration of the rainfall events (4-5 days to ensure a 95% probability) in both watersheds. However, the magnitude of 330 the event (cumulated precipitation) was a more significant predictor in Algeciras (20.7 mm) than Upper Mula, where maximums (cumulated hourly maximums of each day) showed a higher significance (3.8 mm). 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 on water management from rainfall events and producing a different response than 335 Algeciras.
Results show that the precipitation regime is very irregular, and an average event of 1.2 days and less than 1.5 mm is clearly insufficient to generate new flow. Almost a third part of the rainfall events are non-contributing for flow generation (flows are similar or lower than previous day to the rainfall event). A long-term analysis through the calculation of return levels showed that a 10-year return period for Algeciras and a 4-year for Upper Mula are enough to produce a contributing rainfall 340 event. 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 increase the return periods for the required magnitude of rainfall events to generate flows. 345