The Rheraya research catchment (Jarlan et al., 2015) is located in the Moroccan High Atlas Mountains (Fig. 1), with an altitude ranging from 1027 to 4167 m and an area of 225 km2. The climate in the basin is semiarid and strongly influenced by altitude, with a mean annual precipitation of 732 mm, including 30 % as snow in altitudes above 2000 m (Boudhar et al., 2009). The geology is characterized by volcanic formations that are considered impermeable in the highest elevation areas, while the lowest elevation areas are made of granites with clays and marls. In the highest elevation areas, very steep slopes are found with an average of 19 % (Chaponnière et al., 2008). The vegetation cover is only located in the lowest areas, with a concentration of cultivated areas found along the river channel. These natural conditions favor runoff generation. There is very low human disturbance for runoff, with only some local water uptake in the lower part of the river.

The Issyl basin (Fig. 1) is located in the foothills of the Moroccan High Atlas Mountains, with an altitude ranging from 632 to 2300 m, an area of 160 km2, and a mean annual precipitation of 666 mm. It is an ephemeral river with discharge occurring only after rainfall events. The climate is semiarid to arid, and the downstream part of the basin reaches the city of Marrakech. The geological formations in this downstream are alluvial conglomerates that are relatively permeable. The upstream of the basin consists of clays and calcareous marl. The basin area includes agricultural activities that are irrigated in the downstream part of the basin. The irrigation comes from seguias, earthen-made channels that traditionally draw their water supply from the river itself by building small diverting dams on the side of the river (Pérennès, 1994). The seguias channels are usually filled up during floods, and water is distributed to the neighboring agricultural parcels. A map of the seguias in the Issyl basin can be seen in Fig. 1, covering the northern part of the basin. The system is unmonitored, and in the context of high evaporation rates, the portion of runoff diverted from the stream is not quantified. Due to the temporary nature of seguias, they can be partially destroyed during large floods, and consequently their hydraulic properties and the amount of water collected can be modified over time. In the Ourika catchment, located upstream of the Issyl, Bouimouass et al. (2020) estimated that irrigation by streamflow diversion due to seguias could represent up to 65 % of the total surface runoff.

In the Rheraya basin, we used eight rainfall stations (Table 1), five of them from the data network of the Joint International Laboratory Télédétection et Ressources en Eau en Méditerranée semi-Aride “LMI TREMA” (Jarlan et al., 2015; Khabba et al., 2013) and the remaining ones from the Tensift Hydraulic Basin Agency. The data cover the period 2008 to 2016. For the Issyl basin, only two rainfall gauges are available from the Tensift Hydraulic Basin Agency, covering the years from 2010 to 2015. In this type of basin, the spatial variability of rainfall is very significant (Chaponnière et al., 2008). The hydrometric data were provided by a radar sensor installed in each basin's outlet. The data cover only the year 2014 for Rheraya since the sensor was installed at the end of 2013 and the years 2010 to 2015 for Issyl. The discharge data are provided with a time step of 10 min converted into an hourly time step as for rainfall.

Table 1, in front of the ligne containing Tahnaout, add ”Precipitation and discharge” (similarly to the ligne right below)

The precipitation data are missing for some events, especially for high-altitude gauges during snowfall events. The percentage of missing values ranges from 2.4 % at PR5 to 10.85 % at PR7. The highest percentage of missing data is 19.7 % at PR1 where the gauge underwent technical problems. Overall, the total percentage of missing values (7.8 %) is low; hence no gap filling method is used. The discharge data are missing in some events that are not selected. For this reason we considered only the events with complete discharge data. Some of the flood events considered in this study (Table 2) occurred in the winter season, when rainfall can be in the form of snow above 2000 m elevation. According to El Khalki et al. (2018), the snow does not contribute to runoff during the winter season in the Rheraya basin because it does not melt during the coldest months (Hajhouji et al., 2018), when only 17 % of the basin area is occupied by snow. The runoff coefficient is calculated by relating the amount of direct runoff to the amount of precipitation for each selected event. It is larger when the basin has low infiltration and lower for permeable basins. In our case, the runoff coefficient ranges from 13.1 % to 34.1 % for Rheraya and from 1.2 % to 7.2 % for Issyl. This indicates the important role of initial conditions in both basins, with a much higher infiltration capacity in the Issyl basin in addition to potential water loss due to irrigation. We used five temperature stations located in the Rheraya basin and one temperature station located in the Issyl basin with an hourly time step to calculate the average temperature over each basin, ranging from 2008 to 2016. These data enabled us to calculate potential evapotranspiration (PET) with the Oudin formula (Oudin et al., 2005), requiring temperature only. This formula was previously applied in Morocco (Marchane et al., 2017; Tramblay et al., 2013) and in Tunisia (Dakhlaoui et al., 2020).

We used seven different types of soil moisture data over the Rheraya basin and six types in the Issyl basin due to the absence of measurements in this basin. Covering the same period of rainfall data mentioned in Sect. 2.2, we used 1.

in situ measurement with three ThetaProbes at 5 and 30 cm depth in the Rheraya basin, located at the SMPR7 station (Fig. 1)

In situ data preparation consists of averaging the 5 cm depth probes in order to get a single value to work with and take into account the plot-scale variability of the measurements. These data are considered as a reference for soil moisture data in the Rheraya basin so that all the other soil moisture products are compared to it. The different soil moisture products are compared to the observed soil moisture over the entire period and also on a seasonal basis.

The SMA model is used to represent the soil moisture aggregated at the catchment scale. The rationale behind the use of such a model here is that continuous rainfall and temperature series are often available in monitored catchments, unlike soil moisture, and a calibrated SMA model can sometimes palliate the lack of soil moisture measurements (Tramblay et al., 2012). For the SMA model, the A parameter, representing the soil water holding capacity, is calibrated to obtain the best correlation between observed and simulated soil moisture (S/A). The calibration with observed data can only be performed in the Rheraya basin where soil moisture is measured. In addition to this calibration, other values of A, ranging from 1 to 1000 mm, are tested in the SMA model to maximize the correlations with the different soil moisture products. The choice of this approach is to check whether there are any possible uncertainties that can be related to the in situ soil moisture measurements, located on a steep slope plot that may not fully represent the average soil moisture conditions over the whole basin. In the case of the Issyl basin, since there is no observed soil moisture data, the model is run for a range of different values of the A parameter. The best value of the A parameter is selected as the one yielding the best correlations with the different satellite products.

The values from ASCAT and SMA are given in percent (values range between 0 and 1), while SMOS, SMOS-IC, ERA5, ESA-CCI, and observations are in cubic meters per cubic meter. To allow a comparison for all soil moisture datasets a rescaling procedure is needed. Before applying the rescaling procedure, according to Albergel et al. (2010), a 95 % confidence interval is chosen to define the higher and lower values to exclude any abnormal outliers using Eqs. (1) and (2). The resulting data are then rescaled to their own maximum and minimum values considering the whole period using Eq. (3). The issue in the validation of satellite soil moisture products and reanalysis product with in situ measurements is the spatial resolution (Jackson et al., 2010). Several studies mentioned that, in the case of the temporal stability introduced by Vachaud et al. (1985), one in situ measurement point can represent the soil moisture condition of a larger area (Brocca et al., 2009b, 2010; Loew and Mauser, 2008; Loew and Schlenz, 2011; Martínez-Fernández and Ceballos, 2005; Miralles et al., 2010; Wagner et al., 2008). According to (Massari et al., 2015), the coarse satellite observations can be beneficial for small basins if the in situ observation falls in the satellite product pixel. This means that the in situ measurements can represent a good benchmark (Liu et al., 2011). In this study we considered the in situ measurement as a benchmark to validate different soil moisture products. 1UpSM=μSM+1.96σSM,2LowSM=μSM-1.96σSM, where UpSM and LowSM are the limits of the confidence interval (the upper and the lower 95 %): 3SM=SM-LowSMLowSM-UpSM.

The correlation coefficient of Pearson (Eq. 4) and the root mean square deviation (RMSD; Eq. 5) are used to compare in situ measurements and humidity modeled by the SMA model and the different soil moisture products. 4r=N∑SMsatSMInsitu-∑SMsat∑SMInsituN∑SMsat2-∑SMsat2N∑SMInsitu2-∑SMInsitu2, 5RMSD=∑SMInsitu-SMsat2N, where SMInsitu is the in situ measurements of soil moisture or the SMA model, which are considered as references; SMsat is the soil moisture from satellite data or reanalysis; and N is the number of values.

In this study, we used the Soil Conservation Service curve number (SCS-CN) model for each basin, implemented in the Hydrologic Engineering Center – Hydrologic Modeling System “HEC-HMS” software (US Army Corps of Engineers, 2015). This model is known by its widespread popularity and the simplicity of the application method (Miliani et al., 2011). SCS-CN is often used in the semiarid context (Brocca et al., 2009a; El Khalki et al., 2018; Tramblay et al., 2010; Zema et al., 2017). Our methodology is based on the use of the SCS-CN model as a production function to compute net rainfall by automatically and manually calibrating the curve number (CN) parameter in order to obtain a realistic hydrograph shape. The value of CN is nondimensional, ranging from 0 (dry) to 100 (wet). The potential maximum retention, S, is related to CN as follows: 6S=25400CN-254.

The transformation of precipitation excess into runoff is provided by the Clark unit hydrograph model (transfer function). The calibration procedure is based on calibrating the Clark unit hydrograph model parameters: storage coefficient (SC) and time of concentration (TC). The two functions (production and transfer) are calibrated separately to avoid the parameter dependence, and the calibration is based on the Nash–Sutcliffe (NS) criterion.

The validation procedure is based on two steps: first, testing the relationship between soil moisture data (in situ, SMA, ERA5, ASCAT, SMOS, SMOS-IC, and ESA-CCI) at two different timescales (daily and hourly) and the S parameter of the event-based model of all the flood events. The hourly time step concerns only the in situ data and ERA5 by choosing the soil moisture state 1 h before the starting time of rainfall for each event. Only the ERA5 product can be used in the Issyl basin at the hourly time step due to the absence of observed data. Then, the soil moisture products that are well correlated with the S parameter are used to validate the model by calculating the S parameter from the linear equation obtained between soil moisture and S using the leave-one-out resampling procedure; each event is successively removed, and a new relationship between the remaining event is recomputed. The relationship is good when the correlation is near r=-1. The negative correlation is related to the fact that the storage capacity (S) is larger when the soil is dry (soil moisture is near 0). The estimated S parameter for a given event is then used in the SCS-CN model in validation. For the Clark unit hydrograph model, the average of the SC and the TC parameters are used in validation in the leave-one-out resampling method; the parameters are recalibrated with the remaining events, and the mean of calibrated values are used in validation.

For the evaluation of the flows simulated by the flood event model, we compared the simulated discharge with those observed using the efficiency coefficient of Nash–Sutcliffe (Nash and Sutcliffe, 1970; Eq. 7) as well as through the bias on peak flow and on volume (Eq. 8). 7NS=1-∑Qobs-Qsim2∑Qobs-Qobs‾2,8BIASQ=∑Qsim-Qobs∑Qobs, where Qsim is the simulated discharge, Qobs is the observed discharge, and n is the number of events. The NS ranges between -∞ and 1; the 1 value of NS indicates that the simulated discharge perfectly matches the observed hydrograph.

The comparison between measured soil moisture at 5 cm depth and the different products of soil moisture shows that the SMOS-IC and ERA5 provide the best correlations, with r=0.77 and r=0.67, respectively, but it should be noted that all the correlations with the different products are also significant. Figure 2 shows that SMOS-IC and ERA5 reproduce dry periods well, whereas ERA5 reproduces wet periods well. This result is in accordance with the results of Massari et al. (2014), who found that ERA-Land is well correlated with in situ data. The ASCAT product shows a correlation of r=0.45, which is less than the correlation given in Albergel et al. (2010), who found r values ranging from 0.59 to 0.64; the lower correlation may be caused by the orography and the coarse resolution. In fact, this result shows that the use of a combined product as ESA-CCI gives an obvious advantage over one single satellite soil moisture product in terms of r values (Ma et al., 2019; Zeng et al., 2015).

The best correlation between observed soil moisture and the soil moisture level (S/A) modeled by the SMA model is obtained for A=8 mm with r=0.86. But it shows higher RMSD than observations (RMSD=0.23), which is due to the overestimation of the wet periods (Fig. 3). This can be related to the averaging of rainfall data in the SMA model over the basin, which could be higher than rainfall in the soil moisture measurement site. It should be noted that the value of the A parameter is very small by comparing to previous studies (Javelle et al., 2010; Tramblay et al., 2012), indicating a much lower soil storage capacity.

We correlated the SMA model output (for A=8 mm) with the satellite products of soil moisture, and the best correlations are found for SMOS-IC and ERA-5, with r=0.74 and r=0.63, respectively (Fig. 4). Other values of A that maximize the correlations with the different soil moisture products have also been tested. Optimal values of A range from 1 mm with ASCAT (with r=0.4) and 8 mm for SMOS (r=0.56), SMOS-IC (r=0.74), and ESA-CCI (r=0.59) up to 16 mm for ERA5 (r=0.68). Comparing Figs. 2 and 4 we notice that the soil moisture products better reproduce in situ measurements than modeled soil moisture with the SMA model, except for ESA-CCI and SMOS. This improvement is directly related to the SMA model performance, which overestimates soil moisture, and should be compared to Fig. 2, where ESA-CCI and SMOS products also overestimate in situ measurements.

For the Issyl basin, as mentioned above, no observed soil moisture data are available to calibrate the A parameter of the SMA model. Therefore, different values of A are tested to correlate the SMA outputs with the different soil moisture datasets. Over all datasets, the value of A best correlated to the majority of soil moisture products is 30 mm. The best correlation is given by A=30 mm with r=0.78, 0.82, and 0.79 for ASCAT, SMOS-IC, and ESA-CCI, respectively. As for SMOS and ERA5, the best correlation is given for A=40 mm with r=0.7 and A=60 mm with r=0.8, respectively. In order to choose a single value of A that represents the basin, we have considered A=30 mm, the optimal value yielding the best correlations with the different soil moisture products. Figure 5 shows that the best correlation between satellite products and S/A is obtained with SMOS-IC (r=0.82) and ESA-CCI (r=0.79). As observed over the Rheraya basin, the SMOS-IC and ERA5 products showed a good reproduction for dry periods, with a better reproduction of wet periods with ERA5; these results are similar to those of Ma et al. (2019), who found that SMOS-IC performs well in arid zones, with a median r value of 0.6. Overall, the higher value for the A parameter found for this basin is coherent with the fact that this basin is located in a plain area with a much higher soil moisture storage capacity than in the mountainous Rheraya basin.

Seasonal evaluation of satellite soil moisture and reanalysis data shows for the Rheraya basin that during the summer season there are low correlations (average r=0.34) for all the products, which is possibly due to very low precipitation amounts mostly as localized convective precipitation (Albergel et al., 2010). In contrast, better performance are obtained with the SMA model (r=0.59) that considers catchment-scale precipitations. Better correlations are obtained in autumn, with an average of r=0.61 and 0.58 for the in situ data and SMA, respectively (Table 5). In the winter we found a poor correlation using SMOS and ESA-CCI that can be related to the significant percentage of missing values. For the Issyl watershed, the satellite products show good correlations with the SMA model outputs (on average r=0.76) except for the SMOS product, especially in winter. The highest mean correlations (i.e., averaged for all the different products) are found during autumn in the Rheraya basin, with r=0.61 with in situ data and r=0.58 with SMA soil moisture. It should be noted that correlations with SMA model outputs in summer are similar, with r=0.59. For the Issyl basin, the correlations are also higher in the autumn, with a mean r=0.87 for the SMA model. The ERA5 product shows good correlations for most seasons. Complementary to this comparison of the different soil moisture products, an extended collocation analysis has also been performed, comforting the results obtained (see the Supplement).

Calibration results (Table 6) of the individual flood events of Table 2 show that the difference between the values of the potential maximum soil moisture retention (S) of each basin is very significant, with larger values for the Issyl basin, where the soil depth is prominent. We noticed that the temporal variability of soil moisture can be significant between two successive events like the events of 2 and 5 April 2012 for the Issyl basin. The SCS-CN model reproduces the floods of the Rheraya basin well, with an average NS of 0.67 and bias on runoff peak (BIASQ) of 4 % (Table 6). The SCS-CN model in calibration is able to reproduce the shape of the different flood events even for the most complex ones (21 April and 22 November 2014). Similarly, for the Issyl basin the SCS-CN model gives good results, with an average NS of 0.66 and an average bias on runoff peak of 6.93 %. The simulated hydrographs are in good agreement with the observations. The lower NS coefficients obtained for the 23 January 2014 event in the Rheraya basin and for the 3 April 2011 and 28 September 2012 events in the Issyl basin are caused by a slight shift in the hydrograph, probably due to a time lag in instantaneous precipitation measurements. For the Clark unit hydrograph model, the averages of calibrated TC and SC parameters are considered for validation (SC=1.42 and 2.54 h and TC=2.85 and 3.64 h for Rheraya and Issyl, respectively).

The S parameters of the hydrological models for the two basins are then compared to the soil moisture products. For the Rheraya basin, there are significant correlations of the S parameter with in situ soil moisture data, ERA5, and SMOS-IC (Table 7). The correlations using observed soil moisture, ESA-CCI, and SMOS data can be computed with only eight and six events, respectively, due to the presence of missing values. The time step of the soil moisture data in the Rheraya basin seems to play a key role in the representation of soil moisture conditions. Indeed, the daily time step shows a weakness in effectively representing the antecedent soil moisture conditions in the SCS model, which indicates the rapid change in soil moisture content in such a semiarid mountainous basin. For the Issyl basin, ESA-CCI is the only satellite product that is significantly correlated to the S parameter at the daily time step. The ERA5 product is also significantly correlated with the S parameter but at the hourly time step. The daily output of the SMA model is also able to estimate the initial condition of the model for the Issyl basin, with a correlation of -0.69 with S. Interestingly, the SMA model does not provide a good performance in the Rheraya basin. It can be due to the fact that in such a mountainous basin, there is a strong spatial variability of rainfall, and it is difficult to obtain reliable precipitation estimates for continuous simulations (Chaponnière et al., 2008).

The validation of the event-based hydrological model is performed on the events of Rheraya and Issyl using only the soil moisture datasets that show relatively good correlations with the initial condition (S) of the model from Table 8. These products include SMOS-IC, ERA5, and observed soil moisture for the Rheraya basin and ESA-CCI, ERA5, SMOS, and SMA for Issyl. The validation of the event-based model is performed with S calculated from the linear equation obtained from the correlation analysis between the different soil moisture products and the calibrated parameter S. The validation results show that for the Rheraya basin the events are well validated using both daily (Fig. 6) and hourly (Fig. 7) time steps of soil moisture products. The best validation result at the daily time step is obtained with SMOS-IC, with an average NS of 0.58 for all events (median NS=0.63). This result should be compared with the results found in the previous sections, where SMOS-IC showed the best correlations with observed soil moisture. ASCAT and ERA5 show similar results in terms of average NS (∼0.45). In contrast, the daily observed soil moisture shows a lower performance with an average NS of 0.25 (median NS=0.49). The hourly time step enhanced the performance of the model, with an average NS using the ERA5 product of 0.64 (median NS=0.73), and also a better performance with the hourly in situ data, with mean NS=0.54 (median NS=0.61). These results show that the hourly time step better represents the saturation content before the flood events in this basin. For the Issyl basin, the validation results are quite different (Fig. 8). For only five events (3 April 2011, 2 and 19 May 2011, 5 April 2012, and 25 March 2015) the event-based model can be validated using the ERA5 hourly data with an average NS coefficient of 0.46. For the events of 16 May and 6 June 2011, an significant spatial variability of precipitation is observed, with no precipitation at the PQI station. In addition to these events, the flood of 28 September 2012 showed an overestimation of the validated value of S compared to the calibrated value. This overestimation is related to the ERA5 estimation that considers the soil to be more saturated than it is. For all other events and with different soil moisture products, the NS coefficients are negative and the hydrographs not adequately reproduced. These validation results should be put in perspective with the fact that the Issyl basin has a land use characterized by agricultural activities with possible large water uptake in the diver channel during floods for irrigation. Some simple methods to compensate for the water losses due to irrigation, such as the application of a varying percentage of runoff added to the observed discharge to compensate for the part of water lost for irrigation, have been tested but with no improvement of the results. This is probably because the quantity taken for irrigation is not constant from one event to another, depending on the farmer needs, as shown by field surveys, and this amount may also depend on discharge thresholds.