A multi-sourced assessment of the spatio-temporal dynamic of soil saturation in the MARINE flash flood model

The MARINE hydrological model is a distributed model dedicated to flash flood simulation. Recent developments of the MARINE model are exploited in this work: on the one hand, formerly relying on water height, transfers of water through the subsurface now take place in a homogeneous soil column based on the volumetric soil water content (SSF model). On the other hand, the soil column is divided into two layers, which represent respectively the upper soil layer and the deep weathered rocks (SSF-DWF model). The aim of the present work is to assess the performances of these new representations for the 5 simulation of soil saturation during flash flood events. An exploration of the various products available in the literature for soil moisture estimation is performed. The performances of the models are estimated with respect to several soil moisture products, either at the local scale or spatially extended: i) The gridded soil moisture product provided by the operational modeling chain SAFRAN-ISBA-MODCOU; ii) The gridded soil moisture product provided by the LDAS-Monde assimilation chain, based on the ISBA-a-gs land surface model and assimilating satellite derived data; iii) the upper soil moisture hourly measurements 10 taken from the SMOSMANIA observation network; iv) The Soil Water Index provided by the Copernicus Global Land Service (CGLS), derived from Sentinel1/C-band SAR and ASCAT satellite data. The case study is performed over two French Mediterranean catchments impacted by flash flood events over the 2017-2019 period. The local comparison of the MARINE outputs with the SMOSMANIA measurements, as well as the comparison at the basin scale of the MARINE outputs with the gridded LDAS-Monde and CGLS data lead to the same conclusions: both the dynamics and the amplitudes of the soil mois15 ture simulated with the SSF and SSF-DWF models are better correlated with both the SMOSMANIA measurements and the LDAS-Monde data than the outputs of the base model. The opportunity of improving the two-layers model calibration is then discussed. In conclusion, the developments presented for the representation of subsurface flow in the MARINE model enhance the soil moisture simulation during flash floods, with respect to both gridded data and local soil moisture measurements.

. The two studied catchments located in the South of France: the Ardeche river at Vogue and the Orbieu river at Lagrasse. Monitoring networks: soil moisture (SMOSMANIA network stations) and the national groundwater ADES network stations (www.ades.eaufrance.fr).

The studied events
In this work, the ANTILOPE quantitatives precipitation estimates (QPE) (Champeaux et al., 2009) are used for precipitation estimation. The ANTILOPE-QPE are based on a fusion between the radar data provided by the operational radar network 150 ARAMIS (Tabary, 2007) and the measurements at pluviometers, spatialised by krigging method. ANTILOPE-QPE precipitation are available on the hourly time step, at the kilometric resolution. The critized observed discharges at the outlet of the two catchments are taken from the hydrometric French database (www.hydro.eaufrance.fr). Table 1 presents the characteristics of the studied event. 155 Three flash flood events are considered for each catchments over the 2017-2019 period. The heterogeneity of the studied events has to be noted: for the Orbieu catchment, the extreme event of October 2018 represents the historical maximum for this region, with well known dramatic damages to infrastructures and populations. This flood has the particularity to be extremely fast, with about two hours between the precipitation peak and the discharge peak at the Lagrasse station. This response time appears to be faster than the response time regularly considered for this station (about 5 hours). On the opposite, the two other For the event defined for this study (November 2018, 22nd to 28th), the precipitation amounts do not represent extreme value, however, flood damages have been noticed during this period. In addition, different hydrological responses can by distinguished 165 for spring or autumn seasons, due to different soil and vegetation conditions, possible snow contribution and meteorological antecedents. This variety in the structures of the six events considered for this study represents both a robustness guaranty and a challenge for the modeling exercise. Table 1. The six events considered in this work for the Ardeche at Vogue and the Orbieu at Lagrasse catchments, with cumulated volume (Precip.) and maximal intensity (I pr max ) of ANTILOPE-QPE precipitation, maximal hourly observed discharge (Q obs max ). The stars indicate the return period of the flood: (*) for a 2-years, (**) for a 5-years, and (***) for a 100-years return period. The given dates and duration are the ones considered for the hydrological simulations. S.M. is the initial soil moisture provided by the SAFRAN-ISBA-MODCOU chain for the first day of the simulations, on average over the catchment. The SAFRAN-ISBA-MODCOU operational modeling chain (SIM) (Habets et al., 2008) uses the ISBA surface scheme, coupled with the MODCOU hydrological model for underground flows and forced by the SAFRAN atmospheric reanalysis. SIM outputs are available since 1958, on an hourly basis, on a regular mesh at the 8-km resolution. In particular, SIM provides moisture data for the root layer of the soil. This work uses the outputs of two available versions of SIM: 1) SIM1, which uses the force-restore version of ISBA, ISBA-3L (Noilhan and Planton, 1989;Noilhan and Mahfouf, 1996) Dewaele et al. (2017) and Barbu et al. (2011). In this work, the version of LDAS-Monde which uses the AROME atmospheric 190 model outputs for the atmospheric forcing of the model is used (Albergel et al., 2018;Bonan et al., 2020). These AROMEforced outputs are available since July 2017, at the 2.5 kilometer resolution and at three-hour time steps.

Satellite derived products
Various products derived from remote imagery are available for soil moisture estimation, at various spatial and temporal scales.
In particular, the relevance of five products is investigated for this study. Table 2 summarizes the investigated products and their 195 main characteristics.  -Marschallinger et al. (2018b), whereas the SSM product is derived from only the Sentinel-1/C-SAR band data.
In this work, the SWI values provided for the top 5 cm soil are considered. The uncertainties for the CGLS SSM are computed by adding the different sources of uncertainty occurring in the product preparation and they represent about 8% of the SSM values. No uncertainties estimation is provided for the SWI product.
• The soil moisture with very high spatial resolution product (VHSR) (El Hajj et al., 2017), provided by the THEIA-Land 205 pole (www.theia-land.fr), offers soil moisture maps with a 6-days frequency and at the sub-parcel scale on several sites in France, in Europe and around the Mediterranean basin. The THEIA-Land VHSR soil moisture product exploits the Sentinel-1 radar and Sentinel-2 optical Copernicus image series, following a neural networks signal inversion algorithm.
The extent of the two studied basins is globally covered by this product. However, the footprints of the images being variable depending on the dates, the whole catchments are not covered for all dates. The amount of gaps in this product 210 is significant: only 12 images are available over the studied events. In particular, no data are available over the Ardeche catchment for the studied dates.  than the products at the kilometric resolution (CGLS and THEIA-Land VHSR). In addition, the ESA CCI product is known to provide globally wetter SSM than the SMOS-IC product, as mentioned by Dong et al. (2020). However, it is to be noted that this products inter-comparison is mainly informative regarding the products temporal dynamics but their respective biases cannot be directly compared, mainly for two reasons: i) the compared variables are not necessarily commensurable (i.e. SSM and SWI); ii) the soil depth considered in each product for the SSM estimation might differ.

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Important discrepancies are observed in the temporal dynamics for the different product. Since the study area is rather small, no validation of these products at the very local scale is available and the relatively low uncertainties estimates do not allow to explain these differences (see table 2). As no particular temporal behavior can be distinguished among the five product, the choice has been done for this work to particularly focus on the product that offered the most important data availability and 235 the finest spatial resolution. The amounts of missing values for the SMOS-IC and the THEIA-Land VHSR products, and also for the CGLS SSM products are too important for these data sources to be reliably used. On the contrary, the CGLS SWI product presents a good data availability, despite some events being less covered than others (e.g. March 2018 or November greater than 14% of the catchment area. Consequently, in this work, the CGLS SWI product is taken into account to perform 240 the comparison with the soil moisture simulated in MARINE. Nevertheless, this literature exploration of the data available for soil moisture description illustrates the difficulty to estimate surface soil moisture based on satellite data at small catchment scale (∼ 100km 2 ). properties is taken into account for these calibrations.

The ADES piezometric network
The ADES database (Access to Data on Groundwater, www.ades.eaufrance.fr), coordinated by the French National Geological 255 Survey (BRGM), provides piezometric level measurements throughout France. One point of measurement is available for each of the two studied catchment. Figure 1 shows the location of the two measurement points. For the Orbieu catchment, the water table is 110 km 2 large and 1849 km 2 large for the Ardeche catchment. The measurements are available at the daily time step and the daily value represents the maximum of the water level measurements in 24 hours. In this work, the relative underground water level with respect to the measurement mark is compared to the water content of the deep layer simulated with SSF-DWF 260 model.

Comparison protocol
3.1.1 Choice of layers for the LDAS-Monde soil moisture Figure 3 presents the spatial average of the soil moisture, for each catchment and for each of the eleven soil layers described 265 in the LDAS-Monde product. Two behaviors can be distinguished for the different layers: for the five superficial layers, a fast-responding soil moisture and a more stable soil moisture, with a slower response to precipitation and narrower amplitude range for the deeper layers. Moreover, the diurnal cycle of solar radiation significantly influences up to the fifth layer, i.e. up to 40 cm deep. In addition, over the two studied catchments, the spatial patterns of soil moisture are similar for the eleven layers. Indeed, the spatial distribution of soil moisture is mainly controlled by the soil texture, which is considered as vertically 270 uniform in the ISBA-A-gs model. Consequently, the choice is made in this work to synthesize the eleven LDAS-Monde layers as three average layers: the surface layer (average of layers 1 to 5), the deep layer (average of layers 6 to 11), and the total layer (average of all the 11 layers). Thus, the surface layer represents depths from 0 cm to 40 cm and the deep layer represents depths from 40 cm to 300 cm. Concerning the comparison between the MARINE simulation and LDAS-Monde, for the base and SSF models, which use a one layer soil discretization, the MARINE soil moisture is compared to the moisture of the surface layer, 275 noted HU surf . For the SSF-DWF model, which uses a two-layers soil discretization, the moisture of the MARINE upper layer is compared to LDAS-Monde surface layer, and the moisture of the MARINE deep layer is compared to the LDAS-Monde deep layer (noted HU deep ). The total average LDAS-Monde layer is used for overall comparison.

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The performance of the simulated discharges are estimated at the hourly time step through the usual Nash Sutcliffe Efficiency criteria (NSE) and also through the LNP index, defined by Roux et al. (2011) as in equation 1, where Q obs (Q obs max ) and Q sim (Q sim max ) represent the (maximal) observed and simulated discharged, respectively, and T concentration , the concentration time of the catchment. The advantage of the LNP index is to give equal weight to the NSE values (first term), to the peak value estimation (second term) and to the timing of the peak simulation (third term). LNP appear to be a integrative criteria well-295 suited for flash flood modelling (Lovat et al., 2019). (1) The comparison of the soil moisture simulated in MARINE and provided by LDAS-Monde is performed at the catchment scale using the relative bias and the Kendall correlation over values averaged at the catchment scale. In addition, the spatial 300 dynamics of the simulated soil moisture are quantified using the spatial moments δ 1 and δ 2 defined by Zoccatelli et al. (2011).
The δ 1 and δ 2 moments take into account the distance of each grid cell to the drainage network and they allow to represent both the overall location of the soil moisture field with respect to the outlet and the number of modes (i.e concentration points in this case) of the field. The closer of 1 are the δ 1 values, the more centred around the centroid of the catchment is the field.
Values of δ 1 lower that 1 mean that the field get closer from the outlet, whereas values higher that 1 characterize a field overally 305 located on the highest areas of the catchment. The closer of 1 are the δ 2 values, the more uniform is the distribution of the field.
Values of δ 2 lower that 1 represent an unimodal distribution and values of δ 2 higher that 1 mode likely represent a multimodal distribution. Despite being initially defined by Zoccatelli et al. (2011) to characterize rainfall fields, the δ 1 and δ 2 moments also appear to be particularly relevant when applied to soil moisture fields. and by Douinot (2016) for the Ardeche catchment. The ANTILOPE QPE data are used as hourly precipitation input for the 320 MARINE model, available at the kilometric resolution. Figure 4 presents the IGN-25 m DEM and the soil depth maps used for the two studied catchments. Table 3 presents the calibrated parameter values obtained for each catchment by Douinot (2016) and Garambois et al. (2015) and used in this work.   (2016) and Garambois et al. (2015) for the Orbieu at Lagrasse and Ardeche at Vogue catchments:

Model set up
the multiplier coefficient for soil depth maps (Cz), the multiplier coefficient for the spatialized saturation hydraulic conductivity used in lateral flow modelling (C kss ) the multiplier coefficient for the spatialized hydraulic conductivity at saturation that is used in infiltration modelling (C kga ), two friction coefficients for low and high-water channels (CD1 and CD2), and deep layer depth for the SSF-DWF model  Figure 5 presents the discharges at the outlets, simulated with MARINE using the base, the SSF or the SSF-DWF models 325 together with the observed discharges during the flood events. Table 4 presents the associated LNP and Nash Sutcliffe Efficiency (NSE) performance criterias of the simulated discharges, referring to hourly observed discharges. The main effect of computing the transfers through the subsurface as a function of the volumetric soil water content instead of the water height (SSF model)

Discharge simulation
is to flatten the overestimation of the simulated discharge during the flow rise, at the beginning of the events. This behavior will be explained in the result section: there is no gradient of initial soil water content over the 8x8km SIM mesh and therefore 330 smaller subsurface contribution at the beginning of the events in the SSF and SSF-DWF. However, in the SSF-DWF model, this dynamics is influenced by the contribution of the deep layer, itself mainly controlled by the parametrization of the thickness of this deep layer. Nevertheless, the calibrations of the three models clearly require to be improved in order to better simulate the discharges at the outlets, in particular for the Orbieu catchment and for the SSF-DWF model. However, since this paper focuses on comparing the soil moisture dynamic simulation according to the soil physics considered in the model, and considering that 335 the variety in the structures of the considered events (see section 1) is a limit to model performances, the calibration proposed by Douinot (2016) and Garambois et al. (2015) are directly applied to this work.   and the cells textures, water height gradients are larger than volumic soil water gradient when no precipitation happens. Consequently, lateral flows based on the water height gradients are larger than lateral flows based on the volumic soil water gradient.
On overall, the temporal dynamics of the CGLS SWI, in average per catchment is more consistent with the SSF and SSF-   The general behavior of the δ 2 spatial moment is that the δ 2 decreases with precipitation, with soil moisture fields more centered around the area of maximum rainfall, and then increases with the spread of the soil moisture fields along the drainage 420 network. The δ 2 values for the SSF and SSF-DWF models are globally closer to 1 than for the base model. Indeed, since the soil saturation is globally higher for the SSF and SSF-DWF models (see figure 7), the difference between the soil saturation and saturation in the drainage network (i.e. 100%) is stronger for the base model than for the other two models. This leads to soil moisture fields more uniform for the SSF and SSF-DWF models than for the base model. This result is particularly observed for the Orbieu catchment.

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Both the δ 1 and δ 2 spatial moments computed for the LDAS-Monde HU surf are globally closer to 1 than when computed for the MARINE outputs. Indeed since the spatial resolution is the LDAS-Monde HU surf is 2.5x2.5 km 2 , whereas it is 200x200 m or 250x250 m for the MARINE simulations, the spatial variability of the LDAS-Monde HU surf is lower than for the MARINE outputs. The δ 1 and δ 2 spatial moments computed for the CGLS SWI are very close to 1, with tiny variations. This 430 can be explained not only by the spatial resolution coarser than for the MARINE outputs but also by the important amount of missing pixel in this data source, in particular for the Ardeche catchment. The computation of spatial moments for the CGLS SWI might not lead to robust conclusions.      from Sentinel1/C-band SAR and ASCAT satellite data, at the daily time step and at the kilometric resolution. A comparative assessment of the various products based on remote imagery available for soil moisture in the literature is performed. This lit-485 erature exploration of the data available for soil moisture description illustrates the difficulty to estimate surface soil moisture based on satellite data at small catchment scale (∼ 100km 2 ). Considering its satisfying data availability and its fine spatial resolution, the SWI product provided by CGLS is compared with the soil moisture simulated in MARINE. These products 25 https://doi.org/10.5194/hess-2020-311 Preprint. Discussion started: 14 July 2020 c Author(s) 2020. CC BY 4.0 License.
represent valuable indicators of the spatio-temporal dynamics of soil moisture at various scales.
The case study is performed over two catchments located in the South of France, namely the Orbieu river catchment at the Lagrasse station and the Ardeche river catchment at the Vogue station, particularly impacted by flash flood mediterranean events. The study focuses on three flash flood events for each catchment, that occurred between February 2017 and April 2019.
These six events present various characteristics, regarding mainly the structures of the pluviometric events and the soil moisture antecedent conditions. The MARINE flash flood model is set up following the calibrations provided by Garambois et al. 495 (2015) for the Orbieu catchment and by Douinot (2016) for the Ardeche catchment. The ANTILOPE QPE data are used as hourly precipitation input for the MARINE model at the kilometric resolution. As the scope of this work is to assess the soil moisture simulation according to the physic considered in the soil models, the discharges simulated with the different models are considered as it is, and the calibrations are not further optimized. The comparison between the gridded soil moisture estimates and the local measurements of soil moisture provided by the SMOSMANIA network is performed through a spatial 500 averaging of the gridded simulated values over a 1km 2 area around the measurement point. As the LDAS-Monde provides soil moisture values for 11 soil layers, these values are synthesized by three summary variables representing respectively the upper soil layer, the deep soil layer and the total soil column. The spatial distributions of soil moisture grids are quantitatively described through the definition of the spatial moments δ 1 and δ 2 .

505
The local comparison of the MARINE outputs for surface soil moisture with the SMOSMANIA measurements, as well as the comparison at the basin scale with the gridded LDAS-Monde and CGLS data lead to the same conclusions: soil moisture simulated with the base model significantly differs from the simulations using the SSF and the SSF-DWF models. When no precipitation happens, the soil layer empties faster with the base model, leading to a simulated soil moisture significantly lower with the base model than with the two other models. This behavior can be physically explained by the fact that, in the SSF and 510 the SFF-DWF models, the lateral transfers are computed as a function of the volumic soil water gradients, whereas in the base model, they are computed as a function of the water height gradient. Indeed, since the water height gradient between two cells depends on the slope between the cells and the cells textures, water height gradients are larger than volumic soil water gradient when no precipitation happens. Consequently, lateral flows based on the water height gradients are larger than lateral flows based on the volumic soil water gradient. In addition, the dynamics as well as the amplitudes of the soil moisture simulated in 515 the SSF model and for the upper layer in the SSF-DWF model are better correlated with both the SMOSMANIA measurements and the LDAS-Monde data than the outputs of the base model. Considering that the dynamics of the LDAS-Monde HU surf is of satisfying accuracy, this assessment leads to the conclusion that the SSF-DWF model improves the simulation of the dynamics of the surface layer moisture, compared to both the SSF and the base models. This results appears to be particularly reliable, since it is observed both a the point measurement scale and at the catchment scale.

520
In the SSF-DWF model, the simulation of the moisture in the deep layer is also compared to LDAS-Monde moisture data provided for deeper layers, as well as local piezometric measurements available for each catchment. However, the simulation of the deep layer water content strongly depends on the calibration of the deep layer thickness, the deep layer porosity and the vertical and lateral hydraulic conductivities in the deep layer. These results illustrate the difficulty to represent the hydrological 525 dynamic of the deep soil layers, with limitation due to the lack of knowledge concerning the physical description of the subsurface water storage. Further conclusions concerning the simulation of deep soil moisture would then require an extensive work to enhance the parametrization of the deep layer in the SSF-DWF model. In particular, the Height Above Nearest Drainage (HAND) method (Nobre et al., 2011) would offer the opportunity to take into account the terrain physical characteristics in the deep layer parametrization.

530
In conclusion, this work exposes that enhancing the degree of refinement of the soil physics for the representation of subsurface flow in the MARINE model appears to enhance the upper soil moisture simulation during flash floods, with respect to both spatialized model outputs and satellite-based data, as well as with respect to local soil moisture measurements.