Hydrological Variability from Gauging Stations and Simulated SWOT Data, for Major French Rivers

This study was carried out under the aegis of the program Surface Water and Ocean Topography (SWOT) associated with the National Center of Space Studies (CNES). The future SWOT mission will offer new opportunities to survey the hydrodynamic in the rivers because it will provide data on the water level/ discharges with a high spatial resolution (oceans: 1 km, rivers: 100 m of width) and with a global cover. However, it is important to estimate the capacity of SWOT to reproduce the hydrodynamic phenomena in the estuaries and the temporal and the spatial variability of this dynamic. The aim of this paper is 1) to estimate the capacity of SWOT to reproduce the hydrological variability of watersheds, and 2) to validate the use of these data for other zone without hydrometric station. Based on discharge measurements and simulated Surface Water and Ocean Topography (SWOT) data, we have investigated the hydrological variability of the main French rivers (Seine, Loire, Garonne and Rhône) by applying a series of statistical analyses to the time series of the discharge. A frequency analysis has been also used using a technique of wavelet. Results have shown a similar hydrological variability of the four watersheds. Three different periods of hydrologic variability has been identified: before 1970, between 1970 and 1990, and after 1990. Using these analyses, simulated SWOT samples and discharges were compared during the three studied periods. Simulated SWOT data, obtained by a synthetic sampling of river discharges basing on the number between simulated SWOT data and in-situ discharges. Nevertheless, good correlation was not observed for the minimum and the maximum annual discharge with an underestimation for SWOT maximum annual and an overestimation of the minimum annual SWOT ones. Moreover, best identification of minimum, mean and maximum annual discharge depends on SWOT overpasses.


Introduction
In the present context of intensification of global water cycle associated with climate warming [1] [2], hydrological systems and water resources are continuously affected. Assessing the potential impact of global climate change on hydrological variability becomes crucial, particularly in France, in order to comply with the most recent EU Water Framework Directive and to reduce the potential threats on the national water bodies. The large watersheds, which are integrators of climate change and heterogeneities of many parameters, represent good indicators for global change determination.
Many studies at large global watersheds [3] [4] and at French watersheds [5] [6] have already been performed to characterize the hydrological variability of different global rivers. These studies are usually based on in-situ discharge data. However it is also possible to perform it using satellite data [7] [8]. Recently, a new space mission called Surface Water and Ocean Topography (SWOT) is being developed jointly by a collaborative effort of the international oceanographic and hydrological communities for making high-resolution measurement of the water elevation of both the ocean and land surface water to answer the questions about the oceanic submesoscale processes and the storage and discharge of land surface water.
The key instrument payload is a Ka-band radar interferometer capable of making high-resolution wide swath altimetry measurement. Data, collected by Surface Water and Ocean Topography SWOT, will provide measure 2D water heights over a 120 km wide swath. This satellite allows obtaining water level for all lakes greater than 250 m 2 and discharges for river of width of greater than 100 m [9]. Many studies about the error budget [10] [11] contribution in modeling are carried out to prepare the mission spatial [12] [13].
This study was carried out in the framework of the program Surface Water and Ocean Topography (SWOT) which is a partnership between National Center of Space Studies (CNES) and National Aeronautics and Space Administration (NASA).
The present research focuses on two objectives. The first one is to investigate the hydrological variability in four watersheds of the French rivers using different statistical approaches and frequency analysis with the aim to define a long-term sim-

Surface Water and Ocean Topography Mission
The SWOT mission will provide high-resolution measurements of water surface elevations over the ocean and continental surface water bodies. The main satellite payload is the Ka-band Radar Interferometer (KaRIN), a wide swath radar interferometer. Two antennas separated by a 10 m boom will observe two ground swaths of 50 km on each side of the nadir separated by 20 km. The distance between the two swaths will be partially covered by the measurements from a nadir altimeter [13] [14]. The intrinsic pixel resolution will vary from 60 m (near range) to 10 m (far range) across-track and will be at best around 2 m along-track (however, this value is also dependent upon decorrelation time). The chosen orbit has a 890.5 km altitude and 77.6˚ inclination, in order to observe almost all the continental surfaces. SWOT will measure water surface elevation for all lakes greater than 250 m 2 and rivers with widths greater than 50 -100 m, with a vertical precision of at least 10 cm [14]. The satellite is currently planned to be launched in 2020. The nominal lifetime of the mission ranges approximately between 3 and 5 years. The first three months will be a calibration-validation period. After the initial three months, the remaining time during the mission will be undertaken with an orbit that meets the nominal science requirement to obtain a global coverage of the earth and that has a 21 days repeat. Number of observations change according to the localization of study domain per repeat period (21 days) for this orbit (890.5 km).

Data set and Methods
The different hydrometric stations Montjean sur Loire, Poses, Beaucaire and Mas d'Agenais have been selected, as explored previously in [15], to investigate the hydrological variability of Loire, Seine, Rhone and Garonne rivers, at long term scales ( Figure 1   according to the number of overpasses per repeat cycle (21 days) and the selected orbit (890.5 km). The number of SWOT samples and the temporal sampling intervals were calculated for each hydrometric station of its geographical coordinates (Table 1). First, qualitative statistics (minimum, mean and maximum yearly values) have been applied to the discharge time series to quantify the variability of French rivers discharges.
Then, trend analysis in discharge was realized using a local polynomial regression non-parametric algorithm (LOESS), proposed by [16] and developed by [17]. The locally weighted polynomial non-parametric fitting procedure is applied using three degrees of smoothing successively in decreasing order so as to emphasize both trend behavior and get a first approach of the main leading fluctuations in the se- ries. The three smoothing windows used span, respectively, 100%, 25% and 10% of the data. Finally, continuous wavelet (CWT) was used to decompose a signal on the basis of scaled and translated versions (daughter wavelets) of a reference wave function (mother wavelet). Here, CWT has been used in univariate mode aiming to identify more accurately the dominant modes of variability as spectral components and the time scales involved. For a more complete overview of CWT analysis and its application to hydrometeorological or climatic signals, the reader is referred to literature [15] [18] [19] [20].

Characterization of the Hydrological Variability of the French River from the in Situ Measurements
Using the methods presented previously, the discharge in the different French rives have been studied. Figure   Following, LOESS smoothing was applied to daily time series of discharges. Different degrees of smoothing (100%, 25% and 10%) have been tested. Only, a 25%-span smoothing is presented in Figure 3   Then, the time variability of discharges has been deeply investigated using a frequency analysis of wavelet which is displayed in Figure 4  Obtained results, using different approaches, show a similar hydrological variability between the four studied French watersheds. Then, three periods are indicated: 1) before 1970, 2) between 1970 and 1990, and 3) after 1990. These findings are also confirmed by previous works. Indeed, two discontinuities in hydrological time series has been detected by [22] which have concluded the occurrence of a step increase in discharge variability around 1970. [23] and [24] have studied 79 rivers by wavelet analyses and have shown striking climate-related features before the 1950s and after the 1970s in mean annual discharges. [21] have demonstrated discontinuities, in 1970s and 1990s, around 1970 and 1990 on both in the precipitation, discharge and piezometry of the Atlantic Ocean watersheds (NW France, N Africa, USA).
According to these analyses, three periods with different hydrological variability can be observed: 1) after 1970, 2) between 1970 and 1990 and 3) after 1990.

Determination of the Hydrological Variability Observed by SWOT
SWOT samples have been simulated during a series of time periods of 5 years.
Three periods were selected (1965-1969, 1985-1989 and 2000-2004) and the methods, used previously, were applied to sampled data in order to visualize influence of numbers of SWOT passages on hydrological variability restitution by SWOT.
Initially, compared results of maximum, mean and minimum annual values were studied for 1965-1969, 1985-1989 and 2000-2004 period. Figure 5 represents the maximum, mean and minimum annual values for in-situ (black) and simulated SWOT (grey) data of the four watersheds and for three periods.
Generally, variations of mean annual SWOT data are similar to those of discharges. The annual maximum, mean and minimum discharge is tendency to decrease, except for annual minimum of Garonne and Loire for 1965-1969 periods. However, whatever tendency the ability of SWOT to it reproduces is well.
However, the maximum and the minimum annual data were underestimated and overestimated, respectively ( Figure 5). In order to quantify underestimation and overestimation, averages of under/overestimation are calculated for each river and for three periods ( Table 2 and Table 3). For minimum annual data (Table 2) To conclude, SWOT seems less good restitute 1) maximum annual data for Rhone and Garonne, and 2) minimum annual data for Rhone. These over and underestimations for the maximum and the minimum annual SWOT data are due to probability that SWOT passages coincide with the maximum and the minimum of discharges.
Underestimation and overestimation for the maximum and the minimum annual SWOT data can be explained by the sampling effect. Figure 6 shows discharge in black and sampling SWOT data in grey circle indicating that the maximum and the minimum discharges are less sampled than other values. This point associated with high peak floods for Rhone and Garonne can explain the worst restitution for maximum annual SWOT data for both rivers. However, peak floods of Loire present also high value and minimum/maximum annual values are better restituted by SWOT. Loire presents four passages of SWOT unlike other rivers. It seems to appear a better restitution of maximum/minimum annual value   Figure 7 which shows a strong similarity of loess provided by in-situ discharges and simulated SWOT data. The same variation between both span-LOESS was also observed.
SWOT can reproduce general trends of discharges. However, simulated SWOT data could not describe the maximum annual values and the peak flood events which are poorly shown.
In frequency domain, wavelet analyses were performed (Figure 8) for discharge and simulated SWOT data of Rhone between 2000 and 2004. One year mode corresponds to annual hydrological cycle, and six months mode corresponds to half of year mode. Six months mode is probably associated to annual hydrological cycle. The reconstruction in temporally in domain of two-three months mode, using inverse Fourier transform, confirms the presence of this mode in December and January ( Figure 9). Indeed, the variability is higher in December and January.
In order to quantify the coherence between both variables, wavelet coherence is realized. Wavelet coherence is useful to determine the similar patterns of variability between simulated SWOT data and discharge. The wavelet analyses

Conclusions
This study focuses on the hydrological variability of four French watersheds (Seine, Loire, Garonne and Rhone) with different features basing on discharges (in situ measurements) and simulated SWOT data by the use of a series of statistical analyses.
Time series and spectral analyses of in-situ data between 1959 and 2010 show same results between four watersheds. A high similarity of variability's modes was found for the four stations, with: 1 year, 2 -4 year, 5 -8 year and 16 -32 year modes. The coherence between the four basins was important ranging between 73% and 92% for discharge during the period between 1959 and 2010. Moreover, three periods are identified: 1) before 1970, 2) between 1970 and 1990, and 3) after 1990.
These three periods were chosen for the simulation of SWOT samples which was released during three periods of 5 years: 1968-1969, 1985-1989 and 2000-2004. The comparison between in-situ discharge and simulated SWOT data has demonstrated similar results showing a strong capacity of the satellite to reproduce the hydrological variability of rivers despite the number of SWOT passages. Furthermore, comparison shows that SWOT has difficulties to reproduce the minimum and the maximum annual: the minimum annual discharge is over-estimated and the maximum annual discharge is under-estimated. This discrepancy in estimation seems to be more important for the rivers with high peak flood such as Rhone, Loire and Garonne. However, the river of Loire having four SWOT passages shows a good reproduction of maximum/minimum annual values by SWOT. Best identification of minimum, mean and maximum annual discharge depends on SWOT overpasses. Coherence wavelet indicates a correlation higher than 90% between both variables. The same modes of variability are detected by wavelet analyses: one year mode corresponding to annual hydrological cycle, six months mode associated to annual hydrological cycle, and two-three months mode corresponding to annual flood period.
This finding shows that satellite data provided by SWOT represents a useful step to characterize the variability of hydrological systems and water resources. This database can be an excellent alternative to study the evolution in rivers where the measurements are not available and for large spatial scales. However, care must be taken when using data for rivers with discharges at high peak floods.