SYNERGY BETWEEN SATELLITE OBSERVATIONS OF SOIL MOISTURE

Abstract. This paper presents an innovative approach, STREAM – SaTellite based Runoff Evaluation And Mapping – to derive daily river discharge and runoff estimates from satellite soil moisture, precipitation and terrestrial water storage anomalies observations. Within a very simple model structure, the first two variables (precipitation and soil moisture) are used to estimate the quick-flow river discharge component while the terrestrial water storage anomalies are used for obtaining its complementary part, i.e., the slow-flow river discharge component. The two are then summed up to obtain river discharge and runoff estimates. The method is tested over the Mississippi river basin for the period 2003–2016 by using Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) rainfall data, European Space Agency Climate Change Initiative (ESA CCI) soil moisture data and Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage data. Despite the model simplicity, relatively high-performance scores are obtained in river discharge simulations, with a Kling-Gupta efficiency index greater than 0.65 both at the outlet and over several inner stations used for model calibration highlighting the high information content of satellite observations on surface processes. Potentially useful for multiple operational and scientific applications (from flood warning systems to the understanding of water cycle), the added-value of the STREAM approach is twofold: 1) a simple modelling framework, potentially suitable for global runoff monitoring, at daily time scale when forced with satellite observations only, 2) increased knowledge on the natural processes, human activities and on their interactions on the land.



INTRODUCTION 45
Spatial and temporal continuous river discharge monitoring is paramount for improving the 46 understanding of the hydrological cycle, for planning human activities related to water use as well as 47 to prevent/mitigate the losses due to extreme flood events. To accomplish these tasks, runoff and river 48 discharge data, which represents the aggregated signal of runoff (Fekete et al., 2012), should be 49 available at adequate spatial/temporal resolution, i.e., at basin scale (basin area larger than 10'000 50 km 2 ) and at monthly time step for water resources management and drought monitoring up to grid 51 scale (few km)/(sub-) daily time step for flood prediction. The accurate continuous (in space and 52 time) runoff and river discharge estimation at finer spatial/temporal resolution is still a big challenge 53 for hydrologists. 54 Traditional in situ observations of river discharge, even if generally characterized by high temporal 55 resolution (up to sub-hourly time step), typically offer little information on the spatial distribution of 56 runoff within a watershed. Moreover, river discharge observation networks suffer from many 57 limitations such as low station density and often incomplete temporal coverage, substantial delay in 58 data access and large decline in monitoring capacity (Vörösmarty et al. 2002). Paradoxically, this 59 latter issue is exacerbated in developing nations (Crochemore et al, 2020), where the knowledge of 60 the terrestrial water dynamics deserves greater attention due to huge damages to settlements and 61 especially the loss of human lives that occurs regularly. 62 This precarious situation has led to growing interest in finding alternative solutions, i.e., model-based 63 or observation-based approaches, for runoff and river discharge monitoring. Model-based 64 approaches, based on the mathematical description of the main hydrological processes (e.g., water 65 balance models, WBMs, global hydrological models, GHMs, e.g., Döll et al., 2003 or, increasing in 66 complexity, land surface models, LSM, e.g., Balsamo et al., 2009;Schellekens et al., 2017), are able 67 to provide comprehensive information on a large number of relevant variables of the hydrological 68 cycle including runoff and river discharge at very high temporal and spatial resolution (up to hourly 69 https://doi.org/10.5194/gmd-2020-399 Preprint. Discussion started: 25 January 2021 c Author(s) 2021. CC BY 4.0 License.

Satellite Products 197
Satellite products include observations of precipitation ( ), soil moisture and TWSA. 198 The satellite dataset used in this study is the Multi-satellite Precipitation Analysis 3B42 Version 7 199 (TMPA 3B42 V7) estimate produced by the National Aeronautics and Space Administration (NASA) 200 as the 0.25°×0.25° quasi-global (50°N-S) gridded dataset. The TMPA 3B42 V7 is a gauged-corrected 201 satellite product, with a latency period of two months after the end of the month of record, available 202 at 3h sampling interval from 1998 to present (2020 approximately 1°×1° or about 12'000 km 2 . Although the mascon size is smaller than the inherent 217 spatial resolution of GRACE, the model exhibits a relatively high spatial resolution. This is attributed 218 to a statistically optimal Wiener filtering, which uses signal and noise covariance matrices. The 219 coloured (frequency-dependent) noise characteristic of KBR data was taken in to account when 220 compiling the model, which has allowed for a reliable computation of these noise and signal 221 https://doi.org/10.5194/gmd-2020-399 Preprint. Discussion started: 25 January 2021 c Author(s) 2021. CC BY 4.0 License. covariance matrices. They play a crucial role when filtering and allow to achieve a higher spatial 222 resolution compared to commonly applied GRACE filtering methods such as Gaussian smoothing 223 and/or destriping filters. GRACE data are available for the period 01 January 2003 to 15 July 2016. 224

Model Outputs 225
To establish the quality of the STREAM model in runoff simulation, monthly runoff ( ) data obtained  While the high spatial and temporal (i.e., intermittence) variability of rainfall and the highly changing 240 land cover spatial distribution significantly impact the variability of the quick-flow component (with 241 scales ranging from hours to days and meters to kilometres depending on the basin size), slow-flow 242 river discharge reacts to precipitation inputs more slowly (i.e., months) as water infiltrates, is stored, 243 mixed and is eventually released in times spanning from weeks to months. Therefore, the two 244 components can be estimated by relying upon two different approaches that involve different types 245 of observations. Based on that, within the STREAM model, satellite soil moisture, precipitation and 246 TWSA will be used for deriving river discharge and runoff estimates.
with the gain at the time given by: 285 [days] is a parameter, named characteristic time length, that characterizes the temporal variation 287 of soil moisture within the root-zone profile and the gain ranges between 0 and 1; 288

13
The second key point of STREAM approach concerns the estimation of the slow runoff response, , 292 from the second storage. The hypothesis here, shared also with other studies (e.g., Rakovec et al., 2016), 293 is that the dynamic of the slow runoff component can be represented by the monthly TWSA data. 294 Indeed, the time scale of slow runoff response is typically in the range of seasons to years and it is 295 almost independent upon the water that is contained in that upper storage. For that, the slow runoff 296 response , from the second storage, can be computed through equation (4) as follows: 297 is the TWSA estimated by GRACE normalized by its minimum and maximum values. 300 The assumption behind this equation is that TWSA can be assumed as a proxy of the evolution in 301 time, , of the , i.e., the storage of the lower storage. Note that, being based on a conceptual framework, we assume that soil moisture acts both on the 305 generation of the quick flow part (mainly) and is partly responsible of the slow flow contribution 306 indirectly via TWSA observations (indeed TWSA already contains the soil moisture signal in 307 themselves). 308 The STREAM model runs in a semi-distributed version in which the catchment is divided into s 309 elements, each one representing either a subcatchment with outlet along the main channel or an area 310 draining directly into the main channel. Each element is assumed homogeneous and hence constitutes 311 a lumped system. 312 The routing module (controlled by a parameter) conveys the and response components at 3. Extraction of input data. Precipitation, air , soil moisture and TWSA datasets data have to be 347 extracted for teach sub-basin of the study area. If characterized by different spatial resolution, these 348 datasets need to be resampled over a common spatial grid prior to be used as input into the model. 349 To run the STREAM model over the Mississippi river basin, input data have been resampled over the scale. To establish the goodness-of-fit of the model, the simulated river discharge and runoff 366 timeseries are compared against in situ river discharge and modelled runoff data. 367

Model Evaluation Criteria and Performance Metrics 368
The model has been run over a 13.5-year period split into two sub periods: the first 8 years, from 369 3. External validation aimed to test the capability of the model "to get the right answers for the 384 right reasons" (Kirchner 2006). In this respect, the capability of the model to reproduce 385 variables (e.g., fluxes or state variables) other than discharge and not considered in the 386 calibration phase, should be tested. As runoff is a secondary product of the STREAM model, 387 obtained indirectly from the calibration of the river discharge (basin-integrated runoff), the 388 comparison in terms of runoff can be considered as a further external validation of the model. 389 Runoff, differently from discharge, cannot be directly measured. It is generally modelled 390 through land surface or hydrological models. Its validation requires a comparison against 391 https://doi.org/10.5194/gmd-2020-399 Preprint. Discussion started: 25 January 2021 c Author(s) 2021. CC BY 4.0 License. modelled data that, however, suffer from uncertainties (Beck et al., 2017). Based on that, in 392 this study the GRUN runoff dataset described in the section 3.3 has been used for a qualitative 393 comparison. 394

Performance Metrics 395
To measure the goodness-of-fit between simulated and observed river discharge data three 396 performance scores have been used: 397 • the relative root mean square error, RRMSE: 398 values of KGE greater than 0.5 have been assumed good with respect to their ability to reproduce 416 observed time series (Thiemig et al., 2013). 417

RESULTS 418
The testing and validation of the STREAM model is presented and discussed in this section according 419 to the scheme illustrated in section 5.2. 420

Cross-validation 432
The cross-validation has been carried out over the six river sections illustrated in Figure 5 not used 433 in the calibration step. The performance scores on the top of each plot refer to the entire study periods; 434 the scores split for calibration and validation periods are reported in Table 2. For some river sections 435 the performance is quite low (see, e.g., river section 1, 2 and 5) whereas for others the model is able 436 to simulate the observed discharge data quite accurately (e.g., 7 and 8). In particular, for river sections 437 1, 2 even if KGE reaches values equal to 0.35 and 0.40 (for the whole period), respectively, there is 438 not a good agreement between observed and simulated river discharge and the R score is lower than 439 0.55 for both river sections. The worst performance is obtained over section 5, with negative KGE 440 https://doi.org/10.5194/gmd-2020-399 Preprint. Discussion started: 25 January 2021 c Author(s) 2021. CC BY 4.0 License. and low R (high RRSME). These results are certainly influenced by the presence of dams located 441 upstream to these river sections (see Table 1): the model, not having a specific module for modelling 442 reservoirs, is not able to accurately reproduce the dynamics of river discharge over regulated river 443 sections. Better performances are obtained over river sections 3 (slightly influenced by the presence 444 of dams in section 1 and 2), 7 and 8. In particular, over river section 7, the STREAM model 445 overestimates the observed river discharge highlighting that the model parameters estimated for river 446 section 6 are not suitable to accurately reproduce river discharge for river section 7 (see Figure 3 and 447 Figure 5). Conversely, the performances over river section 8, whose parameters have been set equal 448 to the ones of river section 10, are quite high (KGE equal to 0.71, 0.80 and 0.77 for the entire, the 449 calibration and the validation period, respectively; R equal to 0.83, 0.84 and 0.84 for the entire, 450 calibration and validation periods, respectively). 451 This finding, which could be due to different/similar interbasin characteristics, raises doubts about 452 the robustness of model parameters and whether it is actually possible to transfer model parameters 453 from one river section to another. A more in-depth investigation about the model calibration 454 procedure will be carried out in future studies. 455

External Validation 456
For the external validation, the monthly runoff time series provided by the GRUN datasets have been 457 compared against the ones computed by the STREAM model. For that, STREAM daily runoff time 458 series have been aggregated at monthly scale and re-gridded at the same spatial resolution of the 459 GRUN dataset (0.5°). The comparison is illustrated in Figure 6 for the common period 2003-2014. 460 Although the two datasets consider different rainfall inputs, the two models agree in identifying two 461 distinct zones, i.e., the western and the eastern area. Likely due to the calibration procedure, the 462 STREAM runoff map appears patchier with respect to GRUN and discontinuities along the sub-basin 463 boundaries (identified in Figure 3)  for basins with draining area lower than 160'000 km 2 (see section 7), i.e., at spatial/temporal 476 resolution lower than the ones of the TWSA input data (monthly, 160'000 km 2 ). This is an important 477 result of the study as it demonstrates, on one hand, that the model structure is appropriate with respect 478 to the data used as input and, on the other hand, the great value of information contained into TWSA 479 data that, even if characterized by limited spatial/temporal resolution, can be used to simulate runoff 480 and river discharge at basin scale. Hereinafter, the strengths and the main limitations of the STREAM 481 approach are discussed. data) into the model structure, allowing to take implicitly into account some processes, mainly 492 human-driven (e.g., irrigation, change in the land use), which might have a large impact on the 493 hydrological cycle and hence on total runoff; 2) the independence with respect to existing large scale 494 hydrological models such as, e.g., the evapotranspiration is not explicitly modelled. 495 2. Simplicity. The STREAM data-driven structure: 1) limits the input data required (only 496 precipitation, air , soil moisture and TWSA data are needed as input; LSM/GHMs require many 497 additional inputs such as wind speed, shortwave and longwave radiation, pressure and relative 498 humidity); 2) limits and simplifies the processes to be modelled for runoff/discharge simulation. 499 Processes like evapotranspiration, infiltration or percolation, are not modelled therefore avoiding the 500 need of using sophisticated and highly parameterized equations (e.g. periods not considered in the calibration, and (2) sharp discontinuities along sub-basin boundaries in 528 state flux, and parameter fields (e.g., Merz and Blöschl, 2004). 529 To overcome these issues, several regionalization procedures, as for instance summarized in Cislaghi 530 et al. (2020), could be conveniently applied to transfer model parameters from hydrologically similar 531 catchments to a catchment of interest. In particular, the regionalization of model parameters could 532 allow to: i) estimate discharge and runoff time series over ungauged basins overcoming the need of 533 discharge data recorded from in-situ networks; ii) estimate the model parameter values through a 534 physically consistent approach, linking them to the characteristics of the basins; iii) solve the problem 535 of discontinuities in the model parameters, avoiding to obtain patchy unrealistic runoff maps. 536

CONCLUSIONS 537
This study presents a new data-driven model, STREAM, for runoff and river discharge estimation. 538 By using as input satellite data of precipitation, soil moisture and terrestrial water storage anomalies, 539 the model has been able to provide accurate daily river discharge and runoff estimates at the outlet 540