Introduction

The accurate representation of hydrologic processes in mathematical models remains a key challenge in water resources research and applications (Baroni et al., 2019; Clark et al., 2015; Kirchner, 2006; Nearing et al., 2016; Semenova & Beven, 2015) due to uncertainties in model structure (Wagener et al., 2003), parameterization (Gharari et al., 2014; Shafii & Tolson, 2015), and observations (Di Baldassarre & Montanari, 2009). These uncertainties might lead to inaccurate predictions of hydrological variables for water resources and natural hazards management (Grimaldi et al., 2019; Montanari & Koutsoyiannis, 2014), and for quantification of impacts of climate change and anthropogenic effects on the water cycle (Haddeland et al., 2006; Teutschbein & Seibert, 2012; C. Y. Xu et al., 2005). This problem has led for instance to initiatives to better constrain the terrestrial water budget by fusing models and Earth Observation datasets (M. Pan & Wood, 2006; Pellet et al., 2019).
Traditionally, hydrological models are calibrated against gauged streamflow data, which might hamper predictions in ungauged sites, since it does not guarantee an accurate representation of other water cycle components (e.g., soil moisture and evapotranspiration), thus leading to uncertainty in hydrologic predictions (Hrachowitz et al., 2013). Moreover, many parameter sets can provide equally acceptable performances for streamflow evaluation (i.e., the equifinality thesis), but they might be “right for the wrong reasons” (Beven, 2006; Kirchner, 2006). Several solutions have been proposed to improve process representation and reduce uncertainty in model predictions, such as the generalized likelihood uncertainty estimation (Beven & Binley, 1992), dynamic identifiability analysis (Wagener et al., 2003), multiscale parameter regionalization (Samaniego et al., 2010), and multi-objective calibration (Yapo et al., 1998). However, these are ongoing developments, and stand out as one of the twenty-three unsolved problems in hydrology (Blöschl et al., 2019): “how can we disentangle and reduce model structural/parameter/input uncertainty in hydrological prediction?”.
In addition to the presented solutions, an alternative is the use of complementary datasets besides streamflow observations for model calibration (e.g., Crow et al., 2003; Franks et al., 1998; Lo et al., 2010; López et al., 2017; Rajib et al., 2016), data assimilation (e.g., Brêda et al., 2019; Houser et al., 1998; Mitchell et al., 2004; Paiva et al., 2013; Pathiraja et al., 2016; Reichle et al., 2002; Vrugt et al., 2005), or validation (e.g., Alkama et al., 2010; Motovilov et al., 1999; Neal et al., 2012; Siqueira et al., 2018). Such approaches are promising to improve representation of processes in hydrological models (Clark et al., 2015), reduce uncertainty in hydrological predictions (Gharari et al., 2014), understand equifinality (Beven, 2006), and perform predictions in ungauged or poorly-gauged sites (Sivapalan et al., 2003). However, distributed data of complementary hydrological variables (e.g., evapotranspiration, soil moisture) are scarce, and in-situ measurements present poor spatial and temporal representativeness.
In this context, remote sensing (RS) observations have stood out in the last decade because of their increasing spatial and temporal resolutions, free availability in many cases, and capability to record less monitored hydrological variables such as soil moisture, evapotranspiration, and terrestrial water storage (Lettenmaier et al., 2015). For instance, GRACE mission provided monthly estimates of changes in water storage on a global coverage with an accuracy of 2 cm when uniformly estimated over land and oceans (Tapley et al., 2004). Missions such as SMOS, SMAP, AMSR-E and ASCAT were estimated to provide soil moisture data with a median RMSE of 0.06-0.10 m³/m³ for the CONUS (Karthikeyan et al., 2017). Altimeters such as Envisat, Jason-2 and ICESat-1 and ICESat-2 can yield water level data with an accuracy ranging from 0.04 m to 0.42 m, involving trade-offs between temporal resolution from 10 to 91 days, and cross-track separation from 15 to 315 km (Jarihani et al., 2013), while the future SWOT mission will provide at least one water level measurement every 21 days for global rivers wider than 100 m (Biancamaria et al., 2016).
Although previous studies have analyzed the value of integrating RS data into hydrological modeling through calibration or data assimilation (see review by Xu et al., 2014 and Jiang & Wang, 2019), this topic has not been fully explored to its potential yet. Therefore, in section 1.1, we present major knowledge gaps in the context of RS-based calibration of hydrological models through an extensive literature review. In section 1.2, we describe the aims and contributions of this study.

Literature review on calibration of hydrological models with RS data

A comprehensive, yet non-exhaustive literature review of studies that used RS datasets for parameter estimation in hydrological models is presented in this section and summarized in Figure 1. A total of 62 research articles was found (Supporting Information Table S1). Most publications involved large study areas (> 1000 km²), which is expected because of the usual coarse resolution of RS products. Most studies used RS-derived evapotranspiration for model calibration, followed by soil moisture (Figure 1b), but there were also attempts for calibration of up to eight different RS-derived variables (Nijzink et al., 2018). This indicates a still existent knowledge gap regarding which RS-derived variables are more useful for model calibration. Indeed, many recent studies have investigated the added value of RS-derived information to calibrate hydrological models (Figure 1d; Table S1).
Most of the studies (69.35%) used only one RS product for model calibration (Figure 1e, in black), while twelve studies (19.35%) used two products, and five (8.06%) used three products. Only few studies used more than three RS products for model calibration (Demirel et al., 2019; Nijzink et al., 2018). Some studies addressed the use of RS data to estimate discharge in ungauged basins (Kittel et al., 2018; Sun et al., 2010), while others focused on narrowing the parameter search space, and thus equifinality reduction, by combining multiple variables for calibration (e.g., Nijzink et al., 2018; Pan et al., 2018). This is confirmed by Figure 1e (in blue), which demonstrates that the vast majority of researches used two variables for calibration (in general, discharge and a RS-derived variable). Within these studies, some analyzed model performance in terms of discharge only, while others considered different variables (Figure 1e, in red), providing a more comprehensive discussion on inconsistencies of hydrological models (e.g., Koch et al., 2018; Li et al., 2018).
Regarding how RS is incorporated into the model calibration procedure (Figure 1h), 65.6% of the articles used RS-based spatially distributed information, thus calibrating the model with distributed objective functions (e.g., pixel-by-pixel or by sub-basin). Within these studies, bias-insensitive functions have been recently introduced (e.g., Koch et al., 2018; Demirel et al., 2018; Zink et al., 2018; Dembele et al., 2020), being important for reducing the impact of RS data uncertainty on the parameter estimation procedure. The remaining publications (34.4%) incorporated RS data as an average for the whole basin.
Finally, there is still a need for more studies in tropical regions (especially South America) (Figure 1c), which have particular hydro-climatic characteristics, and so have different requirements than temperate regions on model process representation (e.g., snow-related processes might not be so relevant in some tropical areas, whereas an accurate representation of floodplains might be). In the case of basin with complex river-floodplain interactions as in the Amazon, an accurate flood wave routing method is required to correctly depict the water transport along the drainage network. Our analysis shows that most studies used simple flood wave routing schemes such as kinematic wave or Muskingum (Figure 1g). Only 10.4% attempted to couple hydrologic and river hydrodynamic models, highlighting the necessity of better understanding the applicability of RS-based calibration in basins with major flat regions with wetlands (Hodges, 2013; Neal et al., 2012; Pontes et al., 2017).