## 5 Conclusions  
A major objective of the joint DA approach proposed in this paper is to improve water variables, in addition to vegetation variables. The majority of the ISMN stations (used here as the reference dataset) presented an improvement in the SSM error metrics due to DA, especially when the joint assimilation is adopted. Both in terms of SSM random errors and anomaly correlation coefficients, the number of stations that improved their performance thanks to the DA technique was larger than the number of stations showing a degradation. The joint assimilation was proven to combine the performance of each univariate assimilation and to improve the model performance in almost all the western locations.  
This experiment sheds some light on the potential of merging a set of satellite-based observations within a land surface model to improve our characterization of carbon, energy, and water states and fluxes. Additional DA techniques could be investigated in future studies to combine such observations. For instance, [PERSON] et al. [8] showed that an Ensemble Squared Root Filter performed more efficiently than the Simplified Extended Kalman Filter when jointly assimilating LAI and soil moisture. This DA technique could be used for assimilating GLASS LAI and SMAP SSM and the results could be compared to the findings of this paper.  
The SMAP satellite mission provides soil moisture products at two different resolutions (36 km and 9 km). Here, only the 36 km product was used because of computational constraints, but future work could verify the efficiency of assimilating higher resolution data. Future research should also investigate the impact of the proposed DA techniques on other vegetation and water variables across different regions of the world.  
Conceptualization, A.R. and V.M.; methodology, A.R., V.M. and X.Z.; software, D.M.M.; validation, A.R.; formal analysis, A.R.; investigation, V.M., P.H. and T.S.; resources, D.M.M.; data curation, A.R.; writing--original draft preparation, A.R.; writing--review and editing, V.M., X.Z. and D.M.M.; visualization, A.R.; supervision, V.M.; project administration, V.M., P.H. and T.S.; funding acquisition, V.M. All authors have read and agreed to the published version of the manuscript.  
The research was funded by NASA Modeling, Analysis, and Prediction Program (MAP) program, grant number is 80 NSSC17K0109.  
The study did not require any ethical approval.  
Not applicable for this study.  
The original analysis done by the authors is reported in this article. The dataset used for data assimilation and validation can be found in the following links, which are open for the public. GLASS LAI data: [[http://glass.umd.edu/](http://glass.umd.edu/)]([http://glass.umd.edu/](http://glass.umd.edu/)) (accessed on 9 December 2021); SMAP data: [[https://earthdata.nasa.gov/](https://earthdata.nasa.gov/)]([https://earthdata.nasa.gov/](https://earthdata.nasa.gov/)) (accessed on 9 December 2021); GLEAM data: [[https://www.gleam.eu/](https://www.gleam.eu/)]([https://www.gleam.eu/](https://www.gleam.eu/)) (accessed on 9 December 2021); FLUXCOM data: [[http://fluxcom.org/](http://fluxcom.org/)]([http://fluxcom.org/](http://fluxcom.org/)) (accessed on 9 December 2021); ISMN data: [[https://ismn.geo.tuwien.ac.at/en/](https://ismn.geo.tuwien.ac.at/en/)]([https://ismn.geo.tuwien.ac.at/en/](https://ismn.geo.tuwien.ac.at/en/)) (accessed on 9 December 2021). Further inquiries can be directed to the corresponding authors.  
The authors declare no conflict of interest.