## 4 Discussion  
The results from this work showed that the joint assimilation of GLASS LAI and SMAP SSM has the potential to improve the estimation of vegetation variables (e.g., ET and NEE) and water variables (SSM and RZSM) more efficiently than univariate DA approaches. All three DA techniques have an impact on the model estimation of LAI, ET, NEE, SSM, and RZSM. For all these variables, the joint DA clearly produces a combination of the results obtained by the two univariate DAs.  
Although the impact of DA on several land surface variables is often evident, it may be minimal in some cases, as proven by previous studies. For instance, [PERSON] et al. [24] showed changes in LAI within a range of \(-0.9\) to \(0.9\) and changes of \(-0.04\) to \(0.04\) mm\({}^{3}\)/mm\({}^{3}\) in RZSM after the application of LAI assimilation. Another study by [PERSON] et al. 2012 [67] showed changes in SSM ACC of the order of 9% due to SSM DA, which are comparable to the improvements discussed in Section 3.4. The impact of SMAP DA on RZSM is even more limited, corroborating findings from several previous studies [61; 62]. [PERSON] et al. [61] showed that SMAP DA improves correlations with soil mois  
Figure 10: Same as Figure 8, but for RZSM.  
ture ground observations up to 7% in the top soil layer, but no significant improvements were observed in the 0-30 cm layer.  
The results from this experiment align with previous findings showing an improvement in the random error of several land surface variables thanks to the application of LAI DA, SSM DA, and joint DA. Specifically, GLASS LAI showed an overall improvement of ET compared to the OL simulation, whereas SMAP DA showed a degradation in the southwestern region, where SMAP is known to have detection limitations, as demonstrated by [PERSON] et al. [64]. Such a degradation translated into the joint DA ET estimation, which, however, presented an improvement in the remainder of CONUS (thanks to the LAI DA).  
LAI DA, SMAP DA, and the joint DA were also able to reduce the NEE random error over most of CONUS except for some western regions, mainly characterized by shrublands and grasslands. Furthermore, both LAI DA and the joint DA were able to improve NEE correlations (computed with respect to the FLUXCOM NEE reference) over the OL run across all vegetation types, but SMAP DA presented small impact on NEE anomaly correlations. This was also evident in past studies, such as that of [PERSON] et al. [24], who showed an improvement in ET and NEE over the central plains thanks to LAI DA.  
For soil moisture, the LAI assimilation was shown to be particularly efficient over croplands, as also demonstrated by [PERSON] et al. [24]. SMAP DA was proven to reduce the random error in SSM and RZSM, which corroborates recent findings over Oklahoma by [PERSON] et al. [64]. The reduction in SSM random errors was found to be lower in forested areas, compared to locations characterized by short-rooted plants, which aligns with past studies. As an example, [PERSON] et al. [8] showed that, by using LDAS-Monde: i) the impact of soil moisture data assimilation was more consistent in areas with sparse vegetation and ii) negative correlations were observed between model and observed SSM over arid regions. Additionally, [PERSON] et al. [31] showed that the joint assimilation of LAI and soil moisture with LDAS-Monde had a small impact on SSM (1-4 cm depth) under severe climatic condition (heat waves and droughs). In terms of correlation coefficients, the proposed DA approaches were able to improve SSM at the majority of the validation sites, but only at a few stations for RZSM. This may be due to the inability of the satellite observations to improve the dynamic range of root zone soil moisture, which is much slower than the SSM one. Analyses based on land cover and soil type may help to shed some light on this topic and temporal aggregations may help to improve such anomaly correlation coefficients.