## 3 Results
### LDAS-Monde Impact  
#### 3.2.1 Model Sensitivity to the Observations  
The Jacobians are governed by the physics of the model and their examination is crucial to understand the data assimilation system performances [19; 40; 41; 75]. Mean Jacobians values over January 2010 to June 2018 for the whole domain of Burkina-Faso are presented in Table 3.  
The top row of Table 3 represents the impact of perturbating individually each control variable of LDAS-Monde (LAI, soil moisture from layers 2 to 8), by a (positive) small amount at the beginning of an assimilation window, on the model equivalent of SSM at the end of the assimilation window (i.e., 24 hours later). As the model equivalent of SSM is the second layer of soil (\(W_{2}\) between 1 and 4 cm depth), it is expected that the sensitivity of SSM to changes in soil moisture of that layer (\(\frac{\delta SSM}{\delta w_{2}}\)) will be higher compared to those of the other layers of soil (\(\frac{\delta SSM}{\delta w_{3}}\) to \(\frac{\delta SSM}{\delta w_{8}}\)). As seen in Table 3, the mean Jacobian value is clearly higher for \(W_{2}\) than for any other layers. The model sensitivity to SSM decreases with depth, suggesting that the assimilation of SSM will be more effective in modifying soil moisture from the first layers than the deeper layers. Over Burkina-Faso, mean Jacobian values with respect to SSM observations (Table 3, top rows) range from 0.5372 to 0.0020 for layers, \(w_{2}\) to \(w_{8}\), respectively and is \(-0.0006\) for LAI (\(\frac{\delta SSM}{\delta LAT}\)). This negative value indicates that a small positive increments of LAI will generally lead to a decrease of SSM (\(w_{2}\)). Table 3, bottom row, shows the same for LAI: The sensitivity of LAI to changes in LAI (\(\frac{\delta LAI}{\delta LAT}\)) and in soil moisture (\(\frac{\delta LAT}{\delta w_{2}}\) to \(\frac{\delta LAT}{\delta w_{8}}\)), from left to right, respectively. The sensitivity of LAI and in soil moisture suggests that the control variables related to soil moisture will also be impacted by the assimilation of LAI. Table 3 also illustrates that the assimilation of LAI will be more effective in modifying soil moisture from layers 4 to 6 than from the surface layers. Figure 6 illustrates the seasonal cycles of the Jacobians averaged over January 2001 to June 2018. For sake of clarity, only \(\frac{\delta LAI}{\delta LAI}\), \(\frac{\delta SSM}{\delta LAT}\), \(\frac{\delta SSM}{\delta w_{4}}\), \(\frac{\delta SSM}{\delta w_{6}}\), and \(\frac{\delta SSM}{\delta w_{8}}\) are presented. Looking at the SSM Jacobians, the depth impact already highlighted by Table 3 is visible (i.e., less sensitivity to surface soil moisture at deeper layers than at upper layers). From Figure 6, a seasonal impact is also visible, \(\frac{\delta SSM}{\delta LAT}\) are higher in winter months than in summer months, suggesting that LDAS-Monde will be more efficient at assimilating SSM during winter months. Similarly, from \(\frac{\delta LAI}{\delta LAT}\), one may notice a dual seasonal cycle; LDAS-Monde will be more efficient at assimilating LAI during April to June, and October to November. It is worth mentioning that the configuration where ERA5 is used to force LDAS-Monde was considered to present the [PERSON] evaluation. Using the ERA-Interim configuration leads to similar results (not shown).