Figure 3 . a) Sensitivity analysis of different model
output variables to varying sets of parameters (hyd=hydraulics, soil,
veg=vegetation, and all together). The a priori dispersion of the model
parameters, for each output variable, is compared to the reported
uncertainty for the in-situ / RS product estimates, previously described
in the Cal/Eval data section (no uncertainty estimation is provided for
the soil moisture root zone product given absence of this estimate for
the Amazon region). b) Correlation matrix (Pearson coefficient)
between performance metrics (KGE) for the six analyzed variables, by
varying all parameters together. KGE values are computed by comparing
multiple runs with the reference simulation (i.e.,
the initial run with the initial
parameter set as defined in Supporting Information Table S2). Q =
discharge, h = water level, A = flood extent, TWS = total water storage
anomalies, ET = vegetation evapotranspiration, W = soil moisture.
How do dispersions in model outputs relate to
uncertainties in
observations?
Some variables present in-situ/RS observations that have uncertainties
significantly lower than the overall dispersion of the model, e.g., 25
% for discharge observations, while model overall parameter dispersion
is ~160%. This pattern is also found for water level
and TWS estimates, and implies that these observations might be useful
to constrain the model. Nonetheless, uncertainties in RS products of
flood extent (~50%) and vegetation ET
(~23%) are in the same order of magnitude of model
overall parameter dispersion, which might hamper their contribution for
model calibration, due to their high uncertainties.
Which sets of parameters are related to which
variables?
The overall model dispersions are related to different sets of
parameters: discharge, water level, and TWS are more strongly related to
hydraulics and soil parameters, and to a lesser extent to vegetation
parameters. Flood extent estimates are strongly related to hydraulic
parameters, and less to soil and vegetation. As expected, soil moisture
and vegetation ET estimates relate to vertical water balance processes,
being insensitive to hydraulic parameters. Soil moisture (W) is more
sensitive to soil parameters, while vegetation ET is more sensitive to
vegetation parameters. These results are very useful to understand the
RS-based calibration experiments addressed in section 3.2. For instance,
if model calibration with ET or W is achieved through optimization of
hydraulic parameters, it would highlight that the model would have
“gotten the right results for the wrong reasons”. The same would occur
if flood extent calibration targeted soil or vegetation parameters.
Which variables are
inter-related?
By varying all parameters together, there is a high correlation (greater
or equal to 0.4) between the performance of discharge and flood extent,
water level and flood extent, flood extent and TWS, and ET and TWS
(Figure 3b). High correlations between discharge, water level and flood
extent are expected because of their strong association through river
transport processes. However, correlation between discharge and water
level is not too high (0.30), and this is
probably due to high uncertainties
in hydraulic parameters, and to the large distance separating the water
level virtual station and the streamflow gauge. Furthermore, high
correlations between TWS and flood extent might be related to surface
water storage dynamics which are especially relevant in regions with
floodplains.
In general, a high correlation between variables in Figure 3b should be
reflected in positive results when calibrating with a given variable and
evaluating with the other highly correlated variable (single-variable
calibration). This may also indicate that observations of these
variables are redundant if used simultaneously in a multi-calibration
framework. However, high
correlations in Figure 3b followed by deterioration after the
single-variable calibration process might indicate structural errors in
the model, or in the observations. We stress however that this study did
not attempt to quantify structural errors. Conversely, low correlations
in Figure 3b, followed by improvement in performances with the
calibration with multiple variables, might indicate complementarity
between variables.
Model calibration
How RS-based model calibration improves discharge
estimates?
For the evaluation time period (2006–2008 for discharge, flood extent,
TWS, ET and 2013–2014 for water level and soil moisture), calibration
with all RS products led to improvements in discharge estimates (Figure
4a). For the calibration time period (2009-2012), TWS, ET and soil
moisture RS products also led to improvements in discharge estimates,
while water level and flood extent led to discharge overestimation in
wet periods (Figure 4a). This could be due to high uncertainties in the
observations (Figure 3a), but if this was the case, it would also be
reflected in a poor performance for water level and flood extent when
discharge is the target variable for calibration (Figure 4b), which does
not occur. Therefore, calibration with discharge leads to reasonable
parameter sets for the performance of discharge itself, and also water
level and flood extent. However, it does not lead to the best hydraulic
arrangement, which might be achieved more successfully when calibrating
with water level or flood extent.
Nonetheless, both water level and flood extent observations are
representative of a specific location in the basin (Figure 2), and
calibration with these variables might lead to the best parameter
arrangement for these locations, but not for the whole watershed. A more
spatially-consistent use of these observations should improve their
usability to constrain models and improve discharge estimates, such as
the studies of Kittel et al. (2018), that used radar altimetry
measurements at 12 locations in the basin, Schneider et al. (2017), that
used data from 13 virtual stations, or Liu et al. (2015), that used
water level measurements at four virtual stations, and flood extent for
stream segments at different locations in the basin.
RS variables as TWS, ET, and soil moisture were able to improve
discharge estimates by S =13.7%, S= 52.9%, and S = 27.0% (Figure 5-I,
calibration period) or S = 27.4%, S= 6.1%, S= 12.3% (Figure 5-II,
evaluation period), which is especially relevant in the context of the
Prediction in Ungauged Basins initiative (Hrachowitz et al., 2013;
Sivapalan et al., 2003). These results agree with previous studies, such
as López et al. (2017) that found good performances in discharge
estimates by model calibration with GLEAM ET and ESA CCI soil moisture,
or Nijzink et al. (2018), that found improvements in discharge by using
soil moisture products (AMSR-E, ASCAT) and TWS from GRACE.
The multi-variable calibration experiment considering all variables
except discharge (Figure 5b) resulted in a Skill Score of S = 17.4% for
discharge in the evaluation period. This is relevant for estimating
discharge in poorly gauged basins. Nonetheless, for the calibration
period, Skill Score had a low value (S = 1.7%), reflecting some
limitations when retrieving discharges, probably because of potential
trade-offs between variables (Koppa et al., 2019). RS uncertainties
could be better incorporated into the calibration, for instance by using
bias-insensitive metrics (e.g., Demirel et al., 2018; Zink et al., 2018;
Dembele et al., 2020), or explicitly including them into the objective
functions (Aires, 2014; Croke, 2009; Foglia et al., 2009; Peña-Arancibia
et al., 2015).