Discharge at the Sola Basin Gauge (Zywiec) for the summer period (1 August to 31 October 2014) and winter period (1 November 2014 to 30 April 2015) were simulated using the HBV model. The analysis was performed in four steps:
Precipitation inputs and simulation results using the HBV model with the observed precipitation (
) and corrected satellite precipitation without assimilation (
) are presented in Figure 4
and Figure 5
. Figure 6
and Figure 7
compare the observed (
) and satellite soil moisture products (
) with the averaged ensemble of the perturbed
without the BC method (avg.
perturbed), the averaged ensemble of perturbed
with the BC method (avg.
perturbed), the averaged ensemble of the HBV simulations with the assimilation procedure using EnKF-BC (avg.
), simulations with the assimilation procedure using EnKF (avg.
, and another using only the corrected satellite soil moisture product without assimilation,
. The figures include the satellite soil moisture product, whose assimilation received the best assessment. Each figure corresponds to one season (summer or winter) of the study period (July 2014 to April 2015). Additionally, each figure contains the
4.3.1. Simulating Discharge with Bias-Corrected Satellite Precipitation without Assimilation
In the first step of the analysis, the effects of the corrected satellite precipitation (
on the accuracy of the HBV model simulation in summer (Figure 4
) and winter (Figure 5
) were examined.
was compared with the HBV simulation
(first input option from the top in Figure 2
) and HBV simulation with
) (second input option from the top in Figure 2
). In both seasons, a slight increase in the efficiency of the HBV model, using satellite precipitation as forcing data,
), was observed. In the summer, the
improved the model
from −0.045 to 0.103 and from −0.185 to 0.195 in the winter compared to
. Furthermore, the highest quantitative and qualitative discrepancy between observed and satellite precipitation was registered in August, which was associated with convective instability in the atmosphere. Differences in the quantitative estimation of precipitation affected the discrepancy between the
. A noticeable improvement in the model simulation using satellite precipitation was observed in the second half of September and October.
In winter, with negative air temperatures and snow cover, quantitative information on the precipitation indirectly influenced the simulation. The main determinant of runoff is groundwater sources, however, when the snowpack disappears and the thawing of topsoil layers begins, surface and sub-surface runoff also play a major role. Therefore, at the end of the winter season during the rainy spring flood, an increase in the accuracy of the simulated hydrographs was seen, due to the impact of the corrected satellite precipitation.
4.3.2. Simulating Discharge Using Two Methods, with Bias-Corrected Satellite Soil Moisture or with the Assimilation Procedure
The best satellite precipitation product for modeling
, and therefore
was used in further analyses. The impact of the assimilation of these observations of soil moisture (
) (fifth input option from top in Figure 2
) in improving the accuracy of the HBV simulation using EnKF-BC as an averaged ensemble, avg. QHBV-BC-EnKF-BC
(solid red line in Figure 6
and Figure 7
) was determined, with results provided in Table 3
. Model simulations using the assimilation procedure were compared to the assimilation of soil moisture (
) (fourth input option from top in Figure 2
) using EnKF, avg.
(solid orange line), to the simulation using only BC satellite soil moisture as an input to the HBV model,
(dashed black line) (third input option from top in Figure 2
), as well as to the HBV simulations with observed precipitation,
(dashed green line) (first input option from top in Figure 2
). The calculations were made separately for the two satellite soil moisture products and the summer and winter seasons (left and right parts of Table 3
, respectively). The upper part of Figure 6
and Figure 7
compares the soil moisture graphs (generated by the HBV model), θHBV
(dashed green line), the unperturbed satellite observations with removed bias,
(dashed black line), the averaged value of perturbed satellite observations without bias correction, avg. H14
(perturbed) (solid orange line), and the averaged value of bias-free perturbed satellite soil moisture, avg.
(perturbed) (solid red line).
In summer, the best overall simulation model for the period of 06:00H, 1 August 2014 to 23:00H, 31 October 2014, was the HBV model using the
precipitation product with EnKF-BC assimilation of the
. As soil moisture dynamics are complex, only the effects of soil moisture on runoff generation at the basin scale were modeled using the HBV. This was based on a modification of the Bucket Theory, which assumes a statistical distribution of storage capacities in a basin [43
]. The rate of evaporation depends on the potential evaporation and soil water content, and similarly, the rate of percolation depends upon rain intensity and soil water content. This implies that the rate of contribution of runoff depends on soil moisture, which is a main part of the model. The largest runoff was attained in the HBV model when all the boxes were full and contributed to the runoff volume. In this case, the routine’s equations lead to maximum soil moisture storage. Precise estimation of this physical quantity (assimilation of the satellite soil moisture observation) greatly affected the simulation of flow during floods.
A good example was the summer floods which occurred from 19:00H on 22 September to 11:00H on 4 October, and from the 23:00H on 21 October to 08:00H on 26 October (Figure 6
). The state variable of the assimilated satellite soil moisture
served as an observation affecting the value of the runoff coefficient.
Moreover, the error in estimating the largest observed flows, in the second part of the summer season, was reduced by using the HBV model with the EnKF-BC (avg. ), resulting in a closer match between the simulated hydrograph and observed values in the last step of the simulation. Such situations were important in the process of estimating a set of initial variables at run-up when using the HBV model in forecasting mode. Of course, too high of an estimation of soil moisture resulted in an overestimation of the flow, which was visible in the period from 12:00H, 11 August to 02:00H, 26 August 2014.
In the summer, the EnKF-BC clearly impacts the simulation of hydrographs compared to the EnKF method, i.e., avg. (, m3s−1, ) vs. avg. (, m3s−1, ). Correction of the ensemble perturbation bias within the EnKF-BC filter reduced soil moisture values in the HBV model, and thus reduced the outflow, especially during convective precipitation, e.g., comparison of hydrographs avg. (solid red line) vs., (orange solid line) from 12:00H, 25 August 2014 to 29 August 2019, or from 19:00H, 22 September 2014 to 11:00H, 4 October 2014.
In summer, the positive impact of the correction and assimilation of the satellite products can be seen in the increased accuracy of the simulated hydrographs. However, in winter (i.e., from 06:00H, 1 November 2014 to 23:00H, 30 April 2015), the Sola Catchment was covered with snow, and air temperatures were negative, thereby deteriorating the quality of the and satellite products.
This resulted in an increase in the
and a decrease in the
when compared to the simulations generated by the HBV model in the summer (Table 3
). In winter, the best simulation result was obtained by the assimilation of
), which proved to be more accurate than the HBV model for
without the assimilation procedure,
The quality of the soil moisture estimation from ASCAT is poor when there is snow cover. The H14
/SM-DAS-2, as an ECMWF product, is validated against ground soil moisture measurement from in situ data (SSM), among others, with a single station in Poland located in the lowland [66
]. The comparison between the observed data (SSM) and the H14
product uses the following statistical scores: Mean bias, standard deviation, correlation coefficient and root mean square difference. A low correlation coefficient was found in Poland (0.61). Therefore, for this station, the winter and late summer data are filtered when temperatures are below +3 °C.
There were five hydrographs produced for winter river flow (Figure 7
, observed flow;
, flow simulated by HBV with precipitation;
, flow simulated by HBV with and ;
Avg. and using and assimilating ,
And avg. using and assimilating with the creation of an unbiased ensemble of model states.
shows that from November to mid-March, all simulated hydrographs underestimated
, yet overestimated the flood event in April. Pre-processing with the assimilation procedure more effectively estimated the flood in March and April of 2015 when compared to
, as shown by the large discrepancy between the dashed blue line with double dots (
), dashed green line (
) and solid red line (avg.
) in Figure 7
. After the disappearance of the permanent snow cover at the end of March and into April, the positive impact of the satellite precipitation product, i.e.,
was evident. There was a slight difference in the March and April hydrographs between
). The influence of the satellite soil moisture and its correction and assimilation was visible only to a small extent, i.e., avg.
) vs. avg.
In Figure 7
, the negative influences of the DA procedure on the outflow from the lower linear reservoir can be seen. There is a clear increasing trend in discharge. In the HBV model, the runoff generation routine was the response function that transformed excess water from the soil moisture zone into the runoff. The water from the soil moisture zone was added to the upper box and percolated towards the lower box, representing the groundwater storage of the catchment contributing to the base flow. With a high yield from the soil, percolation was not sufficient to keep the upper reservoir empty. The generated discharge contributes directly to the upper reservoir, which represents drainage through more superficial channels. The lower reservoir, on the other hand, represents the groundwater storage of the catchment, contributing to rises in base flow. The consequence is a constant trend of flow in Figure 7
. In order to optimize (decrease) the base flow, especially in the winter season (Figure 7
), the procedure would likely need to be extended to interactively update past and present model states (e.g., content of upper and lower boxes in the response routine) to improve model initial conditions, and hence flow forecasts.
4.3.3. Examples of Hydrological Updating the HBV Model Using EnKF-BC and Simulation of the HBV Model in Forecast Mode for the Sola Basin at Zywiec for Selected Flood Events
The last element of the study evaluated the possibility of using satellite products to update hydrological forecasts and to compare forecasts carried out with and without updating between summer and winter. One flood event occurring in each of the summer and winter periods was selected. The HBV model was run in forecast mode in the last step of the updating procedure. The input to the forecast was generated using the hindcast method. For the events examined, the same length of updating (120 h) and window forecast (72 h) were used. The updated input consisted of the corrected satellite precipitation,
for summer, and
for winter events using the EnKF-BC (according to the assessment of the accuracy of the HBV model shown in Table 3
; fifth input option from the top in Figure 2
). The forecasted input consisted of the observed precipitation,
(hindcast method), and the HBV model was run without the assimilation procedure (first input option from the top in Figure 2
). The results showed that forecasts preceded by updating achieved better values of
than the forecasts without updating (Table 4
The performances of the simulations in forecast mode are shown in Figure 8
(summer) and 9 (winter). For each flooding event, three hydrographs were compared:
—observed hydrograph (dotted blue line);
—forecasted hydrograph without updating (solid green line);
and avg. —averaged forecasted hydrograph with updating (solid red line) with the ensemble hydrographs (solid gray lines).
The flood event occurring between 06:00H on 26 September 2014 and 06:00H on 29 September 2014 is an example of a good simulation in forecasting mode. The success is likely due to the effective updating using the EnKF-BC method, which is highlighted by the difference in starting positions on the observed hydrograph (dotted blue line), the averaged hydrograph with updating by the EnKF-BC (solid red line), and the hydrograph without updating (solid green line). In this case, a large part of the forecast horizon was within the ensemble forecast (gray lines) (Figure 8
). The recession in the second part of the hydrograph was smaller than that of the forecast without updating, and the forecast error in the last step of the horizon was comparable.
For the winter updating and forecasting process, two key observed quantitative parameters tied to the forecasted runoff were not available. These included the surface distribution of snow cover and the snow water equivalent. Information about these parameters was only contained within state variables that were recalculated using the snow model that was implemented in a subroutine of the HBV model. Within an update, the satellite snow observations were not assimilated. The hydrological simulation in the forecasting mode of a rainy spring flood (06:00H on 30 March 2015 to 06:00H on 2 April 2015) (Figure 9
) is an example of the effective use of the correction of satellite precipitation data and the assimilation of corrected soil moisture within the updating procedure. Calculations during the update of the matrix of state variables allowed for better precision when generating the ensemble forecast through the HBV model, compared to HBV simulations without updating, which is evident from the difference in starting positions between hydrographs.