Reply on RC2

This study aims at simultaneously assimilating water level observations from static sensors and EO-derived flood extent for improving real-time flood modeling. I have really enjoyed reading this paper, which deals with a timely and important issue. The authors showed the potential of the joint assimilation of water level observations from both static sensors and satellite images. I think this study fits the overall focus of HESS. However, I do have a number of major comments that hopefully will help the authors in strengthening their manuscript.

In this work, a DA framework supported by heterogeneous observations coming from both local water level observations (i.e. stage gauges) and spatially distributed information gathered from satellite images -is proposed and tested. This research seeks to develop a more flexible DA scheme that may value all available sources of observations for distributed flood modelling updates. The aim of this work is to mitigate flood prediction uncertainties by combining heterogeneous data and an integrated topographic-hydrologichydraulic modelling approach, while maintaining inundation forecasting robustness, scalability and numerical stability. In achieving this goal, novel scientific advances and technical challenges of EO-driven DA approaches for flood prediction are investigated and in particular: A methodology for updating the state variable from multiple local stage gauges observations of a hydraulic model for distributed flood routing in floodplain domains; the gathering of spatially distributed water level observations by means of flood extension processing and detection from satellite images, also adopting GIS algorithms for overcoming the issues of the different resolutions between the ensembles of the flood extents retrieved from the satellite derived images and the ones generated from the hydraulic model simulations. " " ID: R2_03

Referee comments:
-The proposed DA approach should be better described in the paper. What I think is still missing is the information about the size of each DA variable/matrix (e.g. the size of the model covariance matrix P) and how the merging between hydraulic model and DA is performed. Observations from static sensors are used to update the channel water level (1-D model), while satellite images are used for updating the floodplain water level (2-D model). The assimilation of one observation at a given time step allows updating not only the water level at that specific point along the channel but also upstream and downstream. This is partially solved by introducing the distributed gain (initially proposed in Madsen and Skotner, 2005), but how then the updated upstream flow will numerically influence the downstream water levels? It would be nice to show the covariance matrix P at different time steps in case of assimilation of only static sensor, only SI, and joint assimilation. This will allow visualizing the distributed effect of assimilating heterogenous observations at once.

Authors' reply and actions:
We thank the referee for the useful comments. We extended Section 2.2.1.1 for better explaining how the model updating is performed at the assimilation steps. The model updating are applied "serially", allowing to reduce the DA variable matrix to sequences of one observation at time and avoiding potential spurious correlations of observations located far from each other. This serial updating is commonly used also in observation localization techniques where, for example, at each point of the domain, the covariance of the observation is divided by a term that is inversely proportional to the inverse of a distance-based correlation. We also clarified that in both cases of assimilating satellite derived images or stage gauges observation, the model updating is performed in both channel and floodplain cells. We also set a new simulation in which only the upstream SG observations are observed in order to show the performance in the downstream part of the basin, far from the observation locations. Finally, we also add 2 new figures to show the distribution of the covariance matrix at specific time step ID: R2_04

Referee comments:
-The abstracts read well but I would include a couple of brief sentences summarizing (quantitatively) the benefits of the joint assimilation (e.g. "Our findings reveal that assimilating observations from static sensors and satellite led to an overall reduction of the Bias and RMSE of about ---" ). In addition, at the beginning and at the end of the abstract you referred to the issue of data scarcity. However, your approach is based on the case in which you have observations from static sensors, which may be not available in data-scarce regions.

Authors' reply and actions:
We added some lines in the abstract specifying some quantitative findings of the proposed approach. We mentioned the issue of data scarcity because our proposed methodology is able to work even if gauging stations are missing and satellite derived data are the only sources of observations.

Referee comments:
-In line 143 the authors state that "In case the observation is a stage gauge measurement, the state variable position is determined by identifying the closest channel cell". However, after a few lines (153) they stated "The updating of the water levels from Static Sensors (SH) […] aims to correct both the channel and the floodplain water level". Are the static water level observations used to update only channel water levels of also the ones in the floodplains?