I have a DEM raster and daily average flows (e.g., 50Ml/day). And I want to determine how far the water extent goes when the flow accumulates for 7 days based on 50 ml per day?
This quickly becomes a very complicated problem if you're trying to compute true flood extents. You can estimate flow through an open channel using Manning's Equation, but flow velocities over different land cover types complicate the equation and therefore the flood extent. The folks associated with the National Water Model have been working towards this goal for some time.
What you probably need to do is develop a rating curve for your channel to estimate stage from flow and then use a Height Above Nearest Drainage computation to fill the flooded area, i.e. the bathtub model. A recent paper in JAWRA lays out some of the background for how to tackle the problem (Zheng et al., 2018).
I would look into HAZUS Flood Model
The Hazus Flood Model allows planners and other practitioners to carry out a wide range of flood hazard analyses, including:
Studies of specific return intervals of floods (e.g., 100-year return interval). Studies of discharge frequencies, including analysis of discharges from specific streams and the exposure to buildings and population from the resultant flooding. Studies of annualized losses from flooding.
Quick Look assessments, which allows the user to quickly evaluate potential flooding from specific flood depths at specific locations.
What if scenarios, which allow users to evaluate the consequences of specific actions, such as the introduction of flow regulation devices, acquisition of flood-prone properties and other mitigation measures.
The flood loss estimation methodology consists of two modules that carry out basic analytical processes: flood hazard generation and flood loss estimation analysis for coastal and riverine flooding. The riverine flood hazard analysis module uses characteristics, such as frequency, discharge and ground elevation to estimate flood depth, flood elevation and flow velocity (simplified).
The coastal flood model determines flood inundation extents, depths, and wave heights using elevation, shoreline characteristics, and regional wave parameters. The flood loss estimation module calculates physical damage and economic loss from the results of the hazard analysis.
I would suggest reaching Enhancing digital elevation models for hydraulic modelling using flood frequency detection
Medium-resolution DEMs have limited applicability to flood mapping in large river systems within data sparse regions such as Sub-Saharan Africa. We present a novel approach for the enhancement of the SRTM (30 m) Digital Elevation Model (DEM) in The Gambia, West Africa: A time-series analysis of flood frequency and land cover was used to delineate differences in the vertical limits between morphological units within an alluvial floodplain. Combined with supplementary river stage data and vegetation removal techniques, these methods were used to improve the estimation of bare-earth terrain in flood modelling applications for a region with no access to high-resolution alternatives. The results demonstrate an improvement in floodplain topography for the River Gambia. The technique allows the reestablishment of small-scale complex morphology, instrumental in the routing of floodwater within a noise-filled DEM. The technique will be beneficial to flood-risk modelling applications within data sparse regions
Flood extent prediction with stage at the downstream boundary of 1.25–2 m above sea level.
Predicted flood extent where: A = 2 m over enhanced DEM; B 2.5 m over enhanced DEM; C = 2 m over original DEM and D = 2.5 m over original DEM. Flood predictions overlay hill shade imagery (dark grey = floodplain; light grey = outside of floodplain). Black line = extent of alluvial sediments.