Runoff data are usually not available on a grid basis, if not from land surface modelling (e.g., ECMWF reanalysis).

A recent interesting study for deriving gridded monthly runoff data over Europe was published by L. Gudmundsson and S. I. Seneviratne: Towards observation-based gridded runoff estimates for Europe (see link)

http://www.hydrol-earth-syst-sci.net/19/2859/2015/hess-19-2859-2015.html

You have to do it by yourself if you have a ground data at many stations in the study area whoever daily, monthly or annually. 

Maybe you can go to the web of USGS, and it appeared a new function to see the runoff data. hope can help you! 

Thank you very much for your suggestions !

H Kouakou Valentin, 

This is really interesting. You have a simple assumption Q=P-ET. Let both P and ET are in mm, then when you subtract you will get mm of runoff on each pixel. But, in real life each pixel are connected to each other and they drain to the outlet. So if you want to know the depth accumlated runoff on each pixel you have to map the flow accumulation map. Flow accumulation map can be done by many GIS tool, ArcGIS has Hydrology tool on spatial analyst tool, ILWIS has DEM-hydro processing tool. First get DEM of the study site then do the Fill sink operation followed by flow direction and flow accumulation. 

Finally the total accumulated runoff depth on each pixel will be Flow accumulation * (P-ET). this is with the simple assumption rainfall - evaporation = runoff . 

Abeyou Wale 

Thank you Mr Abeyou Wale!

In addition to what mentioned above, If your case study is located in Asian-Pacific region, you can access to runoff data via below website:

http://www.wenfo.org/apwm/

Regards 

You can download monthly gridded data set for Africa period January 1940 December 1999 for free

here

https://www.researchgate.net/publication/312383645_Monthly_rainfall_gridded_dataset_for_Africa_for_the_period_1940-1949_at_the_half_a_square_degree_interpolation_Inverse_Distance_Weighted

Data Monthly rainfall gridded dataset for Africa for the period 1...

An update of the available Info:

There are daily gridded available surface runoff data which can be obtained from the GLDAS model. There is another dataset up to 2012 where surface runoff can be obtained from the following webpage. 

https://wci.earth2observe.eu/portal/?wms_url=http://wci.earth2observe.eu/thredd/wms/cnrs/wrr1-daily-agg.nc?&url_name=Qs

Regards

Thanks for giving useful references about surface runoff data in raster format. However, most runoff data was limit in spatial scale. Can I use soil moisture data as a substitution for the potential of runoff generation?