Negative data could be backflow, or could be representing missing data.To determine that there is backflow, there would have needed to be velocity measurements made that show that the flow was running backwards. Do you have velocity data? If missing data, then this is likely to be the same value (e.g. -99), but no guarantee of that. Basically, you need to be sure that it is backflow before trying to model it as such. Is your gauge near a confluence with another stream?

If it is backflow, then this would indicate a higher water level downstream - usually occuring at a confluence, where one inflowing stream is higher than the other. You would need to model both streams, and get the relative flow depths. You could then use this to estimate the backflow using an empirical relationship between the 2 flow depths and the discharge at your gauged site.

I agree with Barry.  There is another approach to capture the reverse flow.  If you confirm that there is indeed reverse flow, and if you have good measurements of water level at the end of the stream you are modeling, you can use it as a boundary condition.  If the model you are using is based on the dynamic equation, then it would capture a reverse flow due to high tailwater.  

Negative data could be due to the influence of tides from downstream side or at a confluence as Mr Barry said. In this case, the discharge data is not only generated by rain, so you can not use only RR model to calculate. You should combine RR model with Hydrodynamic model for better results.