Runoff depth = Excess rainfall (or effective rainfall).

Rainfall = Excess rainfall+Losses (infiltration and other losses)

Now, you need to get the losses accurately to obtain the rainfall totals.

Calculating rainfall depth from runoff depth is not straightforward because runoff is a product of various factors, including the characteristics of the watershed, land use, soil type, and rainfall intensity, among others. Rainfall depth itself is typically a known input in hydrological calculations, and runoff depth is one of the outcomes. However, if you have runoff depth and you want to estimate the rainfall depth that might have caused it, you can use hydrological models or equations to make an approximation.

One commonly used method for estimating rainfall depth from runoff depth is to use a rainfall-runoff model like the Rational Method or Soil Conservation Service Curve Number (SCS-CN) method.

Hi Shagun,

I'll assume that the runoff depth is the runoff at the outlet / catchment area.

If this is the case, then one approach is to use water budget closure equation.

Precipitation (P) - Evapotranspiratoin (ET) - Runoff (R) = change in storage (ds/dt)

Therefore; P = ds/dt + ET + R

for the ds/dt you can estimate it from terrestrial water storage anomalies provided by GRACE for example!

The results of the precipitation is dependent on the quality of the three independent variables. So, if you consider remote sensing or geostatistical techniques, uncertainty estimation is important to be considered.

Good luck!

I would use the SCS Curve number method to back-calculate a rainfall depth from observed runoff. It is a very straight forward equation with lot of publications about its applications. I have attached a book chapter that describes the method and has input tables to guide the user in selecting the correct coefficients. You will have to use your algebraic skills to derive rainfall from runoff, rather than runoff from rainfall for which the method was developed.

I use the SCS curve number to calculate rainfall depth from observed runoff. I also use the flood modeller software to achieving accuracy.

If you are dealing with a single event, you can calculate rainfall depth over a catchment (roughly) from the following equation.

Q=(P-0.2S)^2/(P+0.2S) for P>0.2S

Where

Q - accumulated runoff depth (mm) at the catchment outlet

P - accumulated rainfall depth (mm)

S - potential maximum retention.

‘S’ can be estimated with the CN (Curve Number) of the catchment from the following equation.

CN=25400/(254+S)

‘CN’ is a function of catchment characteristics (land use and cover, soil, treatment or practice, slope etc.) and the antecedent moisture condition. You may refer into a textbook to find out CN (I recommend chapter 4 of ILRI Publication 16, Drainage Principles and Applications, which can be downloaded from internet).

If you want to estimate continuous rainfall (monthly, seasonal, or annual basis), I think using runoff coefficient (runoff/rainfall ratio) is more appropriate. Normally, this has been estimated, monthly or seasonal basis, in many catchments using previous observations or theoretical methods.