12 step ahead prediction desired
If you don't have a model, you need to make one up. For example if your data indicates that the flow is more of a function of the month than the year, you could simply predict the flow in say, March, as the average of the flows in March from 1900-1950.

Now there may be also variation in the yearly flow. You can check whether the yearly average varies randomly (and is such unpredictable other than by mean)or whether there is correlation between neighboring years. If there is correlation you could try linear prediction and/or auto regression or polynomial extrapolation to refine your number for the average flow in 1951.

A good way to test and tweak your model is to use the data from 1900 to for example 1940 to predict the data for 1941 and then compare to the actual data. You can repeat for the last 10 or 20 years of actual data.