Bayesian approach to daily rainfall modelling to estimate monthly net infiltration using the Thornthwaite water budget and Curve Number methods

The Thornthwaite and Mather water budget is a simple and frequently applicable tool to estimate surpluses of water, which are not stored in the soil profile. Combining it with the empiric CN-method of the US Soil Conservation Service (US-SCS), which is applied to daily rainfall records, it is possible to estimate the runoff, and this way, from the difference between surpluses and runoff, to estimate the net infiltration that would recharge a phreatic aquifer. In order to apply both methods during a sequence of years, it is necessary to predict the number of rain events per month, and the rainfall depth for each event. In this work, the author proposes a methodology based on the theorem of Bayes to estimate the number of occurrences of rainy events in a considered month conditioning the forecast to the monthly rainfall. In addition, an exponential distribution to generate rainfall depth knowing the monthly rainfall was done. Both algorithms were applied in four stations of the southern region of Santa Fe province (Argentina). More than 7,600 forecasts of rain occurrences and rainfall depths were compared with the observed records. Moreover, the runoff values estimated by means of the US-SCS method, using the observed rainfall and using rainfalls predicted with the algorithms were also compared. In both cases, the obtained results were also very satisfactory. The proposed methodologies allow the correct application of the balance of Thornthwaite and Mather together with the US-SCS method and: a good forecast of monthly runoff and net infiltration.