Bayesian estimation of inflow hydrographs in ungauged sites of multiple reach systems

• We use a Bayesian approach to evaluate upstream flow hydrograph in ungauged sites.
• We use downstream level data as input for the inverse approach.
• Inflow hydrographs of multiple reach systems can be estimated.
• Any forward numerical model can be used to apply the proposed approach.
• Uncertainty of the unknown discharge hydrographs can be evaluated.

A Bayesian Geostatistical Approach to evaluate unknown upstream flow hydrographs in multiple reach systems is implemented. The methodology was, firstly, tested through three synthetic examples of river confluences, that differ in the available data, boundary conditions and number of the estimated inflow time series. Input discharge hydrographs were routed downstream by means of the widely known HEC-RAS river analysis system to obtain the downstream stage hydrographs used as known observations for the reverse procedure. In almost all cases, the observed water levels were corrupted with random errors to highlight the reliability of the methodology in preventing instabilities and overfitting. Then the procedure was applied to the real case study of the Parma–Baganza river confluence located at the city of Parma (Italy) to assess the tributary Baganza River inflow hydrograph (supposed completely ungauged) using water level data collected downstream on the main reach. The results show that the methodology properly reproduces the unknown inflows even in presence of errors affecting the downstream water levels. The practical applicability of the proposed approach is also demonstrated in complex river systems.