Using level data to estimate inflow hydrographs in ungauged sites of multiple reach systems

Considering a natural river system, usually only few sites are monitored and equipped to measure discharge over time. However, the knowledge of the discharge hydrograph in a specific station is important for many purposes: calibration of rainfall-runoff model, building of new structures, flood frequency analysis, water resource management, etc.. In addition, continuous direct measurement of discharges in open channels can be impossible and in any way difficult to assess. Therefore, most frequently, only level gauges are used for monitoring the system. In this work we propose a methodology to estimate a flow hydrograph in completely ungauged upstream sites of multiple reach systems by means of level data available at monitored stations downstream. In particular, a Bayesian approach is proposed to solve this kind of inverse problem. Prior information, in terms of geostatistical models and tools, is used to represent the structure of the unknowns and to regularize the solution. The methodology requires a forward hydraulic model of the considered river system able to reproduce the routing process and to account for all the reach characteristics: roughness, bed slope, cross sections, confluences, structures, etc.. In this work, the forward model is the widely known HEC-RAS river analysis system. The methodology has been tested through synthetic examples of river confluences, that differ in the available water level data, in the boundary conditions and in the number of the estimated inflow time series. Known inflow time-series were routed downstream by means of HEC-RAS to obtain the downstream stage hydrographs used as observations to test 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. The procedure has been also tested on a real case study of a river confluence located at the city of Parma (Italy) to assess the tributary inflow hydrograph supposed completely ungauged using water level data collected downstream on the main reach. The results show that the proposed methodology is able to properly recover the input inflows even in presence of errors, highlighting the robustness and reliability of the approach. Making always use of a forward routing model that can be as complex as required, the practical applicability of the approach is also demonstrated in a river system with the presence of flow combinations, compound sections and structures, among others.