Reverse level pool routing: Comparison between a deterministic and a stochastic approach

Reverse level pool routing is a technique to estimate the inflow hydrograph in a reservoir based on the knowledge of the outflow hydrograph, usually derived from water levels by means of a rating curve, and the level-storage relationship. In this work a comparison between a deterministic and a stochastic approach for reverse routing is presented. The deterministic approach rearranges and solves the reservoir differential continuity equation for the unknown inflow hydrograph by means of an explicit centered finite difference scheme. The Bayesian Geostatistical Approach, instead, addresses the inversion combining together prior information on the unknown inflow hydrograph and the available observations. For the stochastic inversion a forward solution of the reservoir continuity equation is required and in this work a scheme based on a fourth-order Runge–Kutta method was used. The differences between the two methodologies are highlighted by means of a synthetic example and a case study (Parma river detention reservoir, Italy), considering dams with movable gates. The results show that the stochastic approach always gives better results than the deterministic one, in particular when errors in the reservoir water levels are present and/or the outflow rate changes abruptly after moving the gates. The main reason is the regularization imposed, in the stochastic inverse solution, by assuming the inflow hydrograph auto-correlated. Another advantage of the stochastic approach is that it does not enforce a mass balance through the observed noisy data. Despite this, the volume errors have the same order of magnitude of those obtained with the deterministic procedure.