NUMERICAL SOLUTION OF THE RESERVOIR ROUTING EQUATION

Numerical methods for the solution of the reservoir routing equation are critically reviewed. The methods considered in this study are: (1) the Laurenson-Pilgrim method, (2) the fourth-order Runge-Kutta method, and (3) the fixed order Cash-Karp method. Method (1) does not handle complex outflow rating curves in which discharge may decrease with water level. Method (2) is found to crash under critical conditions occurring especially when large time steps (greater than 10 min in this application) are used at the beginning of the inflow rising limbs and at the end of the inflow recession limbs. Method (3) is computationally intensive and it does not solve the limitations of method (2) mentioned above. In this study it has been found that the limitations of method (2) can be efficiently overcome by reducing the time step in the critical phases of the simulation so as to allow water level to remain within the domains of definition of the storage function and of the outflow rating curve. With this control, the Runge-Kutta method ensures robust and accurate descriptions of reservoir dynamics and it is therefore expected to be suitable for use in distributed catchment models.