Rainfall network design for runoff prediction

Authors:
  • RBRafael L. Bras
    Rafael L. Bras
  • IRIgnacio Rodríguez‐Iturbe
    Ignacio Rodríguez‐Iturbe
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Abstract
A multivariate state‐space stochastic model of rainfall based on a multidimensional rainfall generator suggested by Bras and Rodríguez‐Iturbe (1976a) is used together with a runoff model to study the accuracy of discharge prediction as a function of the rainfall‐sampling network. The runoff model used is a spatially distributed simulation based on a finite difference solution of the kinematic wave equations. Discharge prediction accuracy at any point in a basin can be obtained in terms of the mean square error as a function of the number of rain‐sampling stations, their location, and the errors in sampling devices. The solution is also a function of the physics of the basin at hand which is incorporated in the rainfall‐runoff model. The mean square error of discharge estimation is obtained by using linear estimation theory for dynamic systems. Particularly, the technique used is the Kalman‐Bucy filter, which permits filtering and extrapolation of noisy and incomplete observations.

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