Evaluation of mean square error involved in approximating the areal average of a rainfall event by a discrete summation

Authors:
  • RBRafael L. Bras
    Rafael L. Bras
  • IRIgnacio Rodríguez‐Iturbe
    Ignacio Rodríguez‐Iturbe
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Abstract
Two‐dimensional areal processes are commonly evaluated in hydrology through a discretization in space over the region in which the process is being studied. Such a discretization involves an error in going from the continuous process to the discrete one. This error is studied theoretically, and graphs are presented for its evaluation as function of the size of the area, the functional form of the correlation equation in space, and the level of discretization or size of the sample. Correlation structures of the Bessel type and of the single and double exponential kind are considered, and their different implications are discussed.

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