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Extending the Applicability of the Generalized Likelihood Function for Zero‐Inflated Data Series

Proper uncertainty estimation for data series with a high proportion of zero and near zero observations has been a challenge in hydrologic studies. This technical note proposes a modification to the Generalized Likelihood function that accounts for zero inflation of the error distribution (ZI‐GL). We compare the performance of the proposed ZI‐GL with the original Generalized Likelihood function using the entire data series (GL) and by simply suppressing zero observations (GLy>0). These approaches were applied to two interception modeling examples characterized by data series with a significant number of zeros. The ZI‐GL produced better uncertainty ranges than the GL as measured by the precision, reliability and volumetric bias metrics. The comparison between ZI‐GL and GLy>0 highlights the need for further improvement in the treatment of residuals from near zero simulations when a linear heteroscedastic error model is considered. Aside from the interception modeling examples illustrated herein, the proposed ZI‐GL may be useful for other hydrologic studies, such as for the modeling of the runoff generation in hillslopes and ephemeral catchments.